WorldWideScience

Sample records for linear matrix inversion

  1. Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

    Science.gov (United States)

    El-Gebeily, M.; Yushau, B.

    2008-01-01

    In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

  2. Recursive Matrix Inverse Update On An Optical Processor

    Science.gov (United States)

    Casasent, David P.; Baranoski, Edward J.

    1988-02-01

    A high accuracy optical linear algebraic processor (OLAP) using the digital multiplication by analog convolution (DMAC) algorithm is described for use in an efficient matrix inverse update algorithm with speed and accuracy advantages. The solution of the parameters in the algorithm are addressed and the advantages of optical over digital linear algebraic processors are advanced.

  3. AMDLIBF, IBM 360 Subroutine Library, Eigenvalues, Eigenvectors, Matrix Inversion

    International Nuclear Information System (INIS)

    Wang, Jesse Y.

    1980-01-01

    Description of problem or function: AMDLIBF is a subset of the IBM 360 Subroutine Library at the Applied Mathematics Division at Argonne. This subset includes library category F: Identification/Description: F152S F SYMINV: Invert sym. matrices, solve lin. systems; F154S A DOTP: Double plus precision accum. inner prod.; F156S F RAYCOR: Rayleigh corrections for eigenvalues; F161S F XTRADP: A fast extended precision inner product; F162S A XTRADP: Inner product of two DP real vectors; F202S F1 EIGEN: Eigen-system for real symmetric matrix; F203S F: Driver for F202S; F248S F RITZIT: Largest eigenvalue and vec. real sym. matrix; F261S F EIGINV: Inverse eigenvalue problem; F313S F CQZHES: Reduce cmplx matrices to upper Hess and tri; F314S F CQZVAL: Reduce complex matrix to upper Hess. form; F315S F CQZVEC: Eigenvectors of cmplx upper triang. syst.; F316S F CGG: Driver for complex general Eigen-problem; F402S F MATINV: Matrix inversion and sol. of linear eqns.; F403S F: Driver for F402S; F452S F CHOLLU,CHOLEQ: Sym. decomp. of pos. def. band matrices; F453S F MATINC: Inversion of complex matrices; F454S F CROUT: Solution of simultaneous linear equations; F455S F CROUTC: Sol. of simultaneous complex linear eqns.; F456S F1 DIAG: Integer preserving Gaussian elimination

  4. Linearized inversion of two components seismic data; Inversion linearisee de donnees sismiques a deux composantes

    Energy Technology Data Exchange (ETDEWEB)

    Lebrun, D.

    1997-05-22

    The aim of the dissertation is the linearized inversion of multicomponent seismic data for 3D elastic horizontally stratified media, using Born approximation. A Jacobian matrix is constructed; it will be used to model seismic data from elastic parameters. The inversion technique, relying on single value decomposition (SVD) of the Jacobian matrix, is described. Next, the resolution of inverted elastic parameters is quantitatively studies. A first use of the technique is shown in the frame of an evaluation of a sea bottom acquisition (synthetic data). Finally, a real data set acquired with conventional marine technique is inverted. (author) 70 refs.

  5. Connection between Dirac and matrix Schroedinger inverse-scattering transforms

    International Nuclear Information System (INIS)

    Jaulent, M.; Leon, J.J.P.

    1978-01-01

    The connection between two applications of the inverse scattering method for solving nonlinear equations is established. The inverse method associated with the massive Dirac system (D) : (iσ 3 d/dx - i q 3 σ 1 - q 1 σ 2 + mσ 2 )Y = epsilonY is rediscovered from the inverse method associated with the 2 x 2 matrix Schroedinger equation (S) : Ysub(xx) + (k 2 -Q)Y = 0. Here Q obeys a nonlinear constraint equivalent to a linear constraint on the reflection coefficient for (S). (author)

  6. High performance matrix inversion based on LU factorization for multicore architectures

    KAUST Repository

    Dongarra, Jack

    2011-01-01

    The goal of this paper is to present an efficient implementation of an explicit matrix inversion of general square matrices on multicore computer architecture. The inversion procedure is split into four steps: 1) computing the LU factorization, 2) inverting the upper triangular U factor, 3) solving a linear system, whose solution yields inverse of the original matrix and 4) applying backward column pivoting on the inverted matrix. Using a tile data layout, which represents the matrix in the system memory with an optimized cache-aware format, the computation of the four steps is decomposed into computational tasks. A directed acyclic graph is generated on the fly which represents the program data flow. Its nodes represent tasks and edges the data dependencies between them. Previous implementations of matrix inversions, available in the state-of-the-art numerical libraries, are suffer from unnecessary synchronization points, which are non-existent in our implementation in order to fully exploit the parallelism of the underlying hardware. Our algorithmic approach allows to remove these bottlenecks and to execute the tasks with loose synchronization. A runtime environment system called QUARK is necessary to dynamically schedule our numerical kernels on the available processing units. The reported results from our LU-based matrix inversion implementation significantly outperform the state-of-the-art numerical libraries such as LAPACK (5x), MKL (5x) and ScaLAPACK (2.5x) on a contemporary AMD platform with four sockets and the total of 48 cores for a matrix of size 24000. A power consumption analysis shows that our high performance implementation is also energy efficient and substantially consumes less power than its competitors. © 2011 ACM.

  7. General factorization relations and consistency conditions in the sudden approximation via infinite matrix inversion

    International Nuclear Information System (INIS)

    Chan, C.K.; Hoffman, D.K.; Evans, J.W.

    1985-01-01

    Local, i.e., multiplicative, operators satisfy well-known linear factorization relations wherein matrix elements (between states associated with a complete set of wave functions) can be obtained as a linear combination of those out of the ground state (the input data). Analytic derivation of factorization relations for general state input data results in singular integral expressions for the coefficients, which can, however, be regularized using consistency conditions between matrix elements out of a single (nonground) state. Similar results hold for suitable ''symmetry class'' averaged matrix elements where the symmetry class projection operators are ''complete.'' In several cases where the wave functions or projection operators incorporate orthogonal polynomial dependence, we show that the ground state factorization relations have a simplified structure allowing an alternative derivation of the general factorization relations via an infinite matrix inversion procedure. This form is shown to have some advantages over previous versions. In addition, this matrix inversion procedure obtains all consistency conditions (which is not always the case from regularization of singular integrals)

  8. Computing Generalized Matrix Inverse on Spiking Neural Substrate

    Directory of Open Access Journals (Sweden)

    Rohit Shukla

    2018-03-01

    Full Text Available Emerging neural hardware substrates, such as IBM's TrueNorth Neurosynaptic System, can provide an appealing platform for deploying numerical algorithms. For example, a recurrent Hopfield neural network can be used to find the Moore-Penrose generalized inverse of a matrix, thus enabling a broad class of linear optimizations to be solved efficiently, at low energy cost. However, deploying numerical algorithms on hardware platforms that severely limit the range and precision of representation for numeric quantities can be quite challenging. This paper discusses these challenges and proposes a rigorous mathematical framework for reasoning about range and precision on such substrates. The paper derives techniques for normalizing inputs and properly quantizing synaptic weights originating from arbitrary systems of linear equations, so that solvers for those systems can be implemented in a provably correct manner on hardware-constrained neural substrates. The analytical model is empirically validated on the IBM TrueNorth platform, and results show that the guarantees provided by the framework for range and precision hold under experimental conditions. Experiments with optical flow demonstrate the energy benefits of deploying a reduced-precision and energy-efficient generalized matrix inverse engine on the IBM TrueNorth platform, reflecting 10× to 100× improvement over FPGA and ARM core baselines.

  9. Computing Generalized Matrix Inverse on Spiking Neural Substrate

    Science.gov (United States)

    Shukla, Rohit; Khoram, Soroosh; Jorgensen, Erik; Li, Jing; Lipasti, Mikko; Wright, Stephen

    2018-01-01

    Emerging neural hardware substrates, such as IBM's TrueNorth Neurosynaptic System, can provide an appealing platform for deploying numerical algorithms. For example, a recurrent Hopfield neural network can be used to find the Moore-Penrose generalized inverse of a matrix, thus enabling a broad class of linear optimizations to be solved efficiently, at low energy cost. However, deploying numerical algorithms on hardware platforms that severely limit the range and precision of representation for numeric quantities can be quite challenging. This paper discusses these challenges and proposes a rigorous mathematical framework for reasoning about range and precision on such substrates. The paper derives techniques for normalizing inputs and properly quantizing synaptic weights originating from arbitrary systems of linear equations, so that solvers for those systems can be implemented in a provably correct manner on hardware-constrained neural substrates. The analytical model is empirically validated on the IBM TrueNorth platform, and results show that the guarantees provided by the framework for range and precision hold under experimental conditions. Experiments with optical flow demonstrate the energy benefits of deploying a reduced-precision and energy-efficient generalized matrix inverse engine on the IBM TrueNorth platform, reflecting 10× to 100× improvement over FPGA and ARM core baselines. PMID:29593483

  10. Inverse Interval Matrix: A Survey

    Czech Academy of Sciences Publication Activity Database

    Rohn, Jiří; Farhadsefat, R.

    2011-01-01

    Roč. 22, - (2011), s. 704-719 E-ISSN 1081-3810 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval matrix * inverse interval matrix * NP-hardness * enclosure * unit midpoint * inverse sign stability * nonnegative invertibility * absolute value equation * algorithm Subject RIV: BA - General Mathematics Impact factor: 0.808, year: 2010 http://www.math.technion.ac.il/iic/ ela / ela -articles/articles/vol22_pp704-719.pdf

  11. A recursive algorithm for computing the inverse of the Vandermonde matrix

    Directory of Open Access Journals (Sweden)

    Youness Aliyari Ghassabeh

    2016-12-01

    Full Text Available The inverse of a Vandermonde matrix has been used for signal processing, polynomial interpolation, curve fitting, wireless communication, and system identification. In this paper, we propose a novel fast recursive algorithm to compute the inverse of a Vandermonde matrix. The algorithm computes the inverse of a higher order Vandermonde matrix using the available lower order inverse matrix with a computational cost of $ O(n^2 $. The proposed algorithm is given in a matrix form, which makes it appropriate for hardware implementation. The running time of the proposed algorithm to find the inverse of a Vandermonde matrix using a lower order Vandermonde matrix is compared with the running time of the matrix inversion function implemented in MATLAB.

  12. Refractive index inversion based on Mueller matrix method

    Science.gov (United States)

    Fan, Huaxi; Wu, Wenyuan; Huang, Yanhua; Li, Zhaozhao

    2016-03-01

    Based on Stokes vector and Jones vector, the correlation between Mueller matrix elements and refractive index was studied with the result simplified, and through Mueller matrix way, the expression of refractive index inversion was deduced. The Mueller matrix elements, under different incident angle, are simulated through the expression of specular reflection so as to analyze the influence of the angle of incidence and refractive index on it, which is verified through the measure of the Mueller matrix elements of polished metal surface. Research shows that, under the condition of specular reflection, the result of Mueller matrix inversion is consistent with the experiment and can be used as an index of refraction of inversion method, and it provides a new way for target detection and recognition technology.

  13. Point source reconstruction principle of linear inverse problems

    International Nuclear Information System (INIS)

    Terazono, Yasushi; Matani, Ayumu; Fujimaki, Norio; Murata, Tsutomu

    2010-01-01

    Exact point source reconstruction for underdetermined linear inverse problems with a block-wise structure was studied. In a block-wise problem, elements of a source vector are partitioned into blocks. Accordingly, a leadfield matrix, which represents the forward observation process, is also partitioned into blocks. A point source is a source having only one nonzero block. An example of such a problem is current distribution estimation in electroencephalography and magnetoencephalography, where a source vector represents a vector field and a point source represents a single current dipole. In this study, the block-wise norm, a block-wise extension of the l p -norm, was defined as the family of cost functions of the inverse method. The main result is that a set of three conditions was found to be necessary and sufficient for block-wise norm minimization to ensure exact point source reconstruction for any leadfield matrix that admit such reconstruction. The block-wise norm that satisfies the conditions is the sum of the cost of all the observations of source blocks, or in other words, the block-wisely extended leadfield-weighted l 1 -norm. Additional results are that minimization of such a norm always provides block-wisely sparse solutions and that its solutions form cones in source space

  14. Inverse Operation of Four-dimensional Vector Matrix

    OpenAIRE

    H J Bao; A J Sang; H X Chen

    2011-01-01

    This is a new series of study to define and prove multidimensional vector matrix mathematics, which includes four-dimensional vector matrix determinant, four-dimensional vector matrix inverse and related properties. There are innovative concepts of multi-dimensional vector matrix mathematics created by authors with numerous applications in engineering, math, video conferencing, 3D TV, and other fields.

  15. Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

    KAUST Repository

    Gower, Robert M.; Hanzely, Filip; Richtarik, Peter; Stich, Sebastian

    2018-01-01

    We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite

  16. Advanced linear algebra for engineers with Matlab

    CERN Document Server

    Dianat, Sohail A

    2009-01-01

    Matrices, Matrix Algebra, and Elementary Matrix OperationsBasic Concepts and NotationMatrix AlgebraElementary Row OperationsSolution of System of Linear EquationsMatrix PartitionsBlock MultiplicationInner, Outer, and Kronecker ProductsDeterminants, Matrix Inversion and Solutions to Systems of Linear EquationsDeterminant of a MatrixMatrix InversionSolution of Simultaneous Linear EquationsApplications: Circuit AnalysisHomogeneous Coordinates SystemRank, Nu

  17. Microlocal analysis of a seismic linearized inverse problem

    NARCIS (Netherlands)

    Stolk, C.C.

    1999-01-01

    The seismic inverse problem is to determine the wavespeed c x in the interior of a medium from measurements at the boundary In this paper we analyze the linearized inverse problem in general acoustic media The problem is to nd a left inverse of the linearized forward map F or equivalently to nd the

  18. An investigation on the solutions for the linear inverse problem in gamma ray tomography

    International Nuclear Information System (INIS)

    Araujo, Bruna G.M.; Dantas, Carlos C.; Santos, Valdemir A. dos; Finkler, Christine L.L.; Oliveira, Eric F. de; Melo, Silvio B.; Santos, M. Graca dos

    2009-01-01

    This paper the results obtained in single beam gamma ray tomography are investigated according to direct problem formulation and the applied solution for the linear system of equations. By image reconstruction based algebraic computational algorithms are used. The sparse under and over-determined linear system of equations was analyzed. Build in functions of Matlab software were applied and optimal solutions were investigate. Experimentally a section of the tube is scanned from various positions and at different angles. The solution, to find the vector of coefficients μ, from the vector of measured p values through the W matrix inversion, constitutes an inverse problem. A industrial tomography process requires a numerical solution of the system of equations. The definition of inverse problem according to Hadmard's is considered and as well the requirement of a well posed problem to find stable solutions. The formulation of the basis function and the computational algorithm to structure the weight matrix W were analyzed. For W full rank matrix the obtained solution is unique as expected. Total Least Squares was implemented which theory and computation algorithm gives adequate treatment for the problems due to non-unique solutions of the system of equations. Stability of the solution was investigating by means of a regularization technique and the comparison shows that it improves the results. An optimal solution as a function of the image quality, computation time and minimum residuals were quantified. The corresponding reconstructed images are shown in 3D graphics in order to compare with the solution. (author)

  19. Angle-domain inverse scattering migration/inversion in isotropic media

    Science.gov (United States)

    Li, Wuqun; Mao, Weijian; Li, Xuelei; Ouyang, Wei; Liang, Quan

    2018-07-01

    The classical seismic asymptotic inversion can be transformed into a problem of inversion of generalized Radon transform (GRT). In such methods, the combined parameters are linearly attached to the scattered wave-field by Born approximation and recovered by applying an inverse GRT operator to the scattered wave-field data. Typical GRT-style true-amplitude inversion procedure contains an amplitude compensation process after the weighted migration via dividing an illumination associated matrix whose elements are integrals of scattering angles. It is intuitional to some extent that performs the generalized linear inversion and the inversion of GRT together by this process for direct inversion. However, it is imprecise to carry out such operation when the illumination at the image point is limited, which easily leads to the inaccuracy and instability of the matrix. This paper formulates the GRT true-amplitude inversion framework in an angle-domain version, which naturally degrades the external integral term related to the illumination in the conventional case. We solve the linearized integral equation for combined parameters of different fixed scattering angle values. With this step, we obtain high-quality angle-domain common-image gathers (CIGs) in the migration loop which provide correct amplitude-versus-angle (AVA) behavior and reasonable illumination range for subsurface image points. Then we deal with the over-determined problem to solve each parameter in the combination by a standard optimization operation. The angle-domain GRT inversion method keeps away from calculating the inaccurate and unstable illumination matrix. Compared with the conventional method, the angle-domain method can obtain more accurate amplitude information and wider amplitude-preserved range. Several model tests demonstrate the effectiveness and practicability.

  20. Two-Dimensional Linear Inversion of GPR Data with a Shifting Zoom along the Observation Line

    Directory of Open Access Journals (Sweden)

    Raffaele Persico

    2017-09-01

    Full Text Available Linear inverse scattering problems can be solved by regularized inversion of a matrix, whose calculation and inversion may require significant computing resources, in particular, a significant amount of RAM memory. This effort is dependent on the extent of the investigation domain, which drives a large amount of data to be gathered and a large number of unknowns to be looked for, when this domain becomes electrically large. This leads, in turn, to the problem of inversion of excessively large matrices. Here, we consider the problem of a ground-penetrating radar (GPR survey in two-dimensional (2D geometry, with antennas at an electrically short distance from the soil. In particular, we present a strategy to afford inversion of large investigation domains, based on a shifting zoom procedure. The proposed strategy was successfully validated using experimental radar data.

  1. An Innovative Approach to Balancing Chemical-Reaction Equations: A Simplified Matrix-Inversion Technique for Determining The Matrix Null Space

    OpenAIRE

    Thorne, Lawrence R.

    2011-01-01

    I propose a novel approach to balancing equations that is applicable to all chemical-reaction equations; it is readily accessible to students via scientific calculators and basic computer spreadsheets that have a matrix-inversion application. The new approach utilizes the familiar matrix-inversion operation in an unfamiliar and innovative way; its purpose is not to identify undetermined coefficients as usual, but, instead, to compute a matrix null space (or matrix kernel). The null space then...

  2. Matrix algebra for linear models

    CERN Document Server

    Gruber, Marvin H J

    2013-01-01

    Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. This evolution has made matrix methods a vital part of statistical education. Traditionally, matrix methods are taught in courses on everything from regression analysis to stochastic processes, thus creating a fractured view of the topic. Matrix Algebra for Linear Models offers readers a unique, unified view of matrix analysis theory (where and when necessary), methods, and their applications. Written f

  3. Introduction to the mathematics of inversion in remote sensing and indirect measurements

    CERN Document Server

    Twomey, S

    2013-01-01

    Developments in Geomathematics, 3: Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements focuses on the application of the mathematics of inversion in remote sensing and indirect measurements, including vectors and matrices, eigenvalues and eigenvectors, and integral equations. The publication first examines simple problems involving inversion, theory of large linear systems, and physical and geometric aspects of vectors and matrices. Discussions focus on geometrical view of matrix operations, eigenvalues and eigenvectors, matrix products, inverse of a matrix, transposition and rules for product inversion, and algebraic elimination. The manuscript then tackles the algebraic and geometric aspects of functions and function space and linear inversion methods, as well as the algebraic and geometric nature of constrained linear inversion, least squares solution, approximation by sums of functions, and integral equations. The text examines information content of indirect sensing m...

  4. Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)

    1996-12-31

    A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.

  5. Matrix Tricks for Linear Statistical Models

    CERN Document Server

    Puntanen, Simo; Styan, George PH

    2011-01-01

    In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple "tricks" which simplify and clarify the treatment of a problem - both for the student and

  6. Recurrent Neural Network for Computing Outer Inverse.

    Science.gov (United States)

    Živković, Ivan S; Stanimirović, Predrag S; Wei, Yimin

    2016-05-01

    Two linear recurrent neural networks for generating outer inverses with prescribed range and null space are defined. Each of the proposed recurrent neural networks is based on the matrix-valued differential equation, a generalization of dynamic equations proposed earlier for the nonsingular matrix inversion, the Moore-Penrose inversion, as well as the Drazin inversion, under the condition of zero initial state. The application of the first approach is conditioned by the properties of the spectrum of a certain matrix; the second approach eliminates this drawback, though at the cost of increasing the number of matrix operations. The cases corresponding to the most common generalized inverses are defined. The conditions that ensure stability of the proposed neural network are presented. Illustrative examples present the results of numerical simulations.

  7. Generalized inverses theory and computations

    CERN Document Server

    Wang, Guorong; Qiao, Sanzheng

    2018-01-01

    This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics. It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.

  8. Inverse Modelling Problems in Linear Algebra Undergraduate Courses

    Science.gov (United States)

    Martinez-Luaces, Victor E.

    2013-01-01

    This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

  9. An Improved TA-SVM Method Without Matrix Inversion and Its Fast Implementation for Nonstationary Datasets.

    Science.gov (United States)

    Shi, Yingzhong; Chung, Fu-Lai; Wang, Shitong

    2015-09-01

    Recently, a time-adaptive support vector machine (TA-SVM) is proposed for handling nonstationary datasets. While attractive performance has been reported and the new classifier is distinctive in simultaneously solving several SVM subclassifiers locally and globally by using an elegant SVM formulation in an alternative kernel space, the coupling of subclassifiers brings in the computation of matrix inversion, thus resulting to suffer from high computational burden in large nonstationary dataset applications. To overcome this shortcoming, an improved TA-SVM (ITA-SVM) is proposed using a common vector shared by all the SVM subclassifiers involved. ITA-SVM not only keeps an SVM formulation, but also avoids the computation of matrix inversion. Thus, we can realize its fast version, that is, improved time-adaptive core vector machine (ITA-CVM) for large nonstationary datasets by using the CVM technique. ITA-CVM has the merit of asymptotic linear time complexity for large nonstationary datasets as well as inherits the advantage of TA-SVM. The effectiveness of the proposed classifiers ITA-SVM and ITA-CVM is also experimentally confirmed.

  10. Applied linear algebra and matrix analysis

    CERN Document Server

    Shores, Thomas S

    2018-01-01

    In its second edition, this textbook offers a fresh approach to matrix and linear algebra. Its blend of theory, computational exercises, and analytical writing projects is designed to highlight the interplay between these aspects of an application. This approach places special emphasis on linear algebra as an experimental science that provides tools for solving concrete problems. The second edition’s revised text discusses applications of linear algebra like graph theory and network modeling methods used in Google’s PageRank algorithm. Other new materials include modeling examples of diffusive processes, linear programming, image processing, digital signal processing, and Fourier analysis. These topics are woven into the core material of Gaussian elimination and other matrix operations; eigenvalues, eigenvectors, and discrete dynamical systems; and the geometrical aspects of vector spaces. Intended for a one-semester undergraduate course without a strict calculus prerequisite, Applied Linear Algebra and M...

  11. Inverse problems in linear transport theory

    International Nuclear Information System (INIS)

    Dressler, K.

    1988-01-01

    Inverse problems for a class of linear kinetic equations are investigated. The aim is to identify the scattering kernel of a transport equation (corresponding to the structure of a background medium) by observing the 'albedo' part of the solution operator for the corresponding direct initial boundary value problem. This means to get information on some integral operator in an integrodifferential equation through on overdetermined boundary value problem. We first derive a constructive method for solving direct halfspace problems and prove a new factorization theorem for the solutions. Using this result we investigate stationary inverse problems with respect to well posedness (e.g. reduce them to classical ill-posed problems, such as integral equations of first kind). In the time-dependent case we show that a quite general inverse problem is well posed and solve it constructively. (orig.)

  12. A study of block algorithms for fermion matrix inversion

    International Nuclear Information System (INIS)

    Henty, D.

    1990-01-01

    We compare the convergence properties of Lanczos and Conjugate Gradient algorithms applied to the calculation of columns of the inverse fermion matrix for Kogut-Susskind and Wilson fermions in lattice QCD. When several columns of the inverse are required simultaneously, a block version of the Lanczos algorithm is most efficient at small mass, being over 5 times faster than the single algorithms. The block algorithm is also less susceptible to critical slowing down. (orig.)

  13. MATLAB Simulation of Gradient-Based Neural Network for Online Matrix Inversion

    Science.gov (United States)

    Zhang, Yunong; Chen, Ke; Ma, Weimu; Li, Xiao-Dong

    This paper investigates the simulation of a gradient-based recurrent neural network for online solution of the matrix-inverse problem. Several important techniques are employed as follows to simulate such a neural system. 1) Kronecker product of matrices is introduced to transform a matrix-differential-equation (MDE) to a vector-differential-equation (VDE); i.e., finally, a standard ordinary-differential-equation (ODE) is obtained. 2) MATLAB routine "ode45" is introduced to solve the transformed initial-value ODE problem. 3) In addition to various implementation errors, different kinds of activation functions are simulated to show the characteristics of such a neural network. Simulation results substantiate the theoretical analysis and efficacy of the gradient-based neural network for online constant matrix inversion.

  14. Explicit Inverse of an Interval Matrix with Unit Midpoint

    Czech Academy of Sciences Publication Activity Database

    Rohn, Jiří

    2011-01-01

    Roč. 22, - (2011), s. 138-150 E-ISSN 1081-3810 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval matrix * unit midpoint * inverse interval matrix * regularity Subject RIV: BA - General Mathematics Impact factor: 0.808, year: 2010 http://www.math.technion.ac.il/iic/ ela / ela -articles/articles/vol22_pp138-150.pdf

  15. Syrio. A program for the calculation of the inverse of a matrix

    International Nuclear Information System (INIS)

    Garcia de Viedma Alonso, L.

    1963-01-01

    SYRIO is a code for the inversion of a non-singular square matrix whose order is not higher than 40 for the UNIVAC-UCT (SS-90). The treatment stands from the inversion formula of sherman and Morrison, and following the Herbert S. Wilf's method for special matrices, generalize the procedure to any kind of non-singular square matrices. the limitation of the matrix order is not inherent of the program itself but imposed by the storage capacity of the computer for which it was coded. (Author)

  16. Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

    KAUST Repository

    Gower, Robert M.

    2018-02-12

    We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite matrices in such a way that all iterates (approximate solutions) generated by the algorithm are positive definite matrices themselves. This opens the way for many applications in the field of optimization and machine learning. As an application of our general theory, we develop the {\\\\em first accelerated (deterministic and stochastic) quasi-Newton updates}. Our updates lead to provably more aggressive approximations of the inverse Hessian, and lead to speed-ups over classical non-accelerated rules in numerical experiments. Experiments with empirical risk minimization show that our rules can accelerate training of machine learning models.

  17. Linearized versus non-linear inverse methods for seismic localization of underground sources

    DEFF Research Database (Denmark)

    Oh, Geok Lian; Jacobsen, Finn

    2013-01-01

    The problem of localization of underground sources from seismic measurements detected by several geophones located on the ground surface is addressed. Two main approaches to the solution of the problem are considered: a beamforming approach that is derived from the linearized inversion problem, a...

  18. Generating Nice Linear Systems for Matrix Gaussian Elimination

    Science.gov (United States)

    Homewood, L. James

    2004-01-01

    In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…

  19. Taming waveform inversion non-linearity through phase unwrapping of the model and objective functions

    KAUST Repository

    Alkhalifah, Tariq Ali

    2012-09-25

    Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.

  20. Taming waveform inversion non-linearity through phase unwrapping of the model and objective functions

    KAUST Repository

    Alkhalifah, Tariq Ali; Choi, Yun Seok

    2012-01-01

    Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.

  1. Matrix theory from generalized inverses to Jordan form

    CERN Document Server

    Piziak, Robert

    2007-01-01

    Each chapter ends with a list of references for further reading. Undoubtedly, these will be useful for anyone who wishes to pursue the topics deeper. … the book has many MATLAB examples and problems presented at appropriate places. … the book will become a widely used classroom text for a second course on linear algebra. It can be used profitably by graduate and advanced level undergraduate students. It can also serve as an intermediate course for more advanced texts in matrix theory. This is a lucidly written book by two authors who have made many contributions to linear and multilinear algebra.-K.C. Sivakumar, IMAGE, No. 47, Fall 2011Always mathematically constructive, this book helps readers delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.-L'enseignement Mathématique, January-June 2007, Vol. 53, No. 1-2.

  2. Frequency-domain full-waveform inversion with non-linear descent directions

    Science.gov (United States)

    Geng, Yu; Pan, Wenyong; Innanen, Kristopher A.

    2018-05-01

    Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. We examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss-Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s0 is, in our scheme, proportional to at most (Δs/s0)3 in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss-Newton FWI update is proportional to (Δs/s0)2. For numerical implementation of more complex cases, we introduce a non-linear frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. The inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a

  3. Matrix model and time-like linear dila ton matter

    International Nuclear Information System (INIS)

    Takayanagi, Tadashi

    2004-01-01

    We consider a matrix model description of the 2d string theory whose matter part is given by a time-like linear dilaton CFT. This is equivalent to the c=1 matrix model with a deformed, but very simple Fermi surface. Indeed, after a Lorentz transformation, the corresponding 2d spacetime is a conventional linear dila ton background with a time-dependent tachyon field. We show that the tree level scattering amplitudes in the matrix model perfectly agree with those computed in the world-sheet theory. The classical trajectories of fermions correspond to the decaying D-boranes in the time-like linear dilaton CFT. We also discuss the ground ring structure. Furthermore, we study the properties of the time-like Liouville theory by applying this matrix model description. We find that its ground ring structure is very similar to that of the minimal string. (author)

  4. Technical note: Avoiding the direct inversion of the numerator relationship matrix for genotyped animals in single-step genomic best linear unbiased prediction solved with the preconditioned conjugate gradient.

    Science.gov (United States)

    Masuda, Y; Misztal, I; Legarra, A; Tsuruta, S; Lourenco, D A L; Fragomeni, B O; Aguilar, I

    2017-01-01

    This paper evaluates an efficient implementation to multiply the inverse of a numerator relationship matrix for genotyped animals () by a vector (). The computation is required for solving mixed model equations in single-step genomic BLUP (ssGBLUP) with the preconditioned conjugate gradient (PCG). The inverse can be decomposed into sparse matrices that are blocks of the sparse inverse of a numerator relationship matrix () including genotyped animals and their ancestors. The elements of were rapidly calculated with the Henderson's rule and stored as sparse matrices in memory. Implementation of was by a series of sparse matrix-vector multiplications. Diagonal elements of , which were required as preconditioners in PCG, were approximated with a Monte Carlo method using 1,000 samples. The efficient implementation of was compared with explicit inversion of with 3 data sets including about 15,000, 81,000, and 570,000 genotyped animals selected from populations with 213,000, 8.2 million, and 10.7 million pedigree animals, respectively. The explicit inversion required 1.8 GB, 49 GB, and 2,415 GB (estimated) of memory, respectively, and 42 s, 56 min, and 13.5 d (estimated), respectively, for the computations. The efficient implementation required <1 MB, 2.9 GB, and 2.3 GB of memory, respectively, and <1 sec, 3 min, and 5 min, respectively, for setting up. Only <1 sec was required for the multiplication in each PCG iteration for any data sets. When the equations in ssGBLUP are solved with the PCG algorithm, is no longer a limiting factor in the computations.

  5. Algebraic properties of generalized inverses

    CERN Document Server

    Cvetković‐Ilić, Dragana S

    2017-01-01

    This book addresses selected topics in the theory of generalized inverses. Following a discussion of the “reverse order law” problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses. Particular emphasis is placed on the existence of Drazin invertible completions of an upper triangular operator matrix; on the invertibility and different types of generalized invertibility of a linear combination of operators on Hilbert spaces and Banach algebra elements; on the problem of finding representations of the Drazin inverse of a 2x2 block matrix; and on selected additive results and algebraic properties for the Drazin inverse. In addition to the clarity of its content, the book discusses the relevant open problems for each topic discussed. Comments on the latest references on generalized inverses are also included. Accordingly, the book will be useful for graduate students, Ph...

  6. Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations

    OpenAIRE

    Soleimani, Farahnaz; Stanimirovi´c, Predrag; Soleymani, Fazlollah

    2015-01-01

    An application of iterative methods for computing the Moore–Penrose inverse in balancing chemical equations is considered. With the aim to illustrate proposed algorithms, an improved high order hyper-power matrix iterative method for computing generalized inverses is introduced and applied. The improvements of the hyper-power iterative scheme are based on its proper factorization, as well as on the possibility to accelerate the iterations in the initial phase of the convergence. Although the ...

  7. Inversion assuming weak scattering

    DEFF Research Database (Denmark)

    Xenaki, Angeliki; Gerstoft, Peter; Mosegaard, Klaus

    2013-01-01

    due to the complex nature of the field. A method based on linear inversion is employed to infer information about the statistical properties of the scattering field from the obtained cross-spectral matrix. A synthetic example based on an active high-frequency sonar demonstrates that the proposed...

  8. Calculation of total number of disintegrations after intake of radioactive nuclides using the pseudo inverse matrix

    International Nuclear Information System (INIS)

    Noh, Si Wan; Sol, Jeong; Lee, Jai Ki; Lee, Jong Il; Kim, Jang Lyul

    2012-01-01

    Calculation of total number of disintegrations after intake of radioactive nuclides is indispensable to calculate a dose coefficient which means committed effective dose per unit activity (Sv/Bq). In order to calculate the total number of disintegrations analytically, Birch all's algorithm has been commonly used. As described below, an inverse matrix should be calculated in the algorithm. As biokinetic models have been complicated, however, the inverse matrix does not exist sometime and the total number of disintegrations cannot be calculated. Thus, a numerical method has been applied to DCAL code used to calculate dose coefficients in ICRP publication and IMBA code. In this study, however, we applied the pseudo inverse matrix to solve the problem that the inverse matrix does not exist for. In order to validate our method, the method was applied to two examples and the results were compared to the tabulated data in ICRP publication. MATLAB 2012a was used to calculate the total number of disintegrations and exp m and p inv MATLAB built in functions were employed

  9. Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

    Science.gov (United States)

    Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

    2016-05-01

    The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

  10. A matrix-inversion method for gamma-source mapping from gamma-count data - 59082

    International Nuclear Information System (INIS)

    Bull, Richard K.; Adsley, Ian; Burgess, Claire

    2012-01-01

    Gamma ray counting is often used to survey the distribution of active waste material in various locations. Ideally the output from such surveys would be a map of the activity of the waste. In this paper a simple matrix-inversion method is presented. This allows an array of gamma-count data to be converted to an array of source activities. For each survey area the response matrix is computed using the gamma-shielding code Microshield [1]. This matrix links the activity array to the count array. The activity array is then obtained via matrix inversion. The method was tested on artificially-created arrays of count-data onto which statistical noise had been added. The method was able to reproduce, quite faithfully, the original activity distribution used to generate the dataset. The method has been applied to a number of practical cases, including the distribution of activated objects in a hot cell and to activated Nimonic springs amongst fuel-element debris in vaults at a nuclear plant. (authors)

  11. The linear parameters and the decoupling matrix for linearly coupled motion in 6 dimensional phase space

    International Nuclear Information System (INIS)

    Parzen, G.

    1997-01-01

    It will be shown that starting from a coordinate system where the 6 phase space coordinates are linearly coupled, one can go to a new coordinate system, where the motion is uncoupled, by means of a linear transformation. The original coupled coordinates and the new uncoupled coordinates are related by a 6 x 6 matrix, R. It will be shown that of the 36 elements of the 6 x 6 decoupling matrix R, only 12 elements are independent. A set of equations is given from which the 12 elements of R can be computed form the one period transfer matrix. This set of equations also allows the linear parameters, the β i , α i , i = 1, 3, for the uncoupled coordinates, to be computed from the one period transfer matrix

  12. LinvPy : a Python package for linear inverse problems

    OpenAIRE

    Beaud, Guillaume François Paul

    2016-01-01

    The goal of this project is to make a Python package including the tau-estimator algorithm to solve linear inverse problems. The package must be distributed, well documented, easy to use and easy to extend for future developers.

  13. Mini-lecture course: Introduction into hierarchical matrix technique

    KAUST Repository

    Litvinenko, Alexander

    2017-12-14

    The H-matrix format has a log-linear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations (mesh points). The H-matrix technique allows us to work with general class of matrices (not only structured or Toeplits or sparse). H-matrices can keep the H-matrix data format during linear algebra operations (inverse, update, Schur complement).

  14. Treating experimental data of inverse kinetic method by unitary linear regression analysis

    International Nuclear Information System (INIS)

    Zhao Yusen; Chen Xiaoliang

    2009-01-01

    The theory of treating experimental data of inverse kinetic method by unitary linear regression analysis was described. Not only the reactivity, but also the effective neutron source intensity could be calculated by this method. Computer code was compiled base on the inverse kinetic method and unitary linear regression analysis. The data of zero power facility BFS-1 in Russia were processed and the results were compared. The results show that the reactivity and the effective neutron source intensity can be obtained correctly by treating experimental data of inverse kinetic method using unitary linear regression analysis and the precision of reactivity measurement is improved. The central element efficiency can be calculated by using the reactivity. The result also shows that the effect to reactivity measurement caused by external neutron source should be considered when the reactor power is low and the intensity of external neutron source is strong. (authors)

  15. Linear matrix differential equations of higher-order and applications

    Directory of Open Access Journals (Sweden)

    Mustapha Rachidi

    2008-07-01

    Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.

  16. Refining mortality estimates in shark demographic analyses: a Bayesian inverse matrix approach.

    Science.gov (United States)

    Smart, Jonathan J; Punt, André E; White, William T; Simpfendorfer, Colin A

    2018-01-18

    Leslie matrix models are an important analysis tool in conservation biology that are applied to a diversity of taxa. The standard approach estimates the finite rate of population growth (λ) from a set of vital rates. In some instances, an estimate of λ is available, but the vital rates are poorly understood and can be solved for using an inverse matrix approach. However, these approaches are rarely attempted due to prerequisites of information on the structure of age or stage classes. This study addressed this issue by using a combination of Monte Carlo simulations and the sample-importance-resampling (SIR) algorithm to solve the inverse matrix problem without data on population structure. This approach was applied to the grey reef shark (Carcharhinus amblyrhynchos) from the Great Barrier Reef (GBR) in Australia to determine the demography of this population. Additionally, these outputs were applied to another heavily fished population from Papua New Guinea (PNG) that requires estimates of λ for fisheries management. The SIR analysis determined that natural mortality (M) and total mortality (Z) based on indirect methods have previously been overestimated for C. amblyrhynchos, leading to an underestimated λ. The updated Z distributions determined using SIR provided λ estimates that matched an empirical λ for the GBR population and corrected obvious error in the demographic parameters for the PNG population. This approach provides opportunity for the inverse matrix approach to be applied more broadly to situations where information on population structure is lacking. © 2018 by the Ecological Society of America.

  17. Inverse m-matrices and ultrametric matrices

    CERN Document Server

    Dellacherie, Claude; San Martin, Jaime

    2014-01-01

    The study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains. The main focus of this monograph is the so-called inverse M-matrix problem, which asks for a characterization of nonnegative matrices whose inverses are M-matrices. We present an answer in terms of discrete potential theory based on the Choquet-Deny Theorem. A distinguished subclass of inverse M-matrices is ultrametric matrices, which are important in applications such as taxonomy. Ultrametricity is revealed to be a relevant concept in linear algebra and discrete potential theory because of its relation with trees in graph theory and mean expected value matrices in probability theory. Remarkable properties of Hadamard functions and products for the class of inverse M-matrices are developed and probabilistic insights are provided throughout the monograph.

  18. Degenerated-Inverse-Matrix-Based Channel Estimation for OFDM Systems

    Directory of Open Access Journals (Sweden)

    Makoto Yoshida

    2009-01-01

    Full Text Available This paper addresses time-domain channel estimation for pilot-symbol-aided orthogonal frequency division multiplexing (OFDM systems. By using a cyclic sinc-function matrix uniquely determined by Nc transmitted subcarriers, the performance of our proposed scheme approaches perfect channel state information (CSI, within a maximum of 0.4 dB degradation, regardless of the delay spread of the channel, Doppler frequency, and subcarrier modulation. Furthermore, reducing the matrix size by splitting the dispersive channel impulse response into clusters means that the degenerated inverse matrix estimator (DIME is feasible for broadband, high-quality OFDM transmission systems. In addition to theoretical analysis on normalized mean squared error (NMSE performance of DIME, computer simulations over realistic nonsample spaced channels also showed that the DIME is robust for intersymbol interference (ISI channels and fast time-invariant channels where a minimum mean squared error (MMSE estimator does not work well.

  19. Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations

    OpenAIRE

    Nakamura, Gen; Vashisth, Manmohan

    2017-01-01

    In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...

  20. A conditioning technique for matrix inversion for Wilson fermions

    International Nuclear Information System (INIS)

    DeGrand, T.A.

    1988-01-01

    I report a simple technique for conditioning conjugate gradient or conjugate residue matrix inversion as applied to the lattice gauge theory problem of computing the propagator of Wilson fermions. One form of the technique provides about a factor of three speedup over an unconditioned algorithm while running at the same speed as an unconditioned algorithm. I illustrate the method as it is applied to a conjugate residue algorithm. (orig.)

  1. A Projected Non-linear Conjugate Gradient Method for Interactive Inverse Kinematics

    DEFF Research Database (Denmark)

    Engell-Nørregård, Morten; Erleben, Kenny

    2009-01-01

    Inverse kinematics is the problem of posing an articulated figure to obtain a wanted goal, without regarding inertia and forces. Joint limits are modeled as bounds on individual degrees of freedom, leading to a box-constrained optimization problem. We present A projected Non-linear Conjugate...... Gradient optimization method suitable for box-constrained optimization problems for inverse kinematics. We show application on inverse kinematics positioning of a human figure. Performance is measured and compared to a traditional Jacobian Transpose method. Visual quality of the developed method...

  2. High performance matrix inversion based on LU factorization for multicore architectures

    KAUST Repository

    Dongarra, Jack; Faverge, Mathieu; Ltaief, Hatem; Luszczek, Piotr R.

    2011-01-01

    on the available processing units. The reported results from our LU-based matrix inversion implementation significantly outperform the state-of-the-art numerical libraries such as LAPACK (5x), MKL (5x) and ScaLAPACK (2.5x) on a contemporary AMD platform with four

  3. A genetic meta-algorithm-assisted inversion approach: hydrogeological study for the determination of volumetric rock properties and matrix and fluid parameters in unsaturated formations

    Science.gov (United States)

    Szabó, Norbert Péter

    2018-03-01

    An evolutionary inversion approach is suggested for the interpretation of nuclear and resistivity logs measured by direct-push tools in shallow unsaturated sediments. The efficiency of formation evaluation is improved by estimating simultaneously (1) the petrophysical properties that vary rapidly along a drill hole with depth and (2) the zone parameters that can be treated as constant, in one inversion procedure. In the workflow, the fractional volumes of water, air, matrix and clay are estimated in adjacent depths by linearized inversion, whereas the clay and matrix properties are updated using a float-encoded genetic meta-algorithm. The proposed inversion method provides an objective estimate of the zone parameters that appear in the tool response equations applied to solve the forward problem, which can significantly increase the reliability of the petrophysical model as opposed to setting these parameters arbitrarily. The global optimization meta-algorithm not only assures the best fit between the measured and calculated data but also gives a reliable solution, practically independent of the initial model, as laboratory data are unnecessary in the inversion procedure. The feasibility test uses engineering geophysical sounding logs observed in an unsaturated loessy-sandy formation in Hungary. The multi-borehole extension of the inversion technique is developed to determine the petrophysical properties and their estimation errors along a profile of drill holes. The genetic meta-algorithmic inversion method is recommended for hydrogeophysical logging applications of various kinds to automatically extract the volumetric ratios of rock and fluid constituents as well as the most important zone parameters in a reliable inversion procedure.

  4. Monotone matrix transformations defined by the group inverse and simultaneous diagonalizability

    International Nuclear Information System (INIS)

    Bogdanov, I I; Guterman, A E

    2007-01-01

    Bijective linear transformations of the matrix algebra over an arbitrary field that preserve simultaneous diagonalizability are characterized. This result is used for the characterization of bijective linear monotone transformations . Bibliography: 28 titles.

  5. Identity of the conjugate gradient and Lanczos algorithms for matrix inversion in lattice fermion calculations

    International Nuclear Information System (INIS)

    Burkitt, A.N.; Irving, A.C.

    1988-01-01

    Two of the methods that are widely used in lattice gauge theory calculations requiring inversion of the fermion matrix are the Lanczos and the conjugate gradient algorithms. Those algorithms are already known to be closely related. In fact for matrix inversion, in exact arithmetic, they give identical results at each iteration and are just alternative formulations of a single algorithm. This equivalence survives rounding errors. We give the identities between the coefficients of the two formulations, enabling many of the best features of them to be combined. (orig.)

  6. Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations

    DEFF Research Database (Denmark)

    Garde, Henrik

    2018-01-01

    . For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method...

  7. A Structure-dependent matrix representation of manipulator kinematics and its inverse solution

    International Nuclear Information System (INIS)

    Sasaki, Shinobu

    1987-03-01

    In this paper, derivation of kinematic equations for a six-link manipulator is presented using the homogeneous transformation (A i -matrix) based on Denavit-Hartenberg method, and additionally a solution procedure of its inverse problem is outlined. In order to examine the validity of a system of equations, solutions were compared with the exact ones of the inverse kinematics (for the same type of a manipulator) expressed in arbitrarily given co-ordinate systems. Through complete agreement of joint solutions between the two, the present purpose was accomplished. As shown in this paper, an explicit description between adjacent links will give a possible clue to a systematic treatment of the inverse problem for a class of manipulators. (author)

  8. Inverse kinematics of a dual linear actuator pitch/roll heliostat

    Science.gov (United States)

    Freeman, Joshua; Shankar, Balakrishnan; Sundaram, Ganesh

    2017-06-01

    This work presents a simple, computationally efficient inverse kinematics solution for a pitch/roll heliostat using two linear actuators. The heliostat design and kinematics have been developed, modeled and tested using computer simulation software. A physical heliostat prototype was fabricated to validate the theoretical computations and data. Pitch/roll heliostats have numerous advantages including reduced cost potential and reduced space requirements, with a primary disadvantage being the significantly more complicated kinematics, which are solved here. Novel methods are applied to simplify the inverse kinematics problem which could be applied to other similar problems.

  9. The possibilities of linearized inversion of internally scattered seismic data

    KAUST Repository

    Aldawood, Ali

    2014-08-05

    Least-square migration is an iterative linearized inversion scheme that tends to suppress the migration artifacts and enhance the spatial resolution of the migrated image. However, standard least-square migration, based on imaging single scattering energy, may not be able to enhance events that are mainly illuminated by internal multiples such as vertical and nearly vertical faults. To alleviate this problem, we propose a linearized inversion framework to migrate internally multiply scattered energy. We applied this least-square migration of internal multiples to image a vertical fault. Tests on synthetic data demonstrate the ability of the proposed method to resolve a vertical fault plane that is poorly resolved by least-square imaging using primaries only. We, also, demonstrate the robustness of the proposed scheme in the presence of white Gaussian random observational noise and in the case of imaging the fault plane using inaccurate migration velocities.

  10. The possibilities of linearized inversion of internally scattered seismic data

    KAUST Repository

    Aldawood, Ali; Alkhalifah, Tariq Ali; Hoteit, Ibrahim; Zuberi, Mohammad; Turkiyyah, George

    2014-01-01

    Least-square migration is an iterative linearized inversion scheme that tends to suppress the migration artifacts and enhance the spatial resolution of the migrated image. However, standard least-square migration, based on imaging single scattering energy, may not be able to enhance events that are mainly illuminated by internal multiples such as vertical and nearly vertical faults. To alleviate this problem, we propose a linearized inversion framework to migrate internally multiply scattered energy. We applied this least-square migration of internal multiples to image a vertical fault. Tests on synthetic data demonstrate the ability of the proposed method to resolve a vertical fault plane that is poorly resolved by least-square imaging using primaries only. We, also, demonstrate the robustness of the proposed scheme in the presence of white Gaussian random observational noise and in the case of imaging the fault plane using inaccurate migration velocities.

  11. Solution of the inverse scattering problem at fixed energy with non-physical S matrix elements

    International Nuclear Information System (INIS)

    Eberspaecher, M.; Amos, K.; Apagyi, B.

    1999-12-01

    The quantum mechanical inverse elastic scattering problem is solved with the modified Newton-Sabatier method. A set of S matrix elements calculated from a realistic analytic optical model potential serves as input data. It is demonstrated that the quality of the inversion potential can be improved by including non-physical S matrix elements to half, quarter and eighth valued partial waves if the original set does not contain enough information to determine the interaction potential. We demonstrate that results can be very sensitive to the choice of those non-physical S matrix values both with the analytic potential model and in a real application in which the experimental cross section for the symmetrical scattering system of 12 C+ 12 C at E=7.998 MeV is analyzed

  12. A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems

    Czech Academy of Sciences Publication Activity Database

    Benzi, M.; Tůma, Miroslav

    1998-01-01

    Roč. 19, č. 3 (1998), s. 968-994 ISSN 1064-8275 R&D Projects: GA ČR GA201/93/0067; GA AV ČR IAA230401 Keywords : large sparse systems * interative methods * preconditioning * approximate inverse * sparse linear systems * sparse matrices * incomplete factorizations * conjugate gradient -type methods Subject RIV: BA - General Mathematics Impact factor: 1.378, year: 1998

  13. Efficient computation of the inverse of gametic relationship matrix for a marked QTL

    Directory of Open Access Journals (Sweden)

    Iwaisaki Hiroaki

    2006-04-01

    Full Text Available Abstract Best linear unbiased prediction of genetic merits for a marked quantitative trait locus (QTL using mixed model methodology includes the inverse of conditional gametic relationship matrix (G-1 for a marked QTL. When accounting for inbreeding, the conditional gametic relationships between two parents of individuals for a marked QTL are necessary to build G-1 directly. Up to now, the tabular method and its adaptations have been used to compute these relationships. In the present paper, an indirect method was implemented at the gametic level to compute these few relationships. Simulation results showed that the indirect method can perform faster with significantly less storage requirements than adaptation of the tabular method. The efficiency of the indirect method was mainly due to the use of the sparseness of G-1. The indirect method can also be applied to construct an approximate G-1 for populations with incomplete marker data, providing approximate probabilities of descent for QTL alleles for individuals with incomplete marker data.

  14. Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations

    Directory of Open Access Journals (Sweden)

    Farahnaz Soleimani

    2015-11-01

    Full Text Available An application of iterative methods for computing the Moore–Penrose inverse in balancing chemical equations is considered. With the aim to illustrate proposed algorithms, an improved high order hyper-power matrix iterative method for computing generalized inverses is introduced and applied. The improvements of the hyper-power iterative scheme are based on its proper factorization, as well as on the possibility to accelerate the iterations in the initial phase of the convergence. Although the effectiveness of our approach is confirmed on the basis of the theoretical point of view, some numerical comparisons in balancing chemical equations, as well as on randomly-generated matrices are furnished.

  15. Inverse mass matrix via the method of localized lagrange multipliers

    Czech Academy of Sciences Publication Activity Database

    González, José A.; Kolman, Radek; Cho, S.S.; Felippa, C.A.; Park, K.C.

    2018-01-01

    Roč. 113, č. 2 (2018), s. 277-295 ISSN 0029-5981 R&D Projects: GA MŠk(CZ) EF15_003/0000493; GA ČR GA17-22615S Institutional support: RVO:61388998 Keywords : explicit time integration * inverse mass matrix * localized Lagrange multipliers * partitioned analysis Subject RIV: BI - Acoustics OBOR OECD: Applied mechanics Impact factor: 2.162, year: 2016 https://onlinelibrary.wiley.com/doi/10.1002/nme.5613

  16. Continuity and general perturbation of the Drazin inverse for closed linear operators

    Directory of Open Access Journals (Sweden)

    N. Castro González

    2002-01-01

    Full Text Available We study perturbations and continuity of the Drazin inverse of a closed linear operator A and obtain explicit error estimates in terms of the gap between closed operators and the gap between ranges and nullspaces of operators. The results are used to derive a theorem on the continuity of the Drazin inverse for closed operators and to describe the asymptotic behavior of operator semigroups.

  17. An Entropic Estimator for Linear Inverse Problems

    Directory of Open Access Journals (Sweden)

    Amos Golan

    2012-05-01

    Full Text Available In this paper we examine an Information-Theoretic method for solving noisy linear inverse estimation problems which encompasses under a single framework a whole class of estimation methods. Under this framework, the prior information about the unknown parameters (when such information exists, and constraints on the parameters can be incorporated in the statement of the problem. The method builds on the basics of the maximum entropy principle and consists of transforming the original problem into an estimation of a probability density on an appropriate space naturally associated with the statement of the problem. This estimation method is generic in the sense that it provides a framework for analyzing non-normal models, it is easy to implement and is suitable for all types of inverse problems such as small and or ill-conditioned, noisy data. First order approximation, large sample properties and convergence in distribution are developed as well. Analytical examples, statistics for model comparisons and evaluations, that are inherent to this method, are discussed and complemented with explicit examples.

  18. Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method

    KAUST Repository

    Desmal, Abdulla

    2014-07-01

    A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.

  19. Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method

    KAUST Repository

    Desmal, Abdulla; Bagci, Hakan

    2014-01-01

    A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.

  20. Compressor Surge Control Design Using Linear Matrix Inequality Approach

    OpenAIRE

    Uddin, Nur; Gravdahl, Jan Tommy

    2017-01-01

    A novel design for active compressor surge control system (ASCS) using linear matrix inequality (LMI) approach is presented and including a case study on piston-actuated active compressor surge control system (PAASCS). The non-linear system dynamics of the PAASCS is transformed into linear parameter varying (LPV) system dynamics. The system parameters are varying as a function of the compressor performance curve slope. A compressor surge stabilization problem is then formulated as a LMI probl...

  1. Pinsker estimators for local helioseismology: inversion of travel times for mass-conserving flows

    International Nuclear Information System (INIS)

    Fournier, Damien; Holzke, Martin; Hohage, Thorsten; Gizon, Laurent

    2016-01-01

    A major goal of helioseismology is the three-dimensional reconstruction of the three velocity components of convective flows in the solar interior from sets of wave travel-time measurements. For small amplitude flows, the forward problem is described in good approximation by a large system of convolution equations. The input observations are highly noisy random vectors with a known dense covariance matrix. This leads to a large statistical linear inverse problem. Whereas for deterministic linear inverse problems several computationally efficient minimax optimal regularization methods exist, only one minimax-optimal linear estimator exists for statistical linear inverse problems: the Pinsker estimator. However, it is often computationally inefficient because it requires a singular value decomposition of the forward operator or it is not applicable because of an unknown noise covariance matrix, so it is rarely used for real-world problems. These limitations do not apply in helioseismology. We present a simplified proof of the optimality properties of the Pinsker estimator and show that it yields significantly better reconstructions than traditional inversion methods used in helioseismology, i.e. regularized least squares (Tikhonov regularization) and SOLA (approximate inverse) methods. Moreover, we discuss the incorporation of the mass conservation constraint in the Pinsker scheme using staggered grids. With this improvement we can reconstruct not only horizontal, but also vertical velocity components that are much smaller in amplitude. (paper)

  2. A method to compute the inverse of a complex n-block tridiagonal quasi-hermitian matrix

    International Nuclear Information System (INIS)

    Godfrin, Elena

    1990-01-01

    This paper presents a method to compute the inverse of a complex n-block tridiagonal quasi-hermitian matrix using adequate partitions of the complete matrix. This type of matrix is very usual in quantum mechanics and, more specifically, in solid state physics (e.g., interfaces and superlattices), when the tight-binding approximation is used. The efficiency of the method is analyzed comparing the required CPU time and work-area for different usual techniques. (Author)

  3. Contributions to Large Covariance and Inverse Covariance Matrices Estimation

    OpenAIRE

    Kang, Xiaoning

    2016-01-01

    Estimation of covariance matrix and its inverse is of great importance in multivariate statistics with broad applications such as dimension reduction, portfolio optimization, linear discriminant analysis and gene expression analysis. However, accurate estimation of covariance or inverse covariance matrices is challenging due to the positive definiteness constraint and large number of parameters, especially in the high-dimensional cases. In this thesis, I develop several approaches for estimat...

  4. Chosen interval methods for solving linear interval systems with special type of matrix

    Science.gov (United States)

    Szyszka, Barbara

    2013-10-01

    The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.

  5. Isotropic-resolution linear-array-based photoacoustic computed tomography through inverse Radon transform

    Science.gov (United States)

    Li, Guo; Xia, Jun; Li, Lei; Wang, Lidai; Wang, Lihong V.

    2015-03-01

    Linear transducer arrays are readily available for ultrasonic detection in photoacoustic computed tomography. They offer low cost, hand-held convenience, and conventional ultrasonic imaging. However, the elevational resolution of linear transducer arrays, which is usually determined by the weak focus of the cylindrical acoustic lens, is about one order of magnitude worse than the in-plane axial and lateral spatial resolutions. Therefore, conventional linear scanning along the elevational direction cannot provide high-quality three-dimensional photoacoustic images due to the anisotropic spatial resolutions. Here we propose an innovative method to achieve isotropic resolutions for three-dimensional photoacoustic images through combined linear and rotational scanning. In each scan step, we first elevationally scan the linear transducer array, and then rotate the linear transducer array along its center in small steps, and scan again until 180 degrees have been covered. To reconstruct isotropic three-dimensional images from the multiple-directional scanning dataset, we use the standard inverse Radon transform originating from X-ray CT. We acquired a three-dimensional microsphere phantom image through the inverse Radon transform method and compared it with a single-elevational-scan three-dimensional image. The comparison shows that our method improves the elevational resolution by up to one order of magnitude, approaching the in-plane lateral-direction resolution. In vivo rat images were also acquired.

  6. A Spreadsheet-Based, Matrix Formulation Linear Programming Lesson

    DEFF Research Database (Denmark)

    Harrod, Steven

    2009-01-01

    The article focuses on the spreadsheet-based, matrix formulation linear programming lesson. According to the article, it makes a higher level of theoretical mathematics approachable by a wide spectrum of students wherein many may not be decision sciences or quantitative methods majors. Moreover...

  7. H∞ /H2 model reduction through dilated linear matrix inequalities

    DEFF Research Database (Denmark)

    Adegas, Fabiano Daher; Stoustrup, Jakob

    2012-01-01

    This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the $H_{infty}$ and $H_{2}$ model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order $n$ to be reduced to an order $r=n/s$ where $n,r,s in field{N}$. Arb......This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the $H_{infty}$ and $H_{2}$ model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order $n$ to be reduced to an order $r=n/s$ where $n,r,s in field...

  8. Mini-lecture course: Introduction into hierarchical matrix technique

    KAUST Repository

    Litvinenko, Alexander

    2017-01-01

    allows us to work with general class of matrices (not only structured or Toeplits or sparse). H-matrices can keep the H-matrix data format during linear algebra operations (inverse, update, Schur complement).

  9. Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

    Directory of Open Access Journals (Sweden)

    Bin Wang

    2015-01-01

    Full Text Available This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.

  10. On The Structure of The Inverse of a Linear Constant Multivariable ...

    African Journals Online (AJOL)

    On The Structure of The Inverse of a Linear Constant Multivariable System. ... It is shown that the use of this representation has certain advantages in the design of multivariable feedback systems. typical examples were considered to indicate the corresponding application. Keywords: Stability Functions, multivariable ...

  11. 3D CSEM inversion based on goal-oriented adaptive finite element method

    Science.gov (United States)

    Zhang, Y.; Key, K.

    2016-12-01

    We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with

  12. Building Generalized Inverses of Matrices Using Only Row and Column Operations

    Science.gov (United States)

    Stuart, Jeffrey

    2010-01-01

    Most students complete their first and only course in linear algebra with the understanding that a real, square matrix "A" has an inverse if and only if "rref"("A"), the reduced row echelon form of "A", is the identity matrix I[subscript n]. That is, if they apply elementary row operations via the Gauss-Jordan algorithm to the partitioned matrix…

  13. Matrix preconditioning: a robust operation for optical linear algebra processors.

    Science.gov (United States)

    Ghosh, A; Paparao, P

    1987-07-15

    Analog electrooptical processors are best suited for applications demanding high computational throughput with tolerance for inaccuracies. Matrix preconditioning is one such application. Matrix preconditioning is a preprocessing step for reducing the condition number of a matrix and is used extensively with gradient algorithms for increasing the rate of convergence and improving the accuracy of the solution. In this paper, we describe a simple parallel algorithm for matrix preconditioning, which can be implemented efficiently on a pipelined optical linear algebra processor. From the results of our numerical experiments we show that the efficacy of the preconditioning algorithm is affected very little by the errors of the optical system.

  14. Multidisciplinary Inverse Reliability Analysis Based on Collaborative Optimization with Combination of Linear Approximations

    Directory of Open Access Journals (Sweden)

    Xin-Jia Meng

    2015-01-01

    Full Text Available Multidisciplinary reliability is an important part of the reliability-based multidisciplinary design optimization (RBMDO. However, it usually has a considerable amount of calculation. The purpose of this paper is to improve the computational efficiency of multidisciplinary inverse reliability analysis. A multidisciplinary inverse reliability analysis method based on collaborative optimization with combination of linear approximations (CLA-CO is proposed in this paper. In the proposed method, the multidisciplinary reliability assessment problem is first transformed into a problem of most probable failure point (MPP search of inverse reliability, and then the process of searching for MPP of multidisciplinary inverse reliability is performed based on the framework of CLA-CO. This method improves the MPP searching process through two elements. One is treating the discipline analyses as the equality constraints in the subsystem optimization, and the other is using linear approximations corresponding to subsystem responses as the replacement of the consistency equality constraint in system optimization. With these two elements, the proposed method realizes the parallel analysis of each discipline, and it also has a higher computational efficiency. Additionally, there are no difficulties in applying the proposed method to problems with nonnormal distribution variables. One mathematical test problem and an electronic packaging problem are used to demonstrate the effectiveness of the proposed method.

  15. IMPACT OF MATRIX INVERSION ON THE COMPLEXITY OF THE FINITE ELEMENT METHOD

    Directory of Open Access Journals (Sweden)

    M. Sybis

    2016-04-01

    Full Text Available Purpose. The development of a wide construction market and a desire to design innovative architectural building constructions has resulted in the need to create complex numerical models of objects having increasingly higher computational complexity. The purpose of this work is to show that choosing a proper method for solving the set of equations can improve the calculation time (reduce the complexity by a few levels of magnitude. Methodology. The article presents an analysis of the impact of matrix inversion algorithm on the deflection calculation in the beam, using the finite element method (FEM. Based on the literature analysis, common methods of calculating set of equations were determined. From the found solutions the Gaussian elimination, LU and Cholesky decomposition methods have been implemented to determine the effect of the matrix inversion algorithm used for solving the equations set on the number of computational operations performed. In addition, each of the implemented method has been further optimized thereby reducing the number of necessary arithmetic operations. Findings. These optimizations have been performed on the use of certain properties of the matrix, such as symmetry or significant number of zero elements in the matrix. The results of the analysis are presented for the division of the beam to 5, 50, 100 and 200 nodes, for which the deflection has been calculated. Originality. The main achievement of this work is that it shows the impact of the used methodology on the complexity of solving the problem (or equivalently, time needed to obtain results. Practical value. The difference between the best (the less complex and the worst (the most complex is in the row of few orders of magnitude. This result shows that choosing wrong methodology may enlarge time needed to perform calculation significantly.

  16. Linear algebra for dense matrices on a hypercube

    International Nuclear Information System (INIS)

    Sears, M.P.

    1990-01-01

    A set of routines has been written for dense matrix operations optimized for the NCUBE/6400 parallel processor. This paper was motivated by a Sandia effort to parallelize certain electronic structure calculations. Routines are included for matrix transpose, multiply, Cholesky decomposition, triangular inversion, and Householder tridiagonalization. The library is written in C and is callable from Fortran. Matrices up to order 1600 can be handled on 128 processors. For each operation, the algorithm used is presented along with typical timings and estimates of performance. Performance for order 1600 on 128 processors varies from 42 MFLOPs (House-holder tridiagonalization, triangular inverse) up to 126 MFLOPs (matrix multiply). The authors also present performance results for communications and basic linear algebra operations (saxpy and dot products)

  17. Minimal solution of linear formed fuzzy matrix equations

    Directory of Open Access Journals (Sweden)

    Maryam Mosleh

    2012-10-01

    Full Text Available In this paper according to the structured element method, the $mimes n$ inconsistent fuzzy matrix equation $Ailde{X}=ilde{B},$ which are linear formed by fuzzy structured element, is investigated. The necessary and sufficient condition for the existence of a fuzzy solution is also discussed. some examples are presented to illustrate the proposed method.

  18. Renormalized nonlinear sensitivity kernel and inverse thin-slab propagator in T-matrix formalism for wave-equation tomography

    International Nuclear Information System (INIS)

    Wu, Ru-Shan; Wang, Benfeng; Hu, Chunhua

    2015-01-01

    We derived the renormalized nonlinear sensitivity operator and the related inverse thin-slab propagator (ITSP) for nonlinear tomographic waveform inversion based on the theory of nonlinear partial derivative operator and its De Wolf approximation. The inverse propagator is based on a renormalization procedure to the forward and inverse transition matrix scattering series. The ITSP eliminates the divergence of the inverse Born series for strong perturbations by stepwise partial summation (renormalization). Numerical tests showed that the inverse Born T-series starts to diverge at moderate perturbation (20% for the given model of Gaussian ball with a radius of 5 wavelength), while the ITSP has no divergence problem for any strong perturbations (up to 100% perturbation for test model). In addition, the ITSP is a non-iterative, marching algorithm with only one sweep, and therefore very efficient in comparison with the iterative inversion based on the inverse-Born scattering series. This convergence and efficiency improvement has potential applications to the iterative procedure of waveform inversion. (paper)

  19. Trimming and procrastination as inversion techniques

    Science.gov (United States)

    Backus, George E.

    1996-12-01

    By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.

  20. A simplified density matrix minimization for linear scaling self-consistent field theory

    International Nuclear Information System (INIS)

    Challacombe, M.

    1999-01-01

    A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 10891 (1993)] and Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimization is introduced that requires four fewer matrix multiplies per minimization step relative to previous formulations. The simplified method also exhibits superior convergence properties, such that the bulk of the work may be shifted to the quadratically convergent McWeeny purification, which brings the density matrix to idempotency. Both orthogonal and nonorthogonal versions are derived. The AINV algorithm of Benzi, Meyer, and Tuma [SIAM J. Sci. Comp. 17, 1135 (1996)] is introduced to linear scaling electronic structure theory, and found to be essential in transformations between orthogonal and nonorthogonal representations. These methods have been developed with an atom-blocked sparse matrix algebra that achieves sustained megafloating point operations per second rates as high as 50% of theoretical, and implemented in the MondoSCF suite of linear scaling SCF programs. For the first time, linear scaling Hartree - Fock theory is demonstrated with three-dimensional systems, including water clusters and estane polymers. The nonorthogonal minimization is shown to be uncompetitive with minimization in an orthonormal representation. An early onset of linear scaling is found for both minimal and double zeta basis sets, and crossovers with a highly optimized eigensolver are achieved. Calculations with up to 6000 basis functions are reported. The scaling of errors with system size is investigated for various levels of approximation. copyright 1999 American Institute of Physics

  1. A Lie-Theoretic Perspective on O(n) Mass Matrix Inversion for Serial Manipulators and Polypeptide Chains.

    Science.gov (United States)

    Lee, Kiju; Wang, Yunfeng; Chirikjian, Gregory S

    2007-11-01

    Over the past several decades a number of O(n) methods for forward and inverse dynamics computations have been developed in the multi-body dynamics and robotics literature. A method was developed in 1974 by Fixman for O(n) computation of the mass-matrix determinant for a serial polymer chain consisting of point masses. In other recent papers, we extended this method in order to compute the inverse of the mass matrix for serial chains consisting of point masses. In the present paper, we extend these ideas further and address the case of serial chains composed of rigid-bodies. This requires the use of relatively deep mathematics associated with the rotation group, SO(3), and the special Euclidean group, SE(3), and specifically, it requires that one differentiates functions of Lie-group-valued argument.

  2. Exploring linear algebra labs and projects with Mathematica

    CERN Document Server

    Arangala, Crista

    2014-01-01

    Matrix Operations Lab 0: An Introduction to Mathematica Lab 1: Matrix Basics and Operations Lab 2: A Matrix Representation of Linear Systems Lab 3: Powers, Inverses, and Special Matrices Lab 4: Graph Theory and Adjacency Matrices Lab 5: Permutations and Determinants Lab 6: 4 x 4 Determinants and Beyond Project Set 1 Invertibility Lab 7: Singular or Nonsingular? Why Singularity Matters Lab 8: Mod It Out, Matrices with Entries in ZpLab 9: It's a Complex World Lab 10: Declaring Independence: Is It Linear? Project Set 2 Vector Spaces Lab 11: Vector Spaces and SubspacesLab 12: Basing It All on Just a Few Vectors Lab 13: Linear Transformations Lab 14: Eigenvalues and Eigenspaces Lab 15: Markov Chains, An Application of Eigenvalues Project Set 3 Orthogonality Lab 16: Inner Product Spaces Lab 17: The Geometry of Vector and Inner Product SpacesLab 18: Orthogonal Matrices, QR Decomposition, and Least Squares Regression Lab 19: Symmetric Matrices and Quadratic Forms Project Set 4 Matrix Decomposition with Applications L...

  3. Inverse scattering solution of non-linear evolution equations in one space dimension: an introduction

    International Nuclear Information System (INIS)

    Alvarez-Estrada, R.F.

    1979-01-01

    A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly

  4. A unified approach to fixed-order controller design via linear matrix inequalities

    Directory of Open Access Journals (Sweden)

    T. Iwasaki

    1995-01-01

    Full Text Available We consider the design of fixed-order (or low-order linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem,-stabilization as a robust stabilization problem, and robust L∞ control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI of the type BGC+(BGCT+Q<0 for the unknown matrix G. Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured positive definite matrix X such that X∈1 and X−1∈2 where 1 and 2 are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

  5. Analysis of smart beams with piezoelectric elements using impedance matrix and inverse Laplace transform

    International Nuclear Information System (INIS)

    Li, Guo-Qing; Miao, Xing-Yuan; Hu, Yuan-Tai; Wang, Ji

    2013-01-01

    A comprehensive study on smart beams with piezoelectric elements using an impedance matrix and the inverse Laplace transform is presented. Based on the authors’ previous work, the dynamics of some elements in beam-like smart structures are represented by impedance matrix equations, including a piezoelectric stack, a piezoelectric bimorph, an elastic straight beam or a circular curved beam. A further transform is applied to the impedance matrix to obtain a set of implicit transfer function matrices. Apart from the analytical solutions to the matrices of smart beams, one computation procedure is proposed to obtained the impedance matrices and transfer function matrices using FEA. By these means the dynamic solution of the elements in the frequency domain is transformed to that in Laplacian s-domain and then inversely transformed to time domain. The connections between the elements and boundary conditions of the smart structures are investigated in detail, and one integrated system equation is finally obtained using the symbolic operation of TF matrices. A procedure is proposed for dynamic analysis and control analysis of the smart beam system using mode superposition and a numerical inverse Laplace transform. The first example is given to demonstrate building transfer function associated impedance matrices using both FEA and analytical solutions. The second example is to verify the ability of control analysis using a suspended beam with PZT patches under close-loop control. The third example is designed for dynamic analysis of beams with a piezoelectric stack and a piezoelectric bimorph under various excitations. The last example of one smart beam with a PPF controller shows the applicability to the control analysis of complex systems using the proposed method. All results show good agreement with the other results in the previous literature. The advantages of the proposed methods are also discussed at the end of this paper. (paper)

  6. A regularized matrix factorization approach to induce structured sparse-low-rank solutions in the EEG inverse problem

    DEFF Research Database (Denmark)

    Montoya-Martinez, Jair; Artes-Rodriguez, Antonio; Pontil, Massimiliano

    2014-01-01

    We consider the estimation of the Brain Electrical Sources (BES) matrix from noisy electroencephalographic (EEG) measurements, commonly named as the EEG inverse problem. We propose a new method to induce neurophysiological meaningful solutions, which takes into account the smoothness, structured...... sparsity, and low rank of the BES matrix. The method is based on the factorization of the BES matrix as a product of a sparse coding matrix and a dense latent source matrix. The structured sparse-low-rank structure is enforced by minimizing a regularized functional that includes the ℓ21-norm of the coding...... matrix and the squared Frobenius norm of the latent source matrix. We develop an alternating optimization algorithm to solve the resulting nonsmooth-nonconvex minimization problem. We analyze the convergence of the optimization procedure, and we compare, under different synthetic scenarios...

  7. H-Shaped Multiple Linear Motor Drive Platform Control System Design Based on an Inverse System Method

    Directory of Open Access Journals (Sweden)

    Caiyan Qin

    2017-12-01

    Full Text Available Due to its simple mechanical structure and high motion stability, the H-shaped platform has been increasingly widely used in precision measuring, numerical control machining and semiconductor packaging equipment, etc. The H-shaped platform is normally driven by multiple (three permanent magnet synchronous linear motors. The main challenges for H-shaped platform-control include synchronous control between the two linear motors in the Y direction as well as total positioning error of the platform mover, a combination of position deviation in X and Y directions. To deal with the above challenges, this paper proposes a control strategy based on the inverse system method through state feedback and dynamic decoupling of the thrust force. First, mechanical dynamics equations have been deduced through the analysis of system coupling based on the platform structure. Second, the mathematical model of the linear motors and the relevant coordinate transformation between dq-axis currents and ABC-phase currents are analyzed. Third, after the main concept of inverse system method being explained, the inverse system model of the platform control system has been designed after defining relevant system variables. Inverse system model compensates the original nonlinear coupled system into pseudo-linear decoupled linear system, for which typical linear control methods, like PID, can be adopted to control the system. The simulation model of the control system is built in MATLAB/Simulink and the simulation result shows that the designed control system has both small synchronous deviation and small total trajectory tracking error. Furthermore, the control program has been run on NI controller for both fixed-loop-time and free-loop-time modes, and the test result shows that the average loop computation time needed is rather small, which makes it suitable for real industrial applications. Overall, it proves that the proposed new control strategy can be used in

  8. Noniterative MAP reconstruction using sparse matrix representations.

    Science.gov (United States)

    Cao, Guangzhi; Bouman, Charles A; Webb, Kevin J

    2009-09-01

    We present a method for noniterative maximum a posteriori (MAP) tomographic reconstruction which is based on the use of sparse matrix representations. Our approach is to precompute and store the inverse matrix required for MAP reconstruction. This approach has generally not been used in the past because the inverse matrix is typically large and fully populated (i.e., not sparse). In order to overcome this problem, we introduce two new ideas. The first idea is a novel theory for the lossy source coding of matrix transformations which we refer to as matrix source coding. This theory is based on a distortion metric that reflects the distortions produced in the final matrix-vector product, rather than the distortions in the coded matrix itself. The resulting algorithms are shown to require orthonormal transformations of both the measurement data and the matrix rows and columns before quantization and coding. The second idea is a method for efficiently storing and computing the required orthonormal transformations, which we call a sparse-matrix transform (SMT). The SMT is a generalization of the classical FFT in that it uses butterflies to compute an orthonormal transform; but unlike an FFT, the SMT uses the butterflies in an irregular pattern, and is numerically designed to best approximate the desired transforms. We demonstrate the potential of the noniterative MAP reconstruction with examples from optical tomography. The method requires offline computation to encode the inverse transform. However, once these offline computations are completed, the noniterative MAP algorithm is shown to reduce both storage and computation by well over two orders of magnitude, as compared to a linear iterative reconstruction methods.

  9. Linear models in matrix form a hands-on approach for the behavioral sciences

    CERN Document Server

    Brown, Jonathon D

    2014-01-01

    This textbook is an approachable introduction to statistical analysis using matrix algebra. Prior knowledge of matrix algebra is not necessary. Advanced topics are easy to follow through analyses that were performed on an open-source spreadsheet using a few built-in functions. These topics include ordinary linear regression, as well as maximum likelihood estimation, matrix decompositions, nonparametric smoothers and penalized cubic splines. Each data set (1) contains a limited number of observations to encourage readers to do the calculations themselves, and (2) tells a coherent story based on statistical significance and confidence intervals. In this way, students will learn how the numbers were generated and how they can be used to make cogent arguments about everyday matters. This textbook is designed for use in upper level undergraduate courses or first year graduate courses. The first chapter introduces students to linear equations, then covers matrix algebra, focusing on three essential operations: sum ...

  10. A unified approach to fixed-order controller design via linear matrix inequalities

    Directory of Open Access Journals (Sweden)

    Iwasaki T.

    1995-01-01

    Full Text Available We consider the design of fixed-order (or low-order linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem, 𝒬 -stabilization as a robust stabilization problem, and robust L ∞ control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI of the type B G C + ( B G C T + Q < 0 for the unknown matrix G . Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured positive definite matrix X such that X ∈ 𝒞 1 and X − 1 ∈ 𝒞 2 where 𝒞 1 and 𝒞 2 are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

  11. Hierarchical probing for estimating the trace of the matrix inverse on toroidal lattices

    Energy Technology Data Exchange (ETDEWEB)

    Stathopoulos, Andreas [College of William and Mary, Williamsburg, VA; Laeuchli, Jesse [College of William and Mary, Williamsburg, VA; Orginos, Kostas [College of William and Mary, Williamsburg, VA; Jefferson Lab

    2013-10-01

    The standard approach for computing the trace of the inverse of a very large, sparse matrix $A$ is to view the trace as the mean value of matrix quadratures, and use the Monte Carlo algorithm to estimate it. This approach is heavily used in our motivating application of Lattice QCD. Often, the elements of $A^{-1}$ display certain decay properties away from the non zero structure of $A$, but random vectors cannot exploit this induced structure of $A^{-1}$. Probing is a technique that, given a sparsity pattern of $A$, discovers elements of $A$ through matrix-vector multiplications with specially designed vectors. In the case of $A^{-1}$, the pattern is obtained by distance-$k$ coloring of the graph of $A$. For sufficiently large $k$, the method produces accurate trace estimates but the cost of producing the colorings becomes prohibitively expensive. More importantly, it is difficult to search for an optimal $k$ value, since none of the work for prior choices of $k$ can be reused.

  12. Mixed linear-nonlinear fault slip inversion: Bayesian inference of model, weighting, and smoothing parameters

    Science.gov (United States)

    Fukuda, J.; Johnson, K. M.

    2009-12-01

    Studies utilizing inversions of geodetic data for the spatial distribution of coseismic slip on faults typically present the result as a single fault plane and slip distribution. Commonly the geometry of the fault plane is assumed to be known a priori and the data are inverted for slip. However, sometimes there is not strong a priori information on the geometry of the fault that produced the earthquake and the data is not always strong enough to completely resolve the fault geometry. We develop a method to solve for the full posterior probability distribution of fault slip and fault geometry parameters in a Bayesian framework using Monte Carlo methods. The slip inversion problem is particularly challenging because it often involves multiple data sets with unknown relative weights (e.g. InSAR, GPS), model parameters that are related linearly (slip) and nonlinearly (fault geometry) through the theoretical model to surface observations, prior information on model parameters, and a regularization prior to stabilize the inversion. We present the theoretical framework and solution method for a Bayesian inversion that can handle all of these aspects of the problem. The method handles the mixed linear/nonlinear nature of the problem through combination of both analytical least-squares solutions and Monte Carlo methods. We first illustrate and validate the inversion scheme using synthetic data sets. We then apply the method to inversion of geodetic data from the 2003 M6.6 San Simeon, California earthquake. We show that the uncertainty in strike and dip of the fault plane is over 20 degrees. We characterize the uncertainty in the slip estimate with a volume around the mean fault solution in which the slip most likely occurred. Slip likely occurred somewhere in a volume that extends 5-10 km in either direction normal to the fault plane. We implement slip inversions with both traditional, kinematic smoothing constraints on slip and a simple physical condition of uniform stress

  13. 2.5D Inversion Algorithm of Frequency-Domain Airborne Electromagnetics with Topography

    Directory of Open Access Journals (Sweden)

    Jianjun Xi

    2016-01-01

    Full Text Available We presented a 2.5D inversion algorithm with topography for frequency-domain airborne electromagnetic data. The forward modeling is based on edge finite element method and uses the irregular hexahedron to adapt the topography. The electric and magnetic fields are split into primary (background and secondary (scattered field to eliminate the source singularity. For the multisources of frequency-domain airborne electromagnetic method, we use the large-scale sparse matrix parallel shared memory direct solver PARDISO to solve the linear system of equations efficiently. The inversion algorithm is based on Gauss-Newton method, which has the efficient convergence rate. The Jacobian matrix is calculated by “adjoint forward modelling” efficiently. The synthetic inversion examples indicated that our proposed method is correct and effective. Furthermore, ignoring the topography effect can lead to incorrect results and interpretations.

  14. TOEPLITZ, Solution of Linear Equation System with Toeplitz or Circulant Matrix

    International Nuclear Information System (INIS)

    Garbow, B.

    1984-01-01

    Description of program or function: TOEPLITZ is a collection of FORTRAN subroutines for solving linear systems Ax=b, where A is a Toeplitz matrix, a Circulant matrix, or has one or several block structures based on Toeplitz or Circulant matrices. Such systems arise in problems of electrodynamics, acoustics, mathematical statistics, algebra, in the numerical solution of integral equations with a difference kernel, and in the theory of stationary time series and signals

  15. Analytical Derivation of the Inverse Moments of One-Sided Correlated Gram Matrices With Applications

    KAUST Repository

    Elkhalil, Khalil

    2016-02-03

    This paper addresses the development of analytical tools for the computation of the inverse moments of random Gram matrices with one side correlation. Such a question is mainly driven by applications in signal processing and wireless communications wherein such matrices naturally arise. In particular, we derive closed-form expressions for the inverse moments and show that the obtained results can help approximate several performance metrics such as the average estimation error corresponding to the Best Linear Unbiased Estimator (BLUE) and the Linear Minimum Mean Square Error (LMMSE) estimator or also other loss functions used to measure the accuracy of covariance matrix estimates.

  16. Hierarchical matrix approximation of large covariance matrices

    KAUST Repository

    Litvinenko, Alexander

    2015-01-05

    We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.

  17. Hierarchical matrix approximation of large covariance matrices

    KAUST Repository

    Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul

    2015-01-01

    We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.

  18. Exact closed-form expression for the inverse moments of one-sided correlated Gram matrices

    KAUST Repository

    Elkhalil, Khalil

    2016-08-15

    In this paper, we derive a closed-form expression for the inverse moments of one sided-correlated random Gram matrices. Such a question is mainly motivated by applications in signal processing and wireless communications for which evaluating this quantity is a question of major interest. This is for instance the case of the best linear unbiased estimator, in which the average estimation error corresponds to the first inverse moment of a random Gram matrix.

  19. Exact closed-form expression for the inverse moments of one-sided correlated Gram matrices

    KAUST Repository

    Elkhalil, Khalil; Kammoun, Abla; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim

    2016-01-01

    In this paper, we derive a closed-form expression for the inverse moments of one sided-correlated random Gram matrices. Such a question is mainly motivated by applications in signal processing and wireless communications for which evaluating this quantity is a question of major interest. This is for instance the case of the best linear unbiased estimator, in which the average estimation error corresponds to the first inverse moment of a random Gram matrix.

  20. LINPACK, Subroutine Library for Linear Equation System Solution and Matrix Calculation

    International Nuclear Information System (INIS)

    Dongarra, J.J.

    1979-01-01

    1 - Description of problem or function: LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE: General, GB: General band, PO: Positive definite, PP: Positive definite packed, PB: Positive definite band, SI: Symmetric indefinite, SP: Symmetric indefinite packed, HI: Hermitian indefinite, HP: Hermitian indefinite packed, TR: Triangular, GT: General tridiagonal, PT: Positive definite tridiagonal, CH: Cholesky decomposition, QR: Orthogonal-triangular decomposition, SV: Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA: Factor, CO: Factor and estimate condition, SL: Solve, DI: Determinant and/or inverse and/or inertia, DC: Decompose, UD: Update, DD: Down-date, EX Exchange. The following chart shows all the LINPACK subroutines. The initial 'S' in the names may be replaced by D, C or Z and the initial 'C' in the complex-only names may be replaced by a Z. SGE: FA, CO, SL, DI; SGB: FA, CO, SL, DI; SPO: FA, CO, SL, DI; SPP: FA, CO, SL, DI; SPB: FA, CO, SL, DI; SSI: FA, CO, SL, DI; SSP: FA, CO, SL, DI; CHI: FA, CO, SL, DI; CHP: FA, CO, SL, DI; STR

  1. Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays

    International Nuclear Information System (INIS)

    Shahverdiev, E.M.; Hashimov, R.H.; Nuriev, R.A.; Hashimova, L.H.; Huseynova, E.M.; Shore, K.A.

    2005-04-01

    We report on inverse chaos synchronization between two unidirectionally linearly and nonlinearly coupled chaotic systems with multiple time-delays and find the existence and stability conditions for different synchronization regimes. We also study the effect of parameter mismatches on synchonization regimes. The method is tested on the famous Ikeda model. Numerical simulations fully support the analytical approach. (author)

  2. Effects of applied electromagnetic fields on the linear and nonlinear optical properties in an inverse parabolic quantum well

    International Nuclear Information System (INIS)

    Ungan, F.; Yesilgul, U.; Kasapoglu, E.; Sari, H.; Sökmen, I.

    2012-01-01

    In this present work, we have investigated theoretically the effects of applied electric and magnetic fields on the linear and nonlinear optical properties in a GaAs/Al x Ga 1−x As inverse parabolic quantum well for different Al concentrations at the well center. The Al concentration at the barriers was always x max =0.3. The energy levels and wave functions are calculated within the effective mass approximation and the envelope function approach. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. The linear, third-order nonlinear and total absorption and refractive index changes depending on the Al concentration at the well center are investigated as a function of the incident photon energy for the different values of the applied electric and magnetic fields. The results show that the applied electric and magnetic fields have a great effect on these optical quantities. - Highlights: ► The x c concentration has a great effect on the optical characteristics of these structures. ► The EM fields have a great effect on the optical properties of these structures. ► The total absorption coefficients increased as the electric and magnetic field increases. ► The RICs reduced as the electric and magnetic field increases.

  3. Linear Matrix Inequalities in Multirate Control over Networks

    Directory of Open Access Journals (Sweden)

    Ángel Cuenca

    2012-01-01

    Full Text Available This paper faces two of the main drawbacks in networked control systems: bandwidth constraints and timevarying delays. The bandwidth limitations are solved by using multirate control techniques. The resultant multirate controller must ensure closed-loop stability in the presence of time-varying delays. Some stability conditions and a state feedback controller design are formulated in terms of linear matrix inequalities. The theoretical proposal is validated in two different experimental environments: a crane-based test-bed over Ethernet, and a maglev based platform over Profibus.

  4. New computational method for non-LTE, the linear response matrix

    International Nuclear Information System (INIS)

    Fournier, K.B.; Grasiani, F.R.; Harte, J.A.; Libby, S.B.; More, R.M.; Zimmerman, G.B.

    1998-01-01

    My coauthors have done extensive theoretical and computational calculations that lay the ground work for a linear response matrix method to calculate non-LTE (local thermodynamic equilibrium) opacities. I will give briefly review some of their work and list references. Then I will describe what has been done to utilize this theory to create a computational package to rapidly calculate mild non-LTE emission and absorption opacities suitable for use in hydrodynamic calculations. The opacities are obtained by performing table look-ups on data that has been generated with a non-LTE package. This scheme is currently under development. We can see that it offers a significant computational speed advantage. It is suitable for mild non-LTE, quasi-steady conditions. And it offers a new insertion path for high-quality non-LTE data. Currently, the linear response matrix data file is created using XSN. These data files could be generated by more detailed and rigorous calculations without changing any part of the implementation in the hydro code. The scheme is running in Lasnex and is being tested and developed

  5. A fast algorithm for sparse matrix computations related to inversion

    International Nuclear Information System (INIS)

    Li, S.; Wu, W.; Darve, E.

    2013-01-01

    We have developed a fast algorithm for computing certain entries of the inverse of a sparse matrix. Such computations are critical to many applications, such as the calculation of non-equilibrium Green’s functions G r and G for nano-devices. The FIND (Fast Inverse using Nested Dissection) algorithm is optimal in the big-O sense. However, in practice, FIND suffers from two problems due to the width-2 separators used by its partitioning scheme. One problem is the presence of a large constant factor in the computational cost of FIND. The other problem is that the partitioning scheme used by FIND is incompatible with most existing partitioning methods and libraries for nested dissection, which all use width-1 separators. Our new algorithm resolves these problems by thoroughly decomposing the computation process such that width-1 separators can be used, resulting in a significant speedup over FIND for realistic devices — up to twelve-fold in simulation. The new algorithm also has the added advantage that desired off-diagonal entries can be computed for free. Consequently, our algorithm is faster than the current state-of-the-art recursive methods for meshes of any size. Furthermore, the framework used in the analysis of our algorithm is the first attempt to explicitly apply the widely-used relationship between mesh nodes and matrix computations to the problem of multiple eliminations with reuse of intermediate results. This framework makes our algorithm easier to generalize, and also easier to compare against other methods related to elimination trees. Finally, our accuracy analysis shows that the algorithms that require back-substitution are subject to significant extra round-off errors, which become extremely large even for some well-conditioned matrices or matrices with only moderately large condition numbers. When compared to these back-substitution algorithms, our algorithm is generally a few orders of magnitude more accurate, and our produced round-off errors

  6. A fast algorithm for sparse matrix computations related to inversion

    Energy Technology Data Exchange (ETDEWEB)

    Li, S., E-mail: lisong@stanford.edu [Institute for Computational and Mathematical Engineering, Stanford University, 496 Lomita Mall, Durand Building, Stanford, CA 94305 (United States); Wu, W. [Department of Electrical Engineering, Stanford University, 350 Serra Mall, Packard Building, Room 268, Stanford, CA 94305 (United States); Darve, E. [Institute for Computational and Mathematical Engineering, Stanford University, 496 Lomita Mall, Durand Building, Stanford, CA 94305 (United States); Department of Mechanical Engineering, Stanford University, 496 Lomita Mall, Durand Building, Room 209, Stanford, CA 94305 (United States)

    2013-06-01

    We have developed a fast algorithm for computing certain entries of the inverse of a sparse matrix. Such computations are critical to many applications, such as the calculation of non-equilibrium Green’s functions G{sup r} and G{sup <} for nano-devices. The FIND (Fast Inverse using Nested Dissection) algorithm is optimal in the big-O sense. However, in practice, FIND suffers from two problems due to the width-2 separators used by its partitioning scheme. One problem is the presence of a large constant factor in the computational cost of FIND. The other problem is that the partitioning scheme used by FIND is incompatible with most existing partitioning methods and libraries for nested dissection, which all use width-1 separators. Our new algorithm resolves these problems by thoroughly decomposing the computation process such that width-1 separators can be used, resulting in a significant speedup over FIND for realistic devices — up to twelve-fold in simulation. The new algorithm also has the added advantage that desired off-diagonal entries can be computed for free. Consequently, our algorithm is faster than the current state-of-the-art recursive methods for meshes of any size. Furthermore, the framework used in the analysis of our algorithm is the first attempt to explicitly apply the widely-used relationship between mesh nodes and matrix computations to the problem of multiple eliminations with reuse of intermediate results. This framework makes our algorithm easier to generalize, and also easier to compare against other methods related to elimination trees. Finally, our accuracy analysis shows that the algorithms that require back-substitution are subject to significant extra round-off errors, which become extremely large even for some well-conditioned matrices or matrices with only moderately large condition numbers. When compared to these back-substitution algorithms, our algorithm is generally a few orders of magnitude more accurate, and our produced round

  7. FUNDAMENTAL MATRIX OF LINEAR CONTINUOUS SYSTEM IN THE PROBLEM OF ESTIMATING ITS TRANSPORT DELAY

    Directory of Open Access Journals (Sweden)

    N. A. Dudarenko

    2014-09-01

    Full Text Available The paper deals with the problem of quantitative estimation for transport delay of linear continuous systems. The main result is received by means of fundamental matrix of linear differential equations solutions specified in the normal Cauchy form for the cases of SISO and MIMO systems. Fundamental matrix has the dual property. It means that the weight function of the system can be formed as a free motion of systems. Last one is generated by the vector of initial system conditions, which coincides with the matrix input of the system being researched. Thus, using the properties of the system- solving for fundamental matrix has given the possibility to solve the problem of estimating transport linear continuous system delay without the use of derivation procedure in hardware environment and without formation of exogenous Dirac delta function. The paper is illustrated by examples. The obtained results make it possible to solve the problem of modeling the pure delay links using consecutive chain of aperiodic links of the first order with the equal time constants. Modeling results have proved the correctness of obtained computations. Knowledge of transport delay can be used when configuring multi- component technological complexes and in the diagnosis of their possible functional degeneration.

  8. The development of computational algorithms for manipulator inverse kinematics

    International Nuclear Information System (INIS)

    Sasaki, Shinobu

    1989-10-01

    A solution technique of the inverse kinematics for multi-joint robot manipulators has been considered to be one of the most cumbersome treatment due to non-linearity properties inclusive of trigonometric functions. The most traditional approach is to use the Jacobian matrix on linearization assumptions. This iterative technique, however, is attended with numerical problems having significant influences on the solution characteristics such as initial guess dependence and singularities. Taking these facts into consideration, new approaches have been proposed from different standpoints, which are based on polynomial transformation of kinematic model, the minimization technique in mathematical programming, vector-geometrical concept, and the separation of joint variables associated with the optimization problem. In terms of computer simulations, each approach was identified to be a useful algorithm which leads to theoretically accurate solutions to complicated inverse problems. In this way, the short-term goal of our studies on manipulator inverse problem in the R and D project of remote handling technology was accomplished with success, and consequently the present report sums up the results of basic studies on this matter. (author)

  9. Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter linearly contained in one of the boundary conditions

    OpenAIRE

    Guliyev, Namig J.

    2008-01-01

    International audience; Inverse problems of recovering the coefficients of Sturm–Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: 1) from the sequences of eigenvalues and norming constants; 2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.

  10. Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers

    CERN Document Server

    Li, Deng-Feng

    2016-01-01

    This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics. .

  11. Syrio. A program for the calculation of the inverse of a matrix; Syrio. Programa para el calculo de la inversa de una matriz

    Energy Technology Data Exchange (ETDEWEB)

    Garcia de Viedma Alonso, L.

    1963-07-01

    SYRIO is a code for the inversion of a non-singular square matrix whose order is not higher than 40 for the UNIVAC-UCT (SS-90). The treatment stands from the inversion formula of sherman and Morrison, and following the Herbert S. Wilf's method for special matrices, generalize the procedure to any kind of non-singular square matrices. the limitation of the matrix order is not inherent of the program itself but imposed by the storage capacity of the computer for which it was coded. (Author)

  12. Hierarchical matrix approximation of large covariance matrices

    KAUST Repository

    Litvinenko, Alexander

    2015-01-07

    We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design

  13. Hierarchical matrix approximation of large covariance matrices

    KAUST Repository

    Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul

    2015-01-01

    We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design

  14. Teaching Linear Algebra: Proceeding More Efficiently by Staying Comfortably within Z

    Science.gov (United States)

    Beaver, Scott

    2015-01-01

    For efficiency in a linear algebra course the instructor may wish to avoid the undue arithmetical distractions of rational arithmetic. In this paper we explore how to write fraction-free problems of various types including elimination, matrix inverses, orthogonality, and the (non-normalizing) Gram-Schmidt process.

  15. Linear and nonlinear intersubband optical absorption in a disk-shaped quantum dot with a parabolic potential plus an inverse squared potential in a static magnetic field

    Energy Technology Data Exchange (ETDEWEB)

    Liu Guanghui [Department of Physics, College of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006 (China); Guo Kangxian, E-mail: axguo@sohu.com [Department of Physics, College of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006 (China); Wang Chao [Institute of Public Administration, Guangzhou University, Guangzhou 510006 (China)

    2012-06-15

    The linear and nonlinear optical absorption in a disk-shaped quantum dot (DSQD) with parabolic potential plus an inverse squared potential in the presence of a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron in the DSQD are obtained by using the effective mass approximation. Numerical calculations are presented for typical GaAs/AlAs DSQD. It is found that the optical absorption coefficients are strongly affected not only by a static magnetic field, but also by the strength of external field, the confinement frequency and the incident optical intensity.

  16. Linear and nonlinear intersubband optical absorption in a disk-shaped quantum dot with a parabolic potential plus an inverse squared potential in a static magnetic field

    International Nuclear Information System (INIS)

    Liu Guanghui; Guo Kangxian; Wang Chao

    2012-01-01

    The linear and nonlinear optical absorption in a disk-shaped quantum dot (DSQD) with parabolic potential plus an inverse squared potential in the presence of a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron in the DSQD are obtained by using the effective mass approximation. Numerical calculations are presented for typical GaAs/AlAs DSQD. It is found that the optical absorption coefficients are strongly affected not only by a static magnetic field, but also by the strength of external field, the confinement frequency and the incident optical intensity.

  17. S-Matrix to potential inversion of low-energy α-12C phase shifts

    Science.gov (United States)

    Cooper, S. G.; Mackintosh, R. S.

    1990-10-01

    The IP S-matrix to potential inversion procedure is applied to phase shifts for selected partial waves over a range of energies below the inelastic threshold for α-12C scattering. The phase shifts were determined by Plaga et al. Potentials found by Buck and Rubio to fit the low-energy alpha cluster resonances need only an increased attraction in the surface to accurately reproduce the phase-shift behaviour. Substantial differences between the potentials for odd and even partial waves are necessary. The surface tail of the potential is postulated to be a threshold effect.

  18. Syrio. A program for the calculation of the inverse of a matrix; Syrio. Programa para el calculo de la inversa de una matriz

    Energy Technology Data Exchange (ETDEWEB)

    Garcia de Viedma Alonso, L.

    1963-07-01

    SYRIO is a code for the inversion of a non-singular square matrix whose order is not higher than 40 for the UNIVAC-UCT (SS-90). The treatment stands from the inversion formula of sherman and Morrison, and following the Herbert S. Wilf's method for special matrices, generalize the procedure to any kind of non-singular square matrices. the limitation of the matrix order is not inherent of the program itself but imposed by the storage capacity of the computer for which it was coded. (Author)

  19. On the internal stability of non-linear dynamic inversion: application to flight control

    Czech Academy of Sciences Publication Activity Database

    Alam, M.; Čelikovský, Sergej

    2017-01-01

    Roč. 11, č. 12 (2017), s. 1849-1861 ISSN 1751-8644 R&D Projects: GA ČR(CZ) GA17-04682S Institutional support: RVO:67985556 Keywords : flight control * non-linear dynamic inversion * stability Subject RIV: BC - Control Systems Theory OBOR OECD: Automation and control systems Impact factor: 2.536, year: 2016 http://library.utia.cas.cz/separaty/2017/TR/celikovsky-0476150.pdf

  20. Resolution limits of migration and linearized waveform inversion images in a lossy medium

    KAUST Repository

    Schuster, Gerard T.; Dutta, Gaurav; Li, Jing

    2017-01-01

    The vertical-and horizontal-resolution limits Delta x(lossy) and Delta z(lossy) of post-stack migration and linearized waveform inversion images are derived for lossy data in the far-field approximation. Unlike the horizontal resolution limit Delta x proportional to lambda z/L in a lossless medium which linearly worsens in depth z, Delta x(lossy) proportional to z(2)/QL worsens quadratically with depth for a medium with small Q values. Here, Q is the quality factor, lambda is the effective wavelength, L is the recording aperture, and loss in the resolution formulae is accounted for by replacing lambda with z/Q. In contrast, the lossy vertical-resolution limit Delta z(lossy) only worsens linearly in depth compared to Delta z proportional to lambda for a lossless medium. For both the causal and acausal Q models, the resolution limits are linearly proportional to 1/Q for small Q. These theoretical predictions are validated with migration images computed from lossy data.

  1. Resolution limits of migration and linearized waveform inversion images in a lossy medium

    KAUST Repository

    Schuster, Gerard T.

    2017-03-10

    The vertical-and horizontal-resolution limits Delta x(lossy) and Delta z(lossy) of post-stack migration and linearized waveform inversion images are derived for lossy data in the far-field approximation. Unlike the horizontal resolution limit Delta x proportional to lambda z/L in a lossless medium which linearly worsens in depth z, Delta x(lossy) proportional to z(2)/QL worsens quadratically with depth for a medium with small Q values. Here, Q is the quality factor, lambda is the effective wavelength, L is the recording aperture, and loss in the resolution formulae is accounted for by replacing lambda with z/Q. In contrast, the lossy vertical-resolution limit Delta z(lossy) only worsens linearly in depth compared to Delta z proportional to lambda for a lossless medium. For both the causal and acausal Q models, the resolution limits are linearly proportional to 1/Q for small Q. These theoretical predictions are validated with migration images computed from lossy data.

  2. Secret Message Decryption: Group Consulting Projects Using Matrices and Linear Programming

    Science.gov (United States)

    Gurski, Katharine F.

    2009-01-01

    We describe two short group projects for finite mathematics students that incorporate matrices and linear programming into fictional consulting requests presented as a letter to the students. The students are required to use mathematics to decrypt secret messages in one project involving matrix multiplication and inversion. The second project…

  3. The detection of influential subsets in linear regression using an influence matrix

    OpenAIRE

    Peña, Daniel; Yohai, Víctor J.

    1991-01-01

    This paper presents a new method to identify influential subsets in linear regression problems. The procedure uses the eigenstructure of an influence matrix which is defined as the matrix of uncentered covariance of the effect on the whole data set of deleting each observation, normalized to include the univariate Cook's statistics in the diagonal. It is shown that points in an influential subset will appear with large weight in at least one of the eigenvector linked to the largest eigenvalue...

  4. Iterative algorithms for the input and state recovery from the approximate inverse of strictly proper multivariable systems

    Science.gov (United States)

    Chen, Liwen; Xu, Qiang

    2018-02-01

    This paper proposes new iterative algorithms for the unknown input and state recovery from the system outputs using an approximate inverse of the strictly proper linear time-invariant (LTI) multivariable system. One of the unique advantages from previous system inverse algorithms is that the output differentiation is not required. The approximate system inverse is stable due to the systematic optimal design of a dummy feedthrough D matrix in the state-space model via the feedback stabilization. The optimal design procedure avoids trial and error to identify such a D matrix which saves tremendous amount of efforts. From the derived and proved convergence criteria, such an optimal D matrix also guarantees the convergence of algorithms. Illustrative examples show significant improvement of the reference input signal tracking by the algorithms and optimal D design over non-iterative counterparts on controllable or stabilizable LTI systems, respectively. Case studies of two Boeing-767 aircraft aerodynamic models further demonstrate the capability of the proposed methods.

  5. The shifting zoom: new possibilities for inverse scattering on electrically large domains

    Science.gov (United States)

    Persico, Raffaele; Ludeno, Giovanni; Soldovieri, Francesco; De Coster, Alberic; Lambot, Sebastien

    2017-04-01

    Inverse scattering is a subject of great interest in diagnostic problems, which are in their turn of interest for many applicative problems as investigation of cultural heritage, characterization of foundations or subservices, identification of unexploded ordnances and so on [1-4]. In particular, GPR data are usually focused by means of migration algorithms, essentially based on a linear approximation of the scattering phenomenon. Migration algorithms are popular because they are computationally efficient and do not require the inversion of a matrix, neither the calculation of the elements of a matrix. In fact, they are essentially based on the adjoint of the linearised scattering operator, which allows in the end to write the inversion formula as a suitably weighted integral of the data [5]. In particular, this makes a migration algorithm more suitable than a linear microwave tomography inversion algorithm for the reconstruction of an electrically large investigation domain. However, this computational challenge can be overcome by making use of investigation domains joined side by side, as proposed e.g. in ref. [3]. This allows to apply a microwave tomography algorithm even to large investigation domains. However, the joining side by side of sequential investigation domains introduces a problem of limited (and asymmetric) maximum view angle with regard to the targets occurring close to the edges between two adjacent domains, or possibly crossing these edges. The shifting zoom is a method that allows to overcome this difficulty by means of overlapped investigation and observation domains [6-7]. It requires more sequential inversion with respect to adjacent investigation domains, but the really required extra-time is minimal because the matrix to be inverted is calculated ones and for all, as well as its singular value decomposition: what is repeated more time is only a fast matrix-vector multiplication. References [1] M. Pieraccini, L. Noferini, D. Mecatti, C

  6. Oblique projections and standard-form transformations for discrete inverse problems

    DEFF Research Database (Denmark)

    Hansen, Per Christian

    2013-01-01

    This tutorial paper considers a specific computational tool for the numerical solution of discrete inverse problems, known as the standard-form transformation, by which we can treat general Tikhonov regularization problems efficiently. In the tradition of B. N. Datta's expositions of numerical li...... linear algebra, we use the close relationship between oblique projections, pseudoinverses, and matrix computations to derive a simple geometric motivation and algebraic formulation of the standard-form transformation....

  7. Classification of the linear canonical transformation and its associated real symplectic matrix

    NARCIS (Netherlands)

    Bastiaans, M.J.; Alieva, T.

    2007-01-01

    Based on the eigenvalues of the real symplectic ABCD-matrix that characterizes the linear canonical integral transformation, a classification of this transformation and the associated ABCD-system is proposed and some nuclei (i.e. elementary members) in each class are described. In the

  8. The Analysis of the Grade of the Students' Understanding in "Linear Algebra" in National College of Technology

    OpenAIRE

    中沢, 喜昌

    1989-01-01

    We gave linear algebra lessons to the fifth grade students as an elective subject and analyzed that to what extent students understood the linear algebra, judging from the result of questionaires and tests. It showed that they are good at the problems accompanied by calculations such as inverse matrix, simultaneous linear equation, and proper value problem and that, on the contrary, it is difficult to understand the abstract notion like linear space and linear map.

  9. Group inverses of M-matrices and their applications

    CERN Document Server

    Kirkland, Stephen J

    2013-01-01

    Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas. After introducing sample problems associated with Leslie matrices and stochastic matrices, the authors develop the basic algebraic and spectral properties of the group inverse of a general matrix. They then derive formulas for derivatives of matrix f

  10. Computer programs for the solution of systems of linear algebraic equations

    Science.gov (United States)

    Sequi, W. T.

    1973-01-01

    FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended.

  11. Polymer sol-gel composite inverse opal structures.

    Science.gov (United States)

    Zhang, Xiaoran; Blanchard, G J

    2015-03-25

    We report on the formation of composite inverse opal structures where the matrix used to form the inverse opal contains both silica, formed using sol-gel chemistry, and poly(ethylene glycol), PEG. We find that the morphology of the inverse opal structure depends on both the amount of PEG incorporated into the matrix and its molecular weight. The extent of organization in the inverse opal structure, which is characterized by scanning electron microscopy and optical reflectance data, is mediated by the chemical bonding interactions between the silica and PEG constituents in the hybrid matrix. Both polymer chain terminus Si-O-C bonding and hydrogen bonding between the polymer backbone oxygens and silanol functionalities can contribute, with the polymer mediating the extent to which Si-O-Si bonds can form within the silica regions of the matrix due to hydrogen-bonding interactions.

  12. The attitude inversion method of geostationary satellites based on unscented particle filter

    Science.gov (United States)

    Du, Xiaoping; Wang, Yang; Hu, Heng; Gou, Ruixin; Liu, Hao

    2018-04-01

    The attitude information of geostationary satellites is difficult to be obtained since they are presented in non-resolved images on the ground observation equipment in space object surveillance. In this paper, an attitude inversion method for geostationary satellite based on Unscented Particle Filter (UPF) and ground photometric data is presented. The inversion algorithm based on UPF is proposed aiming at the strong non-linear feature in the photometric data inversion for satellite attitude, which combines the advantage of Unscented Kalman Filter (UKF) and Particle Filter (PF). This update method improves the particle selection based on the idea of UKF to redesign the importance density function. Moreover, it uses the RMS-UKF to partially correct the prediction covariance matrix, which improves the applicability of the attitude inversion method in view of UKF and the particle degradation and dilution of the attitude inversion method based on PF. This paper describes the main principles and steps of algorithm in detail, correctness, accuracy, stability and applicability of the method are verified by simulation experiment and scaling experiment in the end. The results show that the proposed method can effectively solve the problem of particle degradation and depletion in the attitude inversion method on account of PF, and the problem that UKF is not suitable for the strong non-linear attitude inversion. However, the inversion accuracy is obviously superior to UKF and PF, in addition, in the case of the inversion with large attitude error that can inverse the attitude with small particles and high precision.

  13. KEELE, Minimization of Nonlinear Function with Linear Constraints, Variable Metric Method

    International Nuclear Information System (INIS)

    Westley, G.W.

    1975-01-01

    1 - Description of problem or function: KEELE is a linearly constrained nonlinear programming algorithm for locating a local minimum of a function of n variables with the variables subject to linear equality and/or inequality constraints. 2 - Method of solution: A variable metric procedure is used where the direction of search at each iteration is obtained by multiplying the negative of the gradient vector by a positive definite matrix which approximates the inverse of the matrix of second partial derivatives associated with the function. 3 - Restrictions on the complexity of the problem: Array dimensions limit the number of variables to 20 and the number of constraints to 50. These can be changed by the user

  14. Linearized inversion frameworks toward high-resolution seismic imaging

    KAUST Repository

    Aldawood, Ali

    2016-09-01

    internally multiply scattered seismic waves to obtain highly resolved images delineating vertical faults that are otherwise not easily imaged by primaries. Seismic interferometry is conventionally based on the cross-correlation and convolution of seismic traces to transform seismic data from one acquisition geometry to another. The conventional interferometric transformation yields virtual data that suffers from low temporal resolution, wavelet distortion, and correlation/convolution artifacts. I therefore incorporate a least-squares datuming technique to interferometrically transform vertical-seismic-profile surface-related multiples to surface-seismic-profile primaries. This yields redatumed data with high temporal resolution and less artifacts, which are subsequently imaged to obtain highly resolved subsurface images. Tests on synthetic examples demonstrate the efficiency of the proposed techniques, yielding highly resolved migrated sections compared with images obtained by imaging conventionally redatumed data. I further advance the recently developed cost-effective Generalized Interferometric Multiple Imaging procedure, which aims to not only image first but also higher-order multiples as well. I formulate this procedure as a linearized inversion framework and solve it as a least-squares problem. Tests of the least-squares Generalized Interferometric Multiple imaging framework on synthetic datasets and demonstrate that it could provide highly resolved migrated images and delineate vertical fault planes compared with the standard procedure. The results support the assertion that this linearized inversion framework can illuminate subsurface zones that are mainly illuminated by internally scattered energy.

  15. An efficient, block-by-block algorithm for inverting a block tridiagonal, nearly block Toeplitz matrix

    International Nuclear Information System (INIS)

    Reuter, Matthew G; Hill, Judith C

    2012-01-01

    We present an algorithm for computing any block of the inverse of a block tridiagonal, nearly block Toeplitz matrix (defined as a block tridiagonal matrix with a small number of deviations from the purely block Toeplitz structure). By exploiting both the block tridiagonal and the nearly block Toeplitz structures, this method scales independently of the total number of blocks in the matrix and linearly with the number of deviations. Numerical studies demonstrate this scaling and the advantages of our method over alternatives.

  16. Local hyperspectral data multisharpening based on linear/linear-quadratic nonnegative matrix factorization by integrating lidar data

    Science.gov (United States)

    Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

    2015-10-01

    In this paper, a new Spectral-Unmixing-based approach, using Nonnegative Matrix Factorization (NMF), is proposed to locally multi-sharpen hyperspectral data by integrating a Digital Surface Model (DSM) obtained from LIDAR data. In this new approach, the nature of the local mixing model is detected by using the local variance of the object elevations. The hyper/multispectral images are explored using small zones. In each zone, the variance of the object elevations is calculated from the DSM data in this zone. This variance is compared to a threshold value and the adequate linear/linearquadratic spectral unmixing technique is used in the considered zone to independently unmix hyperspectral and multispectral data, using an adequate linear/linear-quadratic NMF-based approach. The obtained spectral and spatial information thus respectively extracted from the hyper/multispectral images are then recombined in the considered zone, according to the selected mixing model. Experiments based on synthetic hyper/multispectral data are carried out to evaluate the performance of the proposed multi-sharpening approach and literature linear/linear-quadratic approaches used on the whole hyper/multispectral data. In these experiments, real DSM data are used to generate synthetic data containing linear and linear-quadratic mixed pixel zones. The DSM data are also used for locally detecting the nature of the mixing model in the proposed approach. Globally, the proposed approach yields good spatial and spectral fidelities for the multi-sharpened data and significantly outperforms the used literature methods.

  17. Matrix Encryption Scheme

    Directory of Open Access Journals (Sweden)

    Abdelhakim Chillali

    2017-05-01

    Full Text Available In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. In this work, we proposed a new problem applicable to the public key cryptography, based on the Matrices, called “Matrix discrete logarithm problem”, it uses certain elements formed by matrices whose coefficients are elements in a finite field. We have constructed an abelian group and, for the cryptographic part in this unreliable group, we then perform the computation corresponding to the algebraic equations, Returning the encrypted result to a receiver. Upon receipt of the result, the receiver can retrieve the sender’s clear message by performing the inverse calculation.

  18. Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

    Science.gov (United States)

    Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

    2017-04-01

    This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

  19. Computing with linear equations and matrices

    International Nuclear Information System (INIS)

    Churchhouse, R.F.

    1983-01-01

    Systems of linear equations and matrices arise in many disciplines. The equations may accurately represent conditions satisfied by a system or, more likely, provide an approximation to a more complex system of non-linear or differential equations. The system may involve a few or many thousand unknowns and each individual equation may involve few or many of them. Over the past 50 years a vast literature on methods for solving systems of linear equations and the associated problems of finding the inverse or eigenvalues of a matrix has been produced. These lectures cover those methods which have been found to be most useful for dealing with such types of problem. References are given where appropriate and attention is drawn to the possibility of improved methods for use on vector and parallel processors. (orig.)

  20. A simple inversion of induced-polarization data collected in the Haenam area of Korea

    International Nuclear Information System (INIS)

    Jang, Hannuree; Park, Samgyu; Kim, Hee Joon

    2014-01-01

    We develop a two-stage method to invert induced polarization (IP) data. First, DC resistivity data are inverted to recover a background resistivity that is used to generate a sensitivity matrix for the IP inversion. The second stage accepts the background resistivity as the true resistivity of the medium and attempts to find a polarizability that satisfies the IP data. This is done by linearizing the equations for the background resistivity to produce a linear inverse problem that can be solved for the distribution of the subsurface polarizability. Smoothness and base-model constraints are used to stabilize the IP inversion process. These regularization methods are validated by inverting both synthetic and field data obtained in the Haenam epithermal mineralized area, Korea. As a result, the IP anomaly recovered from the base-model constraint indicates that fine-grained pyrite is disseminated in a shallow zone beneath the ridge of this site, which is confirmed by core samples. (paper)

  1. S-matrix to potential inversion of low-energy. alpha. - sup 12 C phase shifts

    Energy Technology Data Exchange (ETDEWEB)

    Cooper, S.G.; Mackintosh, R.S. (Open Univ., Milton Keynes (UK). Dept. of Physics)

    1990-10-22

    The IP S-matrix to potential inversion procedure is applied to phase shifts for selected partial waves over a range of energies below the inelastic threshold for {alpha}-{sup 12}C scattering. The phase shifts were determined by Plaga et al. Potentials found by Buck and Rubio to fit the low-energy alpha cluster resonances need only an increased attraction in the surface to accurately reproduce the phase-shift behaviour. Substantial differences between the potentials for odd and even partial waves are necessary. The surface tail of the potential is postulated to be a threshold effect. (orig.).

  2. A convergence analysis for a sweeping preconditioner for block tridiagonal systems of linear equations

    KAUST Repository

    Bagci, Hakan; Pasciak, Joseph E.; Sirenko, Kostyantyn

    2014-01-01

    We study sweeping preconditioners for symmetric and positive definite block tridiagonal systems of linear equations. The algorithm provides an approximate inverse that can be used directly or in a preconditioned iterative scheme. These algorithms are based on replacing the Schur complements appearing in a block Gaussian elimination direct solve by hierarchical matrix approximations with reduced off-diagonal ranks. This involves developing low rank hierarchical approximations to inverses. We first provide a convergence analysis for the algorithm for reduced rank hierarchical inverse approximation. These results are then used to prove convergence and preconditioning estimates for the resulting sweeping preconditioner.

  3. A convergence analysis for a sweeping preconditioner for block tridiagonal systems of linear equations

    KAUST Repository

    Bagci, Hakan

    2014-11-11

    We study sweeping preconditioners for symmetric and positive definite block tridiagonal systems of linear equations. The algorithm provides an approximate inverse that can be used directly or in a preconditioned iterative scheme. These algorithms are based on replacing the Schur complements appearing in a block Gaussian elimination direct solve by hierarchical matrix approximations with reduced off-diagonal ranks. This involves developing low rank hierarchical approximations to inverses. We first provide a convergence analysis for the algorithm for reduced rank hierarchical inverse approximation. These results are then used to prove convergence and preconditioning estimates for the resulting sweeping preconditioner.

  4. The linearized inversion of the generalized interferometric multiple imaging

    KAUST Repository

    Aldawood, Ali

    2016-09-06

    The generalized interferometric multiple imaging (GIMI) procedure can be used to image duplex waves and other higher order internal multiples. Imaging duplex waves could help illuminate subsurface zones that are not easily illuminated by primaries such as vertical and nearly vertical fault planes, and salt flanks. To image first-order internal multiple, the GIMI framework consists of three datuming steps, followed by applying the zero-lag cross-correlation imaging condition. However, the standard GIMI procedure yields migrated images that suffer from low spatial resolution, migration artifacts, and cross-talk noise. To alleviate these problems, we propose a least-squares GIMI framework in which we formulate the first two steps as a linearized inversion problem when imaging first-order internal multiples. Tests on synthetic datasets demonstrate the ability to localize subsurface scatterers in their true positions, and delineate a vertical fault plane using the proposed method. We, also, demonstrate the robustness of the proposed framework when imaging the scatterers or the vertical fault plane with erroneous migration velocities.

  5. Advanced topics in linear algebra weaving matrix problems through the Weyr form

    CERN Document Server

    O'Meara, Kevin; Vinsonhaler, Charles

    2011-01-01

    The Weyr matrix canonical form is a largely unknown cousin of the Jordan canonical form. Discovered by Eduard Weyr in 1885, the Weyr form outperforms the Jordan form in a number of mathematical situations, yet it remains somewhat of a mystery, even to many who are skilled in linear algebra. Written in an engaging style, this book presents various advanced topics in linear algebra linked through the Weyr form. Kevin O'Meara, John Clark, and Charles Vinsonhaler develop the Weyr form from scratch and include an algorithm for computing it. A fascinating duality exists between the Weyr form and the

  6. Linear programming model for solution of matrix game with payoffs trapezoidal intuitionistic fuzzy number

    Directory of Open Access Journals (Sweden)

    Darunee Hunwisai

    2017-01-01

    Full Text Available In this work, we considered two-person zero-sum games with fuzzy payoffs and matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers (TrIFNs. The concepts of TrIFNs and their arithmetic operations were used. The cut-set based method for matrix game with payoffs of TrIFNs was also considered. Compute the interval-type value of any alfa-constrategies by simplex method for linear programming. The proposed method is illustrated with a numerical example.

  7. The structure of solutions of the matrix linear unilateral polynomial equation with two variables

    Directory of Open Access Journals (Sweden)

    N. S. Dzhaliuk

    2017-07-01

    Full Text Available We investigate the structure of solutions of the matrix linear polynomial equation $A(\\lambdaX(\\lambda+B(\\lambdaY(\\lambda=C(\\lambda,$ in particular, possible degrees of the solutions. The solving of this equation is reduced to the solving of the equivalent matrix polynomial equation with matrix coefficients in triangular forms with invariant factors on the main diagonals, to which the matrices $A (\\lambda, B(\\lambda$ \\ and \\ $C(\\lambda$ are reduced by means of semiscalar equivalent transformations. On the basis of it, we have pointed out the bounds of the degrees of the matrix polynomial equation solutions. Necessary and sufficient conditions for the uniqueness of a solution with a minimal degree are established. An effective method for constructing minimal degree solutions of the equations is suggested. In this article, unlike well-known results about the estimations of the degrees of the solutions of the matrix polynomial equations in which both matrix coefficients are regular or at least one of them is regular, we have considered the case when the matrix polynomial equation has arbitrary matrix coefficients $A(\\lambda$ and $B(\\lambda.$ 

  8. Fundamental Matrix for a Class of Point Delay Linear Systems

    International Nuclear Information System (INIS)

    Sen, M. de la; Alastruey, C. F.

    1998-01-01

    It is difficult to establish explicit analytic forms for fundamental matrices of delayed linear systems. In this paper, an explicit form of exponential type is given for such a matrix in the case of punctual delays. The existence of real and complex fundamental matrices, for the case of real parameterizations of the differential system, is studied and discussed. Some additional commutativity properties involving the matrices parameters and the fundamental matrices as well as explicit expressions for the solution of the delayed differential system are also given. (Author)

  9. Comparison of Damage Models for Predicting the Non-Linear Response of Laminates Under Matrix Dominated Loading Conditions

    Science.gov (United States)

    Schuecker, Clara; Davila, Carlos G.; Rose, Cheryl A.

    2010-01-01

    Five models for matrix damage in fiber reinforced laminates are evaluated for matrix-dominated loading conditions under plane stress and are compared both qualitatively and quantitatively. The emphasis of this study is on a comparison of the response of embedded plies subjected to a homogeneous stress state. Three of the models are specifically designed for modeling the non-linear response due to distributed matrix cracking under homogeneous loading, and also account for non-linear (shear) behavior prior to the onset of cracking. The remaining two models are localized damage models intended for predicting local failure at stress concentrations. The modeling approaches of distributed vs. localized cracking as well as the different formulations of damage initiation and damage progression are compared and discussed.

  10. Batched Triangular Dense Linear Algebra Kernels for Very Small Matrix Sizes on GPUs

    KAUST Repository

    Charara, Ali; Keyes, David E.; Ltaief, Hatem

    2017-01-01

    Batched dense linear algebra kernels are becoming ubiquitous in scientific applications, ranging from tensor contractions in deep learning to data compression in hierarchical low-rank matrix approximation. Within a single API call, these kernels are capable of simultaneously launching up to thousands of similar matrix computations, removing the expensive overhead of multiple API calls while increasing the occupancy of the underlying hardware. A challenge is that for the existing hardware landscape (x86, GPUs, etc.), only a subset of the required batched operations is implemented by the vendors, with limited support for very small problem sizes. We describe the design and performance of a new class of batched triangular dense linear algebra kernels on very small data sizes using single and multiple GPUs. By deploying two-sided recursive formulations, stressing the register usage, maintaining data locality, reducing threads synchronization and fusing successive kernel calls, the new batched kernels outperform existing state-of-the-art implementations.

  11. Batched Triangular Dense Linear Algebra Kernels for Very Small Matrix Sizes on GPUs

    KAUST Repository

    Charara, Ali

    2017-03-06

    Batched dense linear algebra kernels are becoming ubiquitous in scientific applications, ranging from tensor contractions in deep learning to data compression in hierarchical low-rank matrix approximation. Within a single API call, these kernels are capable of simultaneously launching up to thousands of similar matrix computations, removing the expensive overhead of multiple API calls while increasing the occupancy of the underlying hardware. A challenge is that for the existing hardware landscape (x86, GPUs, etc.), only a subset of the required batched operations is implemented by the vendors, with limited support for very small problem sizes. We describe the design and performance of a new class of batched triangular dense linear algebra kernels on very small data sizes using single and multiple GPUs. By deploying two-sided recursive formulations, stressing the register usage, maintaining data locality, reducing threads synchronization and fusing successive kernel calls, the new batched kernels outperform existing state-of-the-art implementations.

  12. Inversion of the fermion matrix and the equivalence of the conjugate gradient and Lanczos algorithms

    International Nuclear Information System (INIS)

    Burkitt, A.N.; Irving, A.C.

    1990-01-01

    The Lanczos and conjugate gradient algorithms are widely used in lattice QCD calculations. The previously known close relationship between the two methods is explored and two commonly used implementations are shown to give identically the same results at each iteration, in exact arithmetic, for matrix inversion. The identities between the coefficients of the two algorithms are given, and many of the features of the two algorithms can now be combined. The effects of finite arithmetic are investigated and the particular Lanczos formulation is found to be most stable with respect to rounding errors. (orig.)

  13. Study of 1D complex resistivity inversion using digital linear filter technique; Linear filter ho wo mochiita fukusohi teiko no gyakukaisekiho no kento

    Energy Technology Data Exchange (ETDEWEB)

    Sakurai, K; Shima, H [OYO Corp., Tokyo (Japan)

    1996-10-01

    This paper proposes a modeling method of one-dimensional complex resistivity using linear filter technique which has been extended to the complex resistivity. In addition, a numerical test of inversion was conducted using the monitoring results, to discuss the measured frequency band. Linear filter technique is a method by which theoretical potential can be calculated for stratified structures, and it is widely used for the one-dimensional analysis of dc electrical exploration. The modeling can be carried out only using values of complex resistivity without using values of potential. In this study, a bipolar method was employed as a configuration of electrodes. The numerical test of one-dimensional complex resistivity inversion was conducted using the formulated modeling. A three-layered structure model was used as a numerical model. A multi-layer structure with a thickness of 5 m was analyzed on the basis of apparent complex resistivity calculated from the model. From the results of numerical test, it was found that both the chargeability and the time constant agreed well with those of the original model. A trade-off was observed between the chargeability and the time constant at the stage of convergence. 3 refs., 9 figs., 1 tab.

  14. Three-Dimensional Inverse Transport Solver Based on Compressive Sensing Technique

    Science.gov (United States)

    Cheng, Yuxiong; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi

    2013-09-01

    According to the direct exposure measurements from flash radiographic image, a compressive sensing-based method for three-dimensional inverse transport problem is presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. It is always very expensive to obtain enough measurements. With limited measurements, compressive sensing sparse reconstruction technique orthogonal matching pursuit is applied to obtain the sparse coefficients by solving an optimization problem. A three-dimensional inverse transport solver is developed based on a compressive sensing-based technique. There are three features in this solver: (1) AutoCAD is employed as a geometry preprocessor due to its powerful capacity in graphic. (2) The forward projection matrix rather than Gauss matrix is constructed by the visualization tool generator. (3) Fourier transform and Daubechies wavelet transform are adopted to convert an underdetermined system to a well-posed system in the algorithm. Simulations are performed and numerical results in pseudo-sine absorption problem, two-cube problem and two-cylinder problem when using compressive sensing-based solver agree well with the reference value.

  15. T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols

    International Nuclear Information System (INIS)

    Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

    2013-01-01

    We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with ground-based, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders. -- Highlights: ► New superposition T-matrix code is applied to soot aerosols. ► Quasi-Rayleigh side-scattering peak in linear depolarization (LD) is explained. ► LD measurements can be used for morphological characterization of soot aerosols

  16. Challenges of inversely estimating Jacobian from metabolomics data

    Directory of Open Access Journals (Sweden)

    Xiaoliang eSun

    2015-11-01

    Full Text Available Inferring dynamics of metabolic networks directly from metabolomics data provides a promising way to elucidate the underlying mechanisms of biological systems, as reported in our previous studies [1-3] by a differential Jacobian approach. The Jacobian is solved from an over-determined system of equations as JC + CJT = -2D, called Lyapunov Equation in its generic form , where J is the Jacobian, C is the covariance matrix of metabolomics data and D is the fluctuation matrix. Lyapunov Equation can be further simplified as the linear form Ax = b. Frequently, this linear equation system is ill-conditioned, i.e., a small variation in the right side b results in a big change in the solution x, thus making the solution unstable and error-prone. At the same time, inaccurate estimation of covariance matrix and uncertainties in the fluctuation matrix bring biases to the solution x. Here, we firstly reviewed common approaches to circumvent the ill-conditioned problems, including total least squares, Tikhonov regularization and truncated singular value decomposition. Then we benchmarked these methods on several in-silico kinetic models with small to large perturbations on the covariance and fluctuation matrices. The results identified that the accuracy of the reverse Jacobian is mainly dependent on the condition number of A, the perturbation amplitude of C and the stiffness of the kinetic models. Our research contributes a systematical comparison of methods to inversely solve Jacobian from metabolomics data.

  17. Azimuthal Seismic Amplitude Variation with Offset and Azimuth Inversion in Weakly Anisotropic Media with Orthorhombic Symmetry

    Science.gov (United States)

    Pan, Xinpeng; Zhang, Guangzhi; Yin, Xingyao

    2018-01-01

    Seismic amplitude variation with offset and azimuth (AVOaz) inversion is well known as a popular and pragmatic tool utilized to estimate fracture parameters. A single set of vertical fractures aligned along a preferred horizontal direction embedded in a horizontally layered medium can be considered as an effective long-wavelength orthorhombic medium. Estimation of Thomsen's weak-anisotropy (WA) parameters and fracture weaknesses plays an important role in characterizing the orthorhombic anisotropy in a weakly anisotropic medium. Our goal is to demonstrate an orthorhombic anisotropic AVOaz inversion approach to describe the orthorhombic anisotropy utilizing the observable wide-azimuth seismic reflection data in a fractured reservoir with the assumption of orthorhombic symmetry. Combining Thomsen's WA theory and linear-slip model, we first derive a perturbation in stiffness matrix of a weakly anisotropic medium with orthorhombic symmetry under the assumption of small WA parameters and fracture weaknesses. Using the perturbation matrix and scattering function, we then derive an expression for linearized PP-wave reflection coefficient in terms of P- and S-wave moduli, density, Thomsen's WA parameters, and fracture weaknesses in such an orthorhombic medium, which avoids the complicated nonlinear relationship between the orthorhombic anisotropy and azimuthal seismic reflection data. Incorporating azimuthal seismic data and Bayesian inversion theory, the maximum a posteriori solutions of Thomsen's WA parameters and fracture weaknesses in a weakly anisotropic medium with orthorhombic symmetry are reasonably estimated with the constraints of Cauchy a priori probability distribution and smooth initial models of model parameters to enhance the inversion resolution and the nonlinear iteratively reweighted least squares strategy. The synthetic examples containing a moderate noise demonstrate the feasibility of the derived orthorhombic anisotropic AVOaz inversion method, and the

  18. A Discrete-Time Recurrent Neural Network for Solving Rank-Deficient Matrix Equations With an Application to Output Regulation of Linear Systems.

    Science.gov (United States)

    Liu, Tao; Huang, Jie

    2017-04-17

    This paper presents a discrete-time recurrent neural network approach to solving systems of linear equations with two features. First, the system of linear equations may not have a unique solution. Second, the system matrix is not known precisely, but a sequence of matrices that converges to the unknown system matrix exponentially is known. The problem is motivated from solving the output regulation problem for linear systems. Thus, an application of our main result leads to an online solution to the output regulation problem for linear systems.

  19. Aging linear viscoelasticity of matrix-inclusion composite materials featuring ellipsoidal inclusions

    OpenAIRE

    LAVERGNE, Francis; SAB, Karam; SANAHUJA, Julien; BORNERT, Michel; TOULEMONDE, Charles

    2016-01-01

    A multi-scale homogenization scheme is proposed to estimate the time-dependent strains of fiber-reinforced concrete. This material is modeled as an aging linear viscoelastic composite material featuring ellipsoidal inclusions embedded in a viscoelastic cementitious matrix characterized by a time-dependent Poisson's ratio. To this end, the homogenization scheme proposed in Lavergne et al. [1] is adapted to the case of a time-dependent Poisson's ratio and it is successfully validated on a non-a...

  20. Reduction of Under-Determined Linear Systems by Sparce Block Matrix Technique

    DEFF Research Database (Denmark)

    Tarp-Johansen, Niels Jacob; Poulsen, Peter Noe; Damkilde, Lars

    1996-01-01

    numerical stability of the aforementioned reduction. Moreover the coefficient matrix for the equilibrium equations is typically very sparse. The objective is to deal efficiently with the full pivoting reduction of sparse rectangular matrices using a dynamic storage scheme based on the block matrix concept.......Under-determined linear equation systems occur in different engineering applications. In structural engineering they typically appear when applying the force method. As an example one could mention limit load analysis based on The Lower Bound Theorem. In this application there is a set of under......-determined equilibrium equation restrictions in an LP-problem. A significant reduction of computer time spent on solving the LP-problem is achieved if the equilib rium equations are reduced before going into the optimization procedure. Experience has shown that for some structures one must apply full pivoting to ensure...

  1. Inverse problems of geophysics

    International Nuclear Information System (INIS)

    Yanovskaya, T.B.

    2003-07-01

    This report gives an overview and the mathematical formulation of geophysical inverse problems. General principles of statistical estimation are explained. The maximum likelihood and least square fit methods, the Backus-Gilbert method and general approaches for solving inverse problems are discussed. General formulations of linearized inverse problems, singular value decomposition and properties of pseudo-inverse solutions are given

  2. Exact solution of some linear matrix equations using algebraic methods

    Science.gov (United States)

    Djaferis, T. E.; Mitter, S. K.

    1977-01-01

    A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

  3. Fast wavelet based sparse approximate inverse preconditioner

    Energy Technology Data Exchange (ETDEWEB)

    Wan, W.L. [Univ. of California, Los Angeles, CA (United States)

    1996-12-31

    Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.

  4. Matrix completion by deep matrix factorization.

    Science.gov (United States)

    Fan, Jicong; Cheng, Jieyu

    2018-02-01

    Conventional methods of matrix completion are linear methods that are not effective in handling data of nonlinear structures. Recently a few researchers attempted to incorporate nonlinear techniques into matrix completion but there still exists considerable limitations. In this paper, a novel method called deep matrix factorization (DMF) is proposed for nonlinear matrix completion. Different from conventional matrix completion methods that are based on linear latent variable models, DMF is on the basis of a nonlinear latent variable model. DMF is formulated as a deep-structure neural network, in which the inputs are the low-dimensional unknown latent variables and the outputs are the partially observed variables. In DMF, the inputs and the parameters of the multilayer neural network are simultaneously optimized to minimize the reconstruction errors for the observed entries. Then the missing entries can be readily recovered by propagating the latent variables to the output layer. DMF is compared with state-of-the-art methods of linear and nonlinear matrix completion in the tasks of toy matrix completion, image inpainting and collaborative filtering. The experimental results verify that DMF is able to provide higher matrix completion accuracy than existing methods do and DMF is applicable to large matrices. Copyright © 2017 Elsevier Ltd. All rights reserved.

  5. An Offline Formulation of MPC for LPV Systems Using Linear Matrix Inequalities

    Directory of Open Access Journals (Sweden)

    P. Bumroongsri

    2014-01-01

    Full Text Available An offline model predictive control (MPC algorithm for linear parameter varying (LPV systems is presented. The main contribution is to develop an offline MPC algorithm for LPV systems that can deal with both time-varying scheduling parameter and persistent disturbance. The norm-bounding technique is used to derive an offline MPC algorithm based on the parameter-dependent state feedback control law and the parameter-dependent Lyapunov functions. The online computational time is reduced by solving offline the linear matrix inequality (LMI optimization problems to find the sequences of explicit state feedback control laws. At each sampling instant, a parameter-dependent state feedback control law is computed by linear interpolation between the precomputed state feedback control laws. The algorithm is illustrated with two examples. The results show that robust stability can be ensured in the presence of both time-varying scheduling parameter and persistent disturbance.

  6. Calculation of U, Ra, Th and K contents in uranium ore by multiple linear regression method

    International Nuclear Information System (INIS)

    Lin Chao; Chen Yingqiang; Zhang Qingwen; Tan Fuwen; Peng Guanghui

    1991-01-01

    A multiple linear regression method was used to compute γ spectra of uranium ore samples and to calculate contents of U, Ra, Th, and K. In comparison with the inverse matrix method, its advantage is that no standard samples of pure U, Ra, Th and K are needed for obtaining response coefficients

  7. Nonconvergence of the plain Newton-min algorithm for linear complementarity problems with a P-matrix --- The full report.

    OpenAIRE

    Ben Gharbia , Ibtihel; Gilbert , Jean Charles

    2012-01-01

    The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) 0 ≤ x ⊥ (Mx+q) ≥ 0 can be viewed as a nonsmooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x,Mx+q)=0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm is known to converge in at most n iterations. We show in this paper that this result no longer holds when M is a P-matrix of order ≥ 3, since then the algorithm may...

  8. Exact results for quantum chaotic systems and one-dimensional fermions from matrix models

    International Nuclear Information System (INIS)

    Simons, B.D.; Lee, P.A.; Altshuler, B.L.

    1993-01-01

    We demonstrate a striking connection between the universal parametric correlations of the spectra of quantum chaotic systems and a class of integrable quantum hamiltonians. We begin by deriving a non-perturbative expression for the universal m-point correlation function of the spectra of random matrix ensembles in terms of a non-linear supermatrix σ-model. These results are shown to coincide with those from previous studies of weakly disordered metallic systems. We then introduce a continuous matrix model which describes the quantum mechanics of the Sutherland hamiltonian describing particles interacting through an inverse-square pairwise potential. We demonstrate that a field theoretic approach can be employed to determine exact analytical expressions for correlations of the quantum hamiltonian. The results, which are expressed in terms of a non-linear σ-model, are shown to coincide with those for analogous correlation functions of random matrix ensembles after an appropriate change of variables. We also discuss possible generalizations of the matrix model to higher dimensions. These results reveal a common mathematical structure which underlies branches of theoretical physics ranging from continuous matrix models to strongly interacting quantum hamiltonians, and universalities in the spectra of quantum chaotic systems. (orig.)

  9. Near constant-time optimal piecewise LDR to HDR inverse tone mapping

    Science.gov (United States)

    Chen, Qian; Su, Guan-Ming; Yin, Peng

    2015-02-01

    In a backward compatible HDR image/video compression, it is a general approach to reconstruct HDR from compressed LDR as a prediction to original HDR, which is referred to as inverse tone mapping. Experimental results show that 2- piecewise 2nd order polynomial has the best mapping accuracy than 1 piece high order or 2-piecewise linear, but it is also the most time-consuming method because to find the optimal pivot point to split LDR range to 2 pieces requires exhaustive search. In this paper, we propose a fast algorithm that completes optimal 2-piecewise 2nd order polynomial inverse tone mapping in near constant time without quality degradation. We observe that in least square solution, each entry in the intermediate matrix can be written as the sum of some basic terms, which can be pre-calculated into look-up tables. Since solving the matrix becomes looking up values in tables, computation time barely differs regardless of the number of points searched. Hence, we can carry out the most thorough pivot point search to find the optimal pivot that minimizes MSE in near constant time. Experiment shows that our proposed method achieves the same PSNR performance while saving 60 times computation time compared to the traditional exhaustive search in 2-piecewise 2nd order polynomial inverse tone mapping with continuous constraint.

  10. Hyperspectral and multispectral data fusion based on linear-quadratic nonnegative matrix factorization

    Science.gov (United States)

    Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

    2017-04-01

    This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.

  11. MARE2DEM: a 2-D inversion code for controlled-source electromagnetic and magnetotelluric data

    Science.gov (United States)

    Key, Kerry

    2016-10-01

    This work presents MARE2DEM, a freely available code for 2-D anisotropic inversion of magnetotelluric (MT) data and frequency-domain controlled-source electromagnetic (CSEM) data from onshore and offshore surveys. MARE2DEM parametrizes the inverse model using a grid of arbitrarily shaped polygons, where unstructured triangular or quadrilateral grids are typically used due to their ease of construction. Unstructured grids provide significantly more geometric flexibility and parameter efficiency than the structured rectangular grids commonly used by most other inversion codes. Transmitter and receiver components located on topographic slopes can be tilted parallel to the boundary so that the simulated electromagnetic fields accurately reproduce the real survey geometry. The forward solution is implemented with a goal-oriented adaptive finite-element method that automatically generates and refines unstructured triangular element grids that conform to the inversion parameter grid, ensuring accurate responses as the model conductivity changes. This dual-grid approach is significantly more efficient than the conventional use of a single grid for both the forward and inverse meshes since the more detailed finite-element meshes required for accurate responses do not increase the memory requirements of the inverse problem. Forward solutions are computed in parallel with a highly efficient scaling by partitioning the data into smaller independent modeling tasks consisting of subsets of the input frequencies, transmitters and receivers. Non-linear inversion is carried out with a new Occam inversion approach that requires fewer forward calls. Dense matrix operations are optimized for memory and parallel scalability using the ScaLAPACK parallel library. Free parameters can be bounded using a new non-linear transformation that leaves the transformed parameters nearly the same as the original parameters within the bounds, thereby reducing non-linear smoothing effects. Data

  12. Two-dimensional inversion of MT (magnetotelluric) data; MT ho no nijigen inversion kaiseki

    Energy Technology Data Exchange (ETDEWEB)

    Ito, S; Okuno, M; Ushijima, K; Mizunaga, H [Kyushu University, Fukuoka (Japan). Faculty of Engineering

    1997-05-27

    A program has been developed to conduct inversion analysis of two-dimensional model using MT data, accurately. For the developed program, finite element method (FEM) was applied to the section of sequential analysis. A method in which Jacobian matrix is calculated only one first time and is inversely analyzed by fixing this during the repetition, and a method in which Jacobian matrix is corrected at each repetition of inversion analysis, were compared mutually. As a result of the numerical simulation, it was revealed that the Jacobian correction method provided more stable convergence for the simple 2D model, and that the calculation time is almost same as that of the Jacobian fixation method. To confirm the applicability of this program to actually measured data, results obtained from this program were compared with those from the Schlumberger method analysis by using MT data obtained in the Hatchobara geothermal area. Consequently, it was demonstrated that the both are well coincided mutually. 17 refs., 7 figs.

  13. Inverse and Ill-posed Problems Theory and Applications

    CERN Document Server

    Kabanikhin, S I

    2011-01-01

    The text demonstrates the methods for proving the existence (if et all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background material for linear ill-posed problems and for coefficient inverse problems for hyperbolic, parabolic, and elliptic equations. A lot of examples for inverse problems from physics, geophysics, biology, medicine, and other areas of application of mathematics are included.

  14. Imaging the complex geometry of a magma reservoir using FEM-based linear inverse modeling of InSAR data: application to Rabaul Caldera, Papua New Guinea

    Science.gov (United States)

    Ronchin, Erika; Masterlark, Timothy; Dawson, John; Saunders, Steve; Martì Molist, Joan

    2017-06-01

    We test an innovative inversion scheme using Green's functions from an array of pressure sources embedded in finite-element method (FEM) models to image, without assuming an a-priori geometry, the composite and complex shape of a volcano deformation source. We invert interferometric synthetic aperture radar (InSAR) data to estimate the pressurization and shape of the magma reservoir of Rabaul caldera, Papua New Guinea. The results image the extended shallow magmatic system responsible for a broad and long-term subsidence of the caldera between 2007 February and 2010 December. Elastic FEM solutions are integrated into the regularized linear inversion of InSAR data of volcano surface displacements in order to obtain a 3-D image of the source of deformation. The Green's function matrix is constructed from a library of forward line-of-sight displacement solutions for a grid of cubic elementary deformation sources. Each source is sequentially generated by removing the corresponding cubic elements from a common meshed domain and simulating the injection of a fluid mass flux into the cavity, which results in a pressurization and volumetric change of the fluid-filled cavity. The use of a single mesh for the generation of all FEM models avoids the computationally expensive process of non-linear inversion and remeshing a variable geometry domain. Without assuming an a-priori source geometry other than the configuration of the 3-D grid that generates the library of Green's functions, the geodetic data dictate the geometry of the magma reservoir as a 3-D distribution of pressure (or flux of magma) within the source array. The inversion of InSAR data of Rabaul caldera shows a distribution of interconnected sources forming an amorphous, shallow magmatic system elongated under two opposite sides of the caldera. The marginal areas at the sides of the imaged magmatic system are the possible feeding reservoirs of the ongoing Tavurvur volcano eruption of andesitic products on the

  15. Linear zonal atmospheric prediction for adaptive optics

    Science.gov (United States)

    McGuire, Patrick C.; Rhoadarmer, Troy A.; Coy, Hanna A.; Angel, J. Roger P.; Lloyd-Hart, Michael

    2000-07-01

    We compare linear zonal predictors of atmospheric turbulence for adaptive optics. Zonal prediction has the possible advantage of being able to interpret and utilize wind-velocity information from the wavefront sensor better than modal prediction. For simulated open-loop atmospheric data for a 2- meter 16-subaperture AO telescope with 5 millisecond prediction and a lookback of 4 slope-vectors, we find that Widrow-Hoff Delta-Rule training of linear nets and Back- Propagation training of non-linear multilayer neural networks is quite slow, getting stuck on plateaus or in local minima. Recursive Least Squares training of linear predictors is two orders of magnitude faster and it also converges to the solution with global minimum error. We have successfully implemented Amari's Adaptive Natural Gradient Learning (ANGL) technique for a linear zonal predictor, which premultiplies the Delta-Rule gradients with a matrix that orthogonalizes the parameter space and speeds up the training by two orders of magnitude, like the Recursive Least Squares predictor. This shows that the simple Widrow-Hoff Delta-Rule's slow convergence is not a fluke. In the case of bright guidestars, the ANGL, RLS, and standard matrix-inversion least-squares (MILS) algorithms all converge to the same global minimum linear total phase error (approximately 0.18 rad2), which is only approximately 5% higher than the spatial phase error (approximately 0.17 rad2), and is approximately 33% lower than the total 'naive' phase error without prediction (approximately 0.27 rad2). ANGL can, in principle, also be extended to make non-linear neural network training feasible for these large networks, with the potential to lower the predictor error below the linear predictor error. We will soon scale our linear work to the approximately 108-subaperture MMT AO system, both with simulations and real wavefront sensor data from prime focus.

  16. Combinatorial matrix theory

    CERN Document Server

    Mitjana, Margarida

    2018-01-01

    This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.

  17. Unified approach to numerical transfer matrix methods for disordered systems: applications to mixed crystals and to elasticity percolation

    International Nuclear Information System (INIS)

    Lemieux, M.A.; Breton, P.; Tremblay, A.M.S.

    1985-01-01

    It is shown that the Negative Eigenvalue Theorem and transfer matrix methods may be considered within a unified framework and generalized to compute projected densities of states or, more generally, any linear combination of matrix elements of the inverse of large symmetric random matrices. As examples of applications, extensive simulations for one- and two-mode behaviour in the Raman spectrum of one-dimensional mixed crystals and a finite-size analysis of critical exponents for the central force percolation universality class are presented

  18. Matrix inversion tomosynthesis improvements in longitudinal x-ray slice imaging

    International Nuclear Information System (INIS)

    Dobbines, J.T. III.

    1990-01-01

    This patent describes a tomosynthesis apparatus. It comprises: an x-ray tomography machine for producing a plurality of x-ray projection images of a subject including an x-ray source, and detection means; and processing means, connected to receive the plurality of projection images, for: shifting and reconstructing the projection x-ray images to obtain a tomosynthesis matrix of images T; acquiring a blurring matrix F having components which represent out-of-focus and in-focus components of the matrix T; obtaining a matrix P representing only in-focus components of the imaged subject by solving a matrix equation including the matrix T and the matrix F; correcting the matrix P for low spatial frequency components; and displaying images indicative of contents of the matrix P

  19. Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing

    Science.gov (United States)

    Chu, W. P.

    1985-01-01

    The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.

  20. The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.

    Science.gov (United States)

    Pang, Haotian; Liu, Han; Vanderbei, Robert

    2014-02-01

    We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L 1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

  1. Obtaining the crystal potential by inversion from electron scattering intensities

    International Nuclear Information System (INIS)

    Allen, L.T.; Josefsson, T.W.; Leeb, H.

    1998-01-01

    A method to obtain the crystal potential from the intensities of the diffracted beams in high energy electron diffraction is proposed. It is based on a series of measurements for specific well determined orientations of the incident beam which determine the moduli of all elements of the scattering matrix. Using unitarity and the specific form of the scattering matrix (including symmetries) an overdetermined set of non-linear equations is obtained from these data. Solution of these equations yields the required phase information and allows the determination of a (projected) crystal potential by inversion which is unique up to an arbitrary shift of the origin. The reconstruction of potentials from intensities is illustrated for two realistic examples, a [111] systematic row case in ZnS and a [110] zone axis orientation in GaAs (both noncentrosymmetric crystals)

  2. Individual and Collective Analyses of the Genesis of Student Reasoning Regarding the Invertible Matrix Theorem in Linear Algebra

    Science.gov (United States)

    Wawro, Megan Jean

    2011-01-01

    In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

  3. Linear algebra

    CERN Document Server

    Liesen, Jörg

    2015-01-01

    This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...

  4. Inverse Kinematics of a Serial Robot

    Directory of Open Access Journals (Sweden)

    Amici Cinzia

    2016-01-01

    Full Text Available This work describes a technique to treat the inverse kinematics of a serial manipulator. The inverse kinematics is obtained through the numerical inversion of the Jacobian matrix, that represents the equation of motion of the manipulator. The inversion is affected by numerical errors and, in different conditions, due to the numerical nature of the solver, it does not converge to a reasonable solution. Thus a soft computing approach is adopted to mix different traditional methods to obtain an increment of algorithmic convergence.

  5. A new approach to the inverse kinematics of a multi-joint robot manipulator using a minimization method

    International Nuclear Information System (INIS)

    Sasaki, Shinobu

    1987-01-01

    This paper proposes a new approach to solve the inverse kinematics of a type of sixlink manipulator. Directing our attention to features of joint structures of the manipulator, the original problem is first formulated by a system of equations with four variables and solved by means of a minimization technique. The remaining two variables are determined from constrained conditions involved. This is the basic idea in the present approach. The results of computer simulation of the present algorithm showed that the accuracies of solutions and convergence speed are much higher and quite satisfactory for practical purposes, as compared with the linearization-iteration method based on the conventional inverse Jacobian matrix. (author)

  6. Recurrent Neural Network for Computing the Drazin Inverse.

    Science.gov (United States)

    Stanimirović, Predrag S; Zivković, Ivan S; Wei, Yimin

    2015-11-01

    This paper presents a recurrent neural network (RNN) for computing the Drazin inverse of a real matrix in real time. This recurrent neural network (RNN) is composed of n independent parts (subnetworks), where n is the order of the input matrix. These subnetworks can operate concurrently, so parallel and distributed processing can be achieved. In this way, the computational advantages over the existing sequential algorithms can be attained in real-time applications. The RNN defined in this paper is convenient for an implementation in an electronic circuit. The number of neurons in the neural network is the same as the number of elements in the output matrix, which represents the Drazin inverse. The difference between the proposed RNN and the existing ones for the Drazin inverse computation lies in their network architecture and dynamics. The conditions that ensure the stability of the defined RNN as well as its convergence toward the Drazin inverse are considered. In addition, illustrative examples and examples of application to the practical engineering problems are discussed to show the efficacy of the proposed neural network.

  7. Total-variation based velocity inversion with Bregmanized operator splitting algorithm

    Science.gov (United States)

    Zand, Toktam; Gholami, Ali

    2018-04-01

    Many problems in applied geophysics can be formulated as a linear inverse problem. The associated problems, however, are large-scale and ill-conditioned. Therefore, regularization techniques are needed to be employed for solving them and generating a stable and acceptable solution. We consider numerical methods for solving such problems in this paper. In order to tackle the ill-conditioning of the problem we use blockiness as a prior information of the subsurface parameters and formulate the problem as a constrained total variation (TV) regularization. The Bregmanized operator splitting (BOS) algorithm as a combination of the Bregman iteration and the proximal forward backward operator splitting method is developed to solve the arranged problem. Two main advantages of this new algorithm are that no matrix inversion is required and that a discrepancy stopping criterion is used to stop the iterations, which allow efficient solution of large-scale problems. The high performance of the proposed TV regularization method is demonstrated using two different experiments: 1) velocity inversion from (synthetic) seismic data which is based on Born approximation, 2) computing interval velocities from RMS velocities via Dix formula. Numerical examples are presented to verify the feasibility of the proposed method for high-resolution velocity inversion.

  8. A finite-difference contrast source inversion method

    International Nuclear Information System (INIS)

    Abubakar, A; Hu, W; Habashy, T M; Van den Berg, P M

    2008-01-01

    We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. The ability to use an inhomogeneous background medium has made this algorithm very suitable to be used in through-wall imaging and time-lapse inversion applications. Similar to the IE-CSI algorithm the unknown contrast sources and contrast function are updated alternately to reconstruct the unknown objects without requiring the solution of the full forward problem at each iteration step in the optimization process. The FD solver is formulated in the frequency domain and it is equipped with a perfectly matched layer (PML) absorbing boundary condition. The FD operator used in the FD-CSI method is only dependent on the background medium and the frequency of operation, thus it does not change throughout the inversion process. Therefore, at least for the two-dimensional (2D) configurations, where the size of the stiffness matrix is manageable, the FD stiffness matrix can be inverted using a non-iterative inversion matrix approach such as a Gauss elimination method for the sparse matrix. In this case, an LU decomposition needs to be done only once and can then be reused for multiple source positions and in successive iterations of the inversion. Numerical experiments show that this FD-CSI algorithm has an excellent performance for inverting inhomogeneous objects embedded in an inhomogeneous background medium

  9. Bayesian inversion of microtremor array dispersion data in southwestern British Columbia

    Science.gov (United States)

    Molnar, Sheri; Dosso, Stan E.; Cassidy, John F.

    2010-11-01

    This paper applies Bayesian inversion, with evaluation of data errors and model parametrization, to produce the most-probable shear-wave velocity profile together with quantitative uncertainty estimates from microtremor array dispersion data. Generally, the most important property for characterizing earthquake site response is the shear-wave velocity (VS) profile. The microtremor array method determines phase velocity dispersion of Rayleigh surface waves from multi-instrument recordings of urban noise. Inversion of dispersion curves for VS structure is a non-unique and non-linear problem such that meaningful evaluation of confidence intervals is required. Quantitative uncertainty estimation requires not only a non-linear inversion approach that samples models proportional to their probability, but also rigorous estimation of the data error statistics and an appropriate model parametrization. This paper applies a Bayesian formulation that represents the solution of the inverse problem in terms of the posterior probability density (PPD) of the geophysical model parameters. Markov-chain Monte Carlo methods are used with an efficient implementation of Metropolis-Hastings sampling to provide an unbiased sample from the PPD to compute parameter uncertainties and inter-relationships. Nonparametric estimation of a data error covariance matrix from residual analysis is applied with rigorous a posteriori statistical tests to validate the covariance estimate and the assumption of a Gaussian error distribution. The most appropriate model parametrization is determined using the Bayesian information criterion, which provides the simplest model consistent with the resolving power of the data. Parametrizations considered vary in the number of layers, and include layers with uniform, linear and power-law gradients. Parameter uncertainties are found to be underestimated when data error correlations are neglected and when compressional-wave velocity and/or density (nuisance

  10. Gravity inversion code

    International Nuclear Information System (INIS)

    Burkhard, N.R.

    1979-01-01

    The gravity inversion code applies stabilized linear inverse theory to determine the topography of a subsurface density anomaly from Bouguer gravity data. The gravity inversion program consists of four source codes: SEARCH, TREND, INVERT, and AVERAGE. TREND and INVERT are used iteratively to converge on a solution. SEARCH forms the input gravity data files for Nevada Test Site data. AVERAGE performs a covariance analysis on the solution. This document describes the necessary input files and the proper operation of the code. 2 figures, 2 tables

  11. Arikan and Alamouti matrices based on fast block-wise inverse Jacket transform

    Science.gov (United States)

    Lee, Moon Ho; Khan, Md Hashem Ali; Kim, Kyeong Jin

    2013-12-01

    Recently, Lee and Hou (IEEE Signal Process Lett 13: 461-464, 2006) proposed one-dimensional and two-dimensional fast algorithms for block-wise inverse Jacket transforms (BIJTs). Their BIJTs are not real inverse Jacket transforms from mathematical point of view because their inverses do not satisfy the usual condition, i.e., the multiplication of a matrix with its inverse matrix is not equal to the identity matrix. Therefore, we mathematically propose a fast block-wise inverse Jacket transform of orders N = 2 k , 3 k , 5 k , and 6 k , where k is a positive integer. Based on the Kronecker product of the successive lower order Jacket matrices and the basis matrix, the fast algorithms for realizing these transforms are obtained. Due to the simple inverse and fast algorithms of Arikan polar binary and Alamouti multiple-input multiple-output (MIMO) non-binary matrices, which are obtained from BIJTs, they can be applied in areas such as 3GPP physical layer for ultra mobile broadband permutation matrices design, first-order q-ary Reed-Muller code design, diagonal channel design, diagonal subchannel decompose for interference alignment, and 4G MIMO long-term evolution Alamouti precoding design.

  12. On the q-exponential of matrix q-Lie algebras

    Directory of Open Access Journals (Sweden)

    Ernst Thomas

    2017-01-01

    Full Text Available In this paper, we define several new concepts in the borderline between linear algebra, Lie groups and q-calculus.We first introduce the ring epimorphism r, the set of all inversions of the basis q, and then the important q-determinant and corresponding q-scalar products from an earlier paper. Then we discuss matrix q-Lie algebras with a modified q-addition, and compute the matrix q-exponential to form the corresponding n × n matrix, a so-called q-Lie group, or manifold, usually with q-determinant 1. The corresponding matrix multiplication is twisted under τ, which makes it possible to draw diagrams similar to Lie group theory for the q-exponential, or the so-called q-morphism. There is no definition of letter multiplication in a general alphabet, but in this article we introduce new q-number systems, the biring of q-integers, and the extended q-rational numbers. Furthermore, we provide examples of matrices in suq(4, and its corresponding q-Lie group. We conclude with an example of system of equations with Ward number coeficients.

  13. Large-scale inverse model analyses employing fast randomized data reduction

    Science.gov (United States)

    Lin, Youzuo; Le, Ellen B.; O'Malley, Daniel; Vesselinov, Velimir V.; Bui-Thanh, Tan

    2017-08-01

    When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally efficient technique for solving inverse problems with a large number of observations (e.g., on the order of 107 or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called "sketching" matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Most importantly, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Therefore, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

  14. Parallelism in matrix computations

    CERN Document Server

    Gallopoulos, Efstratios; Sameh, Ahmed H

    2016-01-01

    This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of pa...

  15. A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate

    Directory of Open Access Journals (Sweden)

    Min Sun

    2014-01-01

    Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.

  16. Seismic inverse scattering in the downward continuation approach

    NARCIS (Netherlands)

    Stolk, C.C.; de Hoop, M.V.

    Seismic data are commonly modeled by a linearization around a smooth background medium in combination with a high frequency approximation. The perturbation of the medium coefficient is assumed to contain the discontinuities. This leads to two inverse problems, first the linearized inverse problem

  17. Analytical techniques for instrument design - matrix methods

    International Nuclear Information System (INIS)

    Robinson, R.A.

    1997-01-01

    We take the traditional Cooper-Nathans approach, as has been applied for many years for steady-state triple-axis spectrometers, and consider its generalisation to other inelastic scattering spectrometers. This involves a number of simple manipulations of exponentials of quadratic forms. In particular, we discuss a toolbox of matrix manipulations that can be performed on the 6- dimensional Cooper-Nathans matrix: diagonalisation (Moller-Nielsen method), coordinate changes e.g. from (Δk I ,Δk F to ΔE, ΔQ ampersand 2 dummy variables), integration of one or more variables (e.g. over such dummy variables), integration subject to linear constraints (e.g. Bragg's Law for analysers), inversion to give the variance-covariance matrix, and so on. We show how these tools can be combined to solve a number of important problems, within the narrow-band limit and the gaussian approximation. We will argue that a generalised program that can handle multiple different spectrometers could (and should) be written in parallel to the Monte-Carlo packages that are becoming available. We will also discuss the complementarity between detailed Monte-Carlo calculations and the approach presented here. In particular, Monte-Carlo methods traditionally simulate the real experiment as performed in practice, given a model scattering law, while the Cooper-Nathans method asks the inverse question: given that a neutron turns up in a particular spectrometer configuration (e.g. angle and time of flight), what is the probability distribution of possible scattering events at the sample? The Monte-Carlo approach could be applied in the same spirit to this question

  18. Matrix kernels for MEG and EEG source localization and imaging

    International Nuclear Information System (INIS)

    Mosher, J.C.; Lewis, P.S.; Leahy, R.M.

    1994-01-01

    The most widely used model for electroencephalography (EEG) and magnetoencephalography (MEG) assumes a quasi-static approximation of Maxwell's equations and a piecewise homogeneous conductor model. Both models contain an incremental field element that linearly relates an incremental source element (current dipole) to the field or voltage at a distant point. The explicit form of the field element is dependent on the head modeling assumptions and sensor configuration. Proper characterization of this incremental element is crucial to the inverse problem. The field element can be partitioned into the product of a vector dependent on sensor characteristics and a matrix kernel dependent only on head modeling assumptions. We present here the matrix kernels for the general boundary element model (BEM) and for MEG spherical models. We show how these kernels are easily interchanged in a linear algebraic framework that includes sensor specifics such as orientation and gradiometer configuration. We then describe how this kernel is easily applied to ''gain'' or ''transfer'' matrices used in multiple dipole and source imaging models

  19. Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

    Science.gov (United States)

    Rodriguez, G.; Scheid, R. E., Jr.

    1987-01-01

    This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

  20. Surface waves tomography and non-linear inversion in the southeast Carpathians

    International Nuclear Information System (INIS)

    Raykova, R.B.; Panza, G.F.

    2005-11-01

    A set of shear-wave velocity models of the lithosphere-asthenosphere system in the southeast Carpathians is determined by the non-linear inversion of surface wave group velocity data, obtained from a tomographic analysis. The local dispersion curves are assembled for the period range 7 s - 150 s, combining regional group velocity measurements and published global Rayleigh wave dispersion data. The lithosphere-asthenosphere velocity structure is reliably reconstructed to depths of about 250 km. The thickness of the lithosphere in the region varies from about 120 km to 250 km and the depth of the asthenosphere between 150 km and 250 km. Mantle seismicity concentrates where the high velocity lid is detected just below the Moho. The obtained results are in agreement with recent seismic refraction, receiver function, and travel time P-wave tomography investigations in the region. The similarity among the results obtained from different kinds of structural investigations (including the present work) highlights some new features of the lithosphere-asthenosphere system in southeast Carpathians, as the relatively thin crust under Transylvania basin and Vrancea zone. (author)

  1. Limits to Nonlinear Inversion

    DEFF Research Database (Denmark)

    Mosegaard, Klaus

    2012-01-01

    For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...... pure meta-heuristics. We study problem-adapted inversion algorithms that exploit the knowledge of the smoothness of the misfit function of the problem. Optimal sampling strategies exist for such problems, but many of these problems remain hard. © 2012 Springer-Verlag....

  2. Solution of the nonlinear inverse scattering problem by T-matrix completion. I. Theory.

    Science.gov (United States)

    Levinson, Howard W; Markel, Vadim A

    2016-10-01

    We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V. An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T-matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016)10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.

  3. Excitation energies with linear response density matrix functional theory along the dissociation coordinate of an electron-pair bond in N-electron systems

    International Nuclear Information System (INIS)

    Meer, R. van; Gritsenko, O. V.; Baerends, E. J.

    2014-01-01

    Time dependent density matrix functional theory in its adiabatic linear response formulation delivers exact excitation energies ω α and oscillator strengths f α for two-electron systems if extended to the so-called phase including natural orbital (PINO) theory. The Löwdin-Shull expression for the energy of two-electron systems in terms of the natural orbitals and their phases affords in this case an exact phase-including natural orbital functional (PILS), which is non-primitive (contains other than just J and K integrals). In this paper, the extension of the PILS functional to N-electron systems is investigated. With the example of an elementary primitive NO functional (BBC1) it is shown that current density matrix functional theory ground state functionals, which were designed to produce decent approximations to the total energy, fail to deliver a qualitatively correct structure of the (inverse) response function, due to essential deficiencies in the reconstruction of the two-body reduced density matrix (2RDM). We now deduce essential features of an N-electron functional from a wavefunction Ansatz: The extension of the two-electron Löwdin-Shull wavefunction to the N-electron case informs about the phase information. In this paper, applications of this extended Löwdin-Shull (ELS) functional are considered for the simplest case, ELS(1): one (dissociating) two-electron bond in the field of occupied (including core) orbitals. ELS(1) produces high quality ω α (R) curves along the bond dissociation coordinate R for the molecules LiH, Li 2 , and BH with the two outer valence electrons correlated. All of these results indicate that response properties are much more sensitive to deficiencies in the reconstruction of the 2RDM than the ground state energy, since derivatives of the functional with respect to both the NOs and the occupation numbers need to be accurate

  4. Truncated Gauss-Newton Implementation for Multi-Parameter Full Waveform Inversion

    Science.gov (United States)

    Liu, Y.; Yang, J.; Dong, L.; Wang, Y.

    2014-12-01

    Full waveform inversion (FWI) is a numerical optimization method which aims at minimizing the difference between the synthetic and recorded seismic data to obtain high resolution subsurface images. A practical implementation for FWI is the adjoint-state method (AD), in which the data residuals at receiver locations are simultaneously back-propagated to form the gradient. Scattering-integral method (SI) is an alternative way which is based on the explicit building of the sensitivity kernel (Fréchet derivative matrix). Although it is more memory-consuming, SI is more efficient than AD when the number of the sources is larger than the number of the receivers. To improve the convergence of FWI, the information carried out by the inverse Hessian operator is crucial. Taking account accurately of the effect of this operator in FWI can correct illumination deficits, reserve the amplitude of the subsurface parameters, and remove artifacts generated by multiple reflections. In multi-parameter FWI, the off-diagonal blocks of the Hessian operator reflect the coupling between different parameter classes. Therefore, incorporating its inverse could help to mitigate the trade-off effects. In this study, we focus on the truncated Gauss-Newton implementation for multi-parameter FWI. The model update is computed through a matrix-free conjugate gradient solution of the Newton linear system. Both the gradient and the Hessian-vector product are calculated using the SI approach instead of the first- and second-order AD. However, the gradient expressed by kernel-vector product is calculated through the accumulation of the decomposed vector-scalar products. Thus, it's not necessary to store the huge sensitivity matrix beforehand. We call this method the matrix decomposition approach (MD). And the Hessian-vector product is replaced by two kernel-vector products which are then calculated by the above MD. By this way, we don't need to solve two additional wave propagation problems as in the

  5. Stress estimation in reservoirs using an integrated inverse method

    Science.gov (United States)

    Mazuyer, Antoine; Cupillard, Paul; Giot, Richard; Conin, Marianne; Leroy, Yves; Thore, Pierre

    2018-05-01

    Estimating the stress in reservoirs and their surroundings prior to the production is a key issue for reservoir management planning. In this study, we propose an integrated inverse method to estimate such initial stress state. The 3D stress state is constructed with the displacement-based finite element method assuming linear isotropic elasticity and small perturbations in the current geometry of the geological structures. The Neumann boundary conditions are defined as piecewise linear functions of depth. The discontinuous functions are determined with the CMA-ES (Covariance Matrix Adaptation Evolution Strategy) optimization algorithm to fit wellbore stress data deduced from leak-off tests and breakouts. The disregard of the geological history and the simplified rheological assumptions mean that only the stress field, statically admissible and matching the wellbore data should be exploited. The spatial domain of validity of this statement is assessed by comparing the stress estimations for a synthetic folded structure of finite amplitude with a history constructed assuming a viscous response.

  6. Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions

    Science.gov (United States)

    Prinari, Barbara; Demontis, Francesco; Li, Sitai; Horikis, Theodoros P.

    2018-04-01

    The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrödinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.

  7. The Inverse System Method Applied to the Derivation of Power System Non—linear Control Laws

    Institute of Scientific and Technical Information of China (English)

    DonghaiLI; XuezhiJIANG; 等

    1997-01-01

    The differential geometric method has been applied to a series of power system non-linear control problems effectively.However a set of differential equations must be solved for obtaining the required diffeomorphic transformation.Therefore the derivation of control laws is very complicated.In fact because of the specificity of power system models the required diffeomorphic transformation may be obtained directly,so it is unnecessary to solve a set of differential equations.In addition inverse system method is equivalent to differential geometric method in reality and not limited to affine nonlinear systems,Its physical meaning is able to be viewed directly and its deduction needs only algebraic operation and derivation,so control laws can be obtained easily and the application to engineering is very convenient.Authors of this paper take steam valving control of power system as a typical case to be studied.It is demonstrated that the control law deduced by inverse system method is just the same as one by differential geometric method.The conclusion will simplify the control law derivations of steam valving,excitation,converter and static var compensator by differential geometric method and may be suited to similar control problems in other areas.

  8. Support minimized inversion of acoustic and elastic wave scattering

    International Nuclear Information System (INIS)

    Safaeinili, A.

    1994-01-01

    This report discusses the following topics on support minimized inversion of acoustic and elastic wave scattering: Minimum support inversion; forward modelling of elastodynamic wave scattering; minimum support linearized acoustic inversion; support minimized nonlinear acoustic inversion without absolute phase; and support minimized nonlinear elastic inversion

  9. Reduced Order Extended Luenberger Observer Based Sensorless Vector Control Fed by Matrix Converter with Non-linearity Modeling

    DEFF Research Database (Denmark)

    Lee, Kyo-Beum; Blaabjerg, Frede

    2004-01-01

    This paper presents a new sensorless vector control system for high performance induction motor drives fed by a matrix converter with non-linearity compensation. The nonlinear voltage distortion that is caused by commutation delay and on-state voltage drop in switching device is corrected by a new...

  10. vSmartMOM: A vector matrix operator method-based radiative transfer model linearized with respect to aerosol properties

    International Nuclear Information System (INIS)

    Sanghavi, Suniti; Davis, Anthony B.; Eldering, Annmarie

    2014-01-01

    In this paper, we build up on the scalar model smartMOM to arrive at a formalism for linearized vector radiative transfer based on the matrix operator method (vSmartMOM). Improvements have been made with respect to smartMOM in that a novel method of computing intensities for the exact viewing geometry (direct raytracing) without interpolation between quadrature points has been implemented. Also, the truncation method employed for dealing with highly peaked phase functions has been changed to a vector adaptation of Wiscombe's delta-m method. These changes enable speedier and more accurate radiative transfer computations by eliminating the need for a large number of quadrature points and coefficients for generalized spherical functions. We verify our forward model against the benchmarking results of Kokhanovsky et al. (2010) [22]. All non-zero Stokes vector elements are found to show agreement up to mostly the seventh significant digit for the Rayleigh atmosphere. Intensity computations for aerosol and cloud show an agreement of well below 0.03% and 0.05% at all viewing angles except around the solar zenith angle (60°), where most radiative models demonstrate larger variances due to the strongly forward-peaked phase function. We have for the first time linearized vector radiative transfer based on the matrix operator method with respect to aerosol optical and microphysical parameters. We demonstrate this linearization by computing Jacobian matrices for all Stokes vector elements for a multi-angular and multispectral measurement setup. We use these Jacobians to compare the aerosol information content of measurements using only the total intensity component against those using the idealized measurements of full Stokes vector [I,Q,U,V] as well as the more practical use of only [I,Q,U]. As expected, we find for the considered example that the accuracy of the retrieved parameters improves when the full Stokes vector is used. The information content for the full Stokes

  11. On the Duality of Forward and Inverse Light Transport.

    Science.gov (United States)

    Chandraker, Manmohan; Bai, Jiamin; Ng, Tian-Tsong; Ramamoorthi, Ravi

    2011-10-01

    Inverse light transport seeks to undo global illumination effects, such as interreflections, that pervade images of most scenes. This paper presents the theoretical and computational foundations for inverse light transport as a dual of forward rendering. Mathematically, this duality is established through the existence of underlying Neumann series expansions. Physically, it can be shown that each term of our inverse series cancels an interreflection bounce, just as the forward series adds them. While the convergence properties of the forward series are well known, we show that the oscillatory convergence of the inverse series leads to more interesting conditions on material reflectance. Conceptually, the inverse problem requires the inversion of a large light transport matrix, which is impractical for realistic resolutions using standard techniques. A natural consequence of our theoretical framework is a suite of fast computational algorithms for light transport inversion--analogous to finite element radiosity, Monte Carlo and wavelet-based methods in forward rendering--that rely at most on matrix-vector multiplications. We demonstrate two practical applications, namely, separation of individual bounces of the light transport and fast projector radiometric compensation, to display images free of global illumination artifacts in real-world environments.

  12. Simultaneous retrieval of aerosols and ocean properties: A classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model

    International Nuclear Information System (INIS)

    Spurr, Robert; Stamnes, Knut; Eide, Hans; Li Wei; Zhang Kexin; Stamnes, Jakob

    2007-01-01

    In this paper and the sequel, we investigate the application of classic inverse methods based on iterative least-squares cost-function minimization to the simultaneous retrieval of aerosol and ocean properties from visible and near infrared spectral radiance measurements such as those from the SeaWiFS and MODIS instruments. Radiance measurements at the satellite are simulated directly using an accurate coupled atmosphere-ocean-discrete-ordinate radiative transfer (CAO-DISORT) code as the main component of the forward model. For this kind of cost-function inverse problem, we require the forward model to generate weighting functions (radiance partial derivatives) with respect to the aerosol and marine properties to be retrieved, and to other model parameters which are sources of error in the retrievals. In this paper, we report on the linearization of the CAO-DISORT model. This linearization provides a complete analytic differentiation of the coupled-media radiative transfer theory, and it allows the model to generate analytic weighting functions for any atmospheric or marine parameter. For high solar zenith angles, we give an implementation of the pseudo-spherical (P-S) approach to solar beam attenuation in the atmosphere in the linearized model. We summarize a number of performance enhancements such as the use of an exact single-scattering calculation to improve accuracy. We derive inherent optical property inputs for the linearized CAO-DISORT code for a simple 2-parameter bio-optical model for the marine environment coupled to a 2-parameter bimodal atmospheric aerosol medium

  13. Novel type of linear mitochondrial genomes with dual flip-flop inversion system in apicomplexan parasites, Babesia microti and Babesia rodhaini

    Directory of Open Access Journals (Sweden)

    Hikosaka Kenji

    2012-11-01

    Full Text Available Abstract Background Mitochondrial (mt genomes vary considerably in size, structure and gene content. The mt genomes of the phylum Apicomplexa, which includes important human pathogens such as the malaria parasite Plasmodium, also show marked diversity of structure. Plasmodium has a concatenated linear mt genome of the smallest size (6-kb; Babesia and Theileria have a linear monomeric mt genome (6.5-kb to 8.2-kb with terminal inverted repeats; Eimeria, which is distantly related to Plasmodium and Babesia/Theileria, possesses a mt genome (6.2-kb with a concatemeric form similar to that of Plasmodium; Cryptosporidium, the earliest branching lineage within the phylum Apicomplexa, has no mt genome. We are interested in the evolutionary origin of linear mt genomes of Babesia/Theileria, and have investigated mt genome structures in members of archaeopiroplasmid, a lineage branched off earlier from Babesia/Theileria. Results The complete mt genomes of archaeopiroplasmid parasites, Babesia microti and Babesia rodhaini, were sequenced. The mt genomes of B. microti (11.1-kb and B. rodhaini (6.9-kb possess two pairs of unique inverted repeats, IR-A and IR-B. Flip-flop inversions between two IR-As and between two IR-Bs appear to generate four distinct genome structures that are present at an equi-molar ratio. An individual parasite contained multiple mt genome structures, with 20 copies and 2 – 3 copies per haploid nuclear genome in B. microti and B. rodhaini, respectively. Conclusion We found a novel linear monomeric mt genome structure of B. microti and B. rhodhaini equipped with dual flip-flop inversion system, by which four distinct genome structures are readily generated. To our knowledge, this study is the first to report the presence of two pairs of distinct IR sequences within a monomeric linear mt genome. The present finding provides insight into further understanding of evolution of mt genome structure.

  14. Laterally constrained inversion for CSAMT data interpretation

    Science.gov (United States)

    Wang, Ruo; Yin, Changchun; Wang, Miaoyue; Di, Qingyun

    2015-10-01

    Laterally constrained inversion (LCI) has been successfully applied to the inversion of dc resistivity, TEM and airborne EM data. However, it hasn't been yet applied to the interpretation of controlled-source audio-frequency magnetotelluric (CSAMT) data. In this paper, we apply the LCI method for CSAMT data inversion by preconditioning the Jacobian matrix. We apply a weighting matrix to Jacobian to balance the sensitivity of model parameters, so that the resolution with respect to different model parameters becomes more uniform. Numerical experiments confirm that this can improve the convergence of the inversion. We first invert a synthetic dataset with and without noise to investigate the effect of LCI applications to CSAMT data, for the noise free data, the results show that the LCI method can recover the true model better compared to the traditional single-station inversion; and for the noisy data, the true model is recovered even with a noise level of 8%, indicating that LCI inversions are to some extent noise insensitive. Then, we re-invert two CSAMT datasets collected respectively in a watershed and a coal mine area in Northern China and compare our results with those from previous inversions. The comparison with the previous inversion in a coal mine shows that LCI method delivers smoother layer interfaces that well correlate to seismic data, while comparison with a global searching algorithm of simulated annealing (SA) in a watershed shows that though both methods deliver very similar good results, however, LCI algorithm presented in this paper runs much faster. The inversion results for the coal mine CSAMT survey show that a conductive water-bearing zone that was not revealed by the previous inversions has been identified by the LCI. This further demonstrates that the method presented in this paper works for CSAMT data inversion.

  15. Limit theorems for linear spectrum statistics of orthogonal polynomial ensembles and their applications in random matrix theory

    Science.gov (United States)

    Pan, Guangming; Wang, Shaochen; Zhou, Wang

    2017-10-01

    In this paper, we consider the asymptotic behavior of Xfn (n )≔∑i=1 nfn(xi ) , where xi,i =1 ,…,n form orthogonal polynomial ensembles and fn is a real-valued, bounded measurable function. Under the condition that Var Xfn (n )→∞ , the Berry-Esseen (BE) bound and Cramér type moderate deviation principle (MDP) for Xfn (n ) are obtained by using the method of cumulants. As two applications, we establish the BE bound and Cramér type MDP for linear spectrum statistics of Wigner matrix and sample covariance matrix in the complex cases. These results show that in the edge case (which means fn has a particular form f (x ) I (x ≥θn ) where θn is close to the right edge of equilibrium measure and f is a smooth function), Xfn (n ) behaves like the eigenvalues counting function of the corresponding Wigner matrix and sample covariance matrix, respectively.

  16. Planktonic food webs revisited: Reanalysis of results from the linear inverse approach

    Science.gov (United States)

    Hlaili, Asma Sakka; Niquil, Nathalie; Legendre, Louis

    2014-01-01

    Identification of the trophic pathway that dominates a given planktonic assemblage is generally based on the distribution of biomasses among food-web compartments, or better, the flows of materials or energy among compartments. These flows are obtained by field observations and a posteriori analyses, including the linear inverse approach. In the present study, we re-analysed carbon flows obtained by inverse analysis at 32 stations in the global ocean and one large lake. Our results do not support two "classical" views of plankton ecology, i.e. that the herbivorous food web is dominated by mesozooplankton grazing on large phytoplankton, and the microbial food web is based on microzooplankton significantly consuming bacteria; our results suggest instead that phytoplankton are generally grazed by microzooplankton, of which they are the main food source. Furthermore, we identified the "phyto-microbial food web", where microzooplankton largely feed on phytoplankton, in addition to the already known "poly-microbial food web", where microzooplankton consume more or less equally various types of food. These unexpected results led to a (re)definition of the conceptual models corresponding to the four trophic pathways we found to exist in plankton, i.e. the herbivorous, multivorous, and two types of microbial food web. We illustrated the conceptual trophic pathways using carbon flows that were actually observed at representative stations. The latter can be calibrated to correspond to any field situation. Our study also provides researchers and managers with operational criteria for identifying the dominant trophic pathway in a planktonic assemblage, these criteria being based on the values of two carbon ratios that could be calculated from flow values that are relatively easy to estimate in the field.

  17. Visco-elastic controlled-source full waveform inversion without surface waves

    Science.gov (United States)

    Paschke, Marco; Krause, Martin; Bleibinhaus, Florian

    2016-04-01

    We developed a frequency-domain visco-elastic full waveform inversion for onshore seismic experiments with topography. The forward modeling is based on a finite-difference time-domain algorithm by Robertsson that uses the image-method to ensure a stress-free condition at the surface. The time-domain data is Fourier-transformed at every point in the model space during the forward modeling for a given set of frequencies. The motivation for this approach is the reduced amount of memory when computing kernels, and the straightforward implementation of the multiscale approach. For the inversion, we calculate the Frechet derivative matrix explicitly, and we implement a Levenberg-Marquardt scheme that allows for computing the resolution matrix. To reduce the size of the Frechet derivative matrix, and to stabilize the inversion, an adapted inverse mesh is used. The node spacing is controlled by the velocity distribution and the chosen frequencies. To focus the inversion on body waves (P, P-coda, and S) we mute the surface waves from the data. Consistent spatiotemporal weighting factors are applied to the wavefields during the Fourier transform to obtain the corresponding kernels. We test our code with a synthetic study using the Marmousi model with arbitrary topography. This study also demonstrates the importance of topography and muting surface waves in controlled-source full waveform inversion.

  18. AN ADA LINEAR ALGEBRA PACKAGE MODELED AFTER HAL/S

    Science.gov (United States)

    Klumpp, A. R.

    1994-01-01

    This package extends the Ada programming language to include linear algebra capabilities similar to those of the HAL/S programming language. The package is designed for avionics applications such as Space Station flight software. In addition to the HAL/S built-in functions, the package incorporates the quaternion functions used in the Shuttle and Galileo projects, and routines from LINPAK that solve systems of equations involving general square matrices. Language conventions in this package follow those of HAL/S to the maximum extent practical and minimize the effort required for writing new avionics software and translating existent software into Ada. Valid numeric types in this package include scalar, vector, matrix, and quaternion declarations. (Quaternions are fourcomponent vectors used in representing motion between two coordinate frames). Single precision and double precision floating point arithmetic is available in addition to the standard double precision integer manipulation. Infix operators are used instead of function calls to define dot products, cross products, quaternion products, and mixed scalar-vector, scalar-matrix, and vector-matrix products. The package contains two generic programs: one for floating point, and one for integer. The actual component type is passed as a formal parameter to the generic linear algebra package. The procedures for solving systems of linear equations defined by general matrices include GEFA, GECO, GESL, and GIDI. The HAL/S functions include ABVAL, UNIT, TRACE, DET, INVERSE, TRANSPOSE, GET, PUT, FETCH, PLACE, and IDENTITY. This package is written in Ada (Version 1.2) for batch execution and is machine independent. The linear algebra software depends on nothing outside the Ada language except for a call to a square root function for floating point scalars (such as SQRT in the DEC VAX MATHLIB library). This program was developed in 1989, and is a copyrighted work with all copyright vested in NASA.

  19. FEM-based linear inverse modeling using a 3D source array to image magma chambers with free geometry. Application to InSAR data from Rabaul Caldera (PNG).

    Science.gov (United States)

    Ronchin, Erika; Masterlark, Timothy; Dawson, John; Saunders, Steve; Martí Molist, Joan

    2015-04-01

    In this study, we present a method to fully integrate a family of finite element models (FEMs) into the regularized linear inversion of InSAR data collected at Rabaul caldera (PNG) between February 2007 and December 2010. During this period the caldera experienced a long-term steady subsidence that characterized surface movement both inside the caldera and outside, on its western side. The inversion is based on an array of FEM sources in the sense that the Green's function matrix is a library of forward numerical displacement solutions generated by the sources of an array common to all FEMs. Each entry of the library is the LOS surface displacement generated by injecting a unity mass of fluid, of known density and bulk modulus, into a different source cavity of the array for each FEM. By using FEMs, we are taking advantage of their capability of including topography and heterogeneous distribution of elastic material properties. All FEMs of the family share the same mesh in which only one source is activated at the time by removing the corresponding elements and applying the unity fluid flux. The domain therefore only needs to be discretized once. This precludes remeshing for each activated source, thus reducing computational requirements, often a downside of FEM-based inversions. Without imposing an a-priori source, the method allows us to identify, from a least-squares standpoint, a complex distribution of fluid flux (or change in pressure) with a 3D free geometry within the source array, as dictated by the data. The results of applying the proposed inversion to Rabaul InSAR data show a shallow magmatic system under the caldera made of two interconnected lobes located at the two opposite sides of the caldera. These lobes could be consistent with feeding reservoirs of the ongoing Tavuvur volcano eruption of andesitic products, on the eastern side, and of the past Vulcan volcano eruptions of more evolved materials, on the western side. The interconnection and

  20. A large inversion in the linear chromosome of Streptomyces griseus caused by replicative transposition of a new Tn3 family transposon.

    Science.gov (United States)

    Murata, M; Uchida, T; Yang, Y; Lezhava, A; Kinashi, H

    2011-04-01

    We have comprehensively analyzed the linear chromosomes of Streptomyces griseus mutants constructed and kept in our laboratory. During this study, macrorestriction analysis of AseI and DraI fragments of mutant 402-2 suggested a large chromosomal inversion. The junctions of chromosomal inversion were cloned and sequenced and compared with the corresponding target sequences in the parent strain 2247. Consequently, a transposon-involved mechanism was revealed. Namely, a transposon originally located at the left target site was replicatively transposed to the right target site in an inverted direction, which generated a second copy and at the same time caused a 2.5-Mb chromosomal inversion. The involved transposon named TnSGR was grouped into a new subfamily of the resolvase-encoding Tn3 family transposons based on its gene organization. At the end, terminal diversity of S. griseus chromosomes is discussed by comparing the sequences of strains 2247 and IFO13350.

  1. An linear matrix inequality approach to global synchronisation of non-parameter perturbations of multi-delay Hopfield neural network

    International Nuclear Information System (INIS)

    Shao Hai-Jian; Cai Guo-Liang; Wang Hao-Xiang

    2010-01-01

    In this study, a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional. This paper presents the comprehensive discussion of the approach and also extensive applications

  2. A Comparison of Closed-Loop Performance of Multirotor Configurations Using Non-Linear Dynamic Inversion Control

    Directory of Open Access Journals (Sweden)

    Murray L. Ireland

    2015-06-01

    Full Text Available Multirotor is the umbrella term for the family of unmanned aircraft, which include the quadrotor, hexarotor and other vertical take-off and landing (VTOL aircraft that employ multiple main rotors for lift and control. Development and testing of novel multirotor designs has been aided by the proliferation of 3D printing and inexpensive flight controllers and components. Different multirotor configurations exhibit specific strengths, while presenting unique challenges with regards to design and control. This article highlights the primary differences between three multirotor platforms: a quadrotor; a fully-actuated hexarotor; and an octorotor. Each platform is modelled and then controlled using non-linear dynamic inversion. The differences in dynamics, control and performance are then discussed.

  3. Linear algebra

    CERN Document Server

    Shilov, Georgi E

    1977-01-01

    Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

  4. The Relaxation Matrix for Symmetric Tops with Inversion Symmetry. I. Effects of Line Coupling on Self-Broadened v (sub 1) and Pure Rotational Bands of NH3

    Science.gov (United States)

    Ma, Q.; Boulet, C.

    2016-01-01

    The Robert-Bonamy formalism has been commonly used to calculate half-widths and shifts of spectral lines for decades. This formalism is based on several approximations. Among them, two have not been fully addressed: the isolated line approximation and the neglect of coupling between the translational and internal motions. Recently, we have shown that the isolated line approximation is not necessary in developing semi-classical line shape theories. Based on this progress, we have been able to develop a new formalism that enables not only to reduce uncertainties on calculated half-widths and shifts, but also to model line mixing effects on spectra starting from the knowledge of the intermolecular potential. In our previous studies, the new formalism had been applied to linear and asymmetric-top molecules. In the present study, the method has been extended to symmetric-top molecules with inversion symmetry. As expected, the inversion splitting induces a complete failure of the isolated line approximation. We have calculated the complex relaxation matrices of selfbroadened NH3. The half-widths and shifts in the ?1 and the pure rotational bands are reported in the present paper. When compared with measurements, the calculated half-widths match the experimental data very well, since the inapplicable isolated line approximation has been removed. With respect to the shifts, only qualitative results are obtained and discussed. Calculated off-diagonal elements of the relaxation matrix and a comparison with the observed line mixing effects are reported in the companion paper (Paper II).

  5. Best linear unbiased prediction of genomic breeding values using a trait-specific marker-derived relationship matrix.

    Directory of Open Access Journals (Sweden)

    Zhe Zhang

    2010-09-01

    Full Text Available With the availability of high density whole-genome single nucleotide polymorphism chips, genomic selection has become a promising method to estimate genetic merit with potentially high accuracy for animal, plant and aquaculture species of economic importance. With markers covering the entire genome, genetic merit of genotyped individuals can be predicted directly within the framework of mixed model equations, by using a matrix of relationships among individuals that is derived from the markers. Here we extend that approach by deriving a marker-based relationship matrix specifically for the trait of interest.In the framework of mixed model equations, a new best linear unbiased prediction (BLUP method including a trait-specific relationship matrix (TA was presented and termed TABLUP. The TA matrix was constructed on the basis of marker genotypes and their weights in relation to the trait of interest. A simulation study with 1,000 individuals as the training population and five successive generations as candidate population was carried out to validate the proposed method. The proposed TABLUP method outperformed the ridge regression BLUP (RRBLUP and BLUP with realized relationship matrix (GBLUP. It performed slightly worse than BayesB with an accuracy of 0.79 in the standard scenario.The proposed TABLUP method is an improvement of the RRBLUP and GBLUP method. It might be equivalent to the BayesB method but it has additional benefits like the calculation of accuracies for individual breeding values. The results also showed that the TA-matrix performs better in predicting ability than the classical numerator relationship matrix and the realized relationship matrix which are derived solely from pedigree or markers without regard to the trait. This is because the TA-matrix not only accounts for the Mendelian sampling term, but also puts the greater emphasis on those markers that explain more of the genetic variance in the trait.

  6. Multivariate Matrix-Exponential Distributions

    DEFF Research Database (Denmark)

    Bladt, Mogens; Nielsen, Bo Friis

    2010-01-01

    be written as linear combinations of the elements in the exponential of a matrix. For this reason we shall refer to multivariate distributions with rational Laplace transform as multivariate matrix-exponential distributions (MVME). The marginal distributions of an MVME are univariate matrix......-exponential distributions. We prove a characterization that states that a distribution is an MVME distribution if and only if all non-negative, non-null linear combinations of the coordinates have a univariate matrix-exponential distribution. This theorem is analog to a well-known characterization theorem...

  7. The Inverse of Banded Matrices

    Science.gov (United States)

    2013-01-01

    indexed entries all zeros. In this paper, generalizing a method of Mallik (1999) [5], we give the LU factorization and the inverse of the matrix Br,n (if it...r ≤ i ≤ r, 1 ≤ j ≤ r, with the remaining un-indexed entries all zeros. In this paper generalizing a method of Mallik (1999) [5...matrices and applications to piecewise cubic approximation, J. Comput. Appl. Math. 8 (4) (1982) 285–288. [5] R.K. Mallik , The inverse of a lower

  8. LS-APC v1.0: a tuning-free method for the linear inverse problem and its application to source-term determination

    Directory of Open Access Journals (Sweden)

    O. Tichý

    2016-11-01

    Full Text Available Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g., concentrations or deposition values as a product of the source-receptor sensitivity (SRS matrix obtained from an atmospheric transport model multiplied by the unknown source-term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation also allows estimation of all tuning parameters from the measurements. The estimation procedure is based on the variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to also estimate all tuning parameters from the observations. The proposed algorithm is tested and compared with the standard methods on data from the European Tracer Experiment (ETEX where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.

  9. LS-APC v1.0: a tuning-free method for the linear inverse problem and its application to source-term determination

    Science.gov (United States)

    Tichý, Ondřej; Šmídl, Václav; Hofman, Radek; Stohl, Andreas

    2016-11-01

    Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g., concentrations or deposition values) as a product of the source-receptor sensitivity (SRS) matrix obtained from an atmospheric transport model multiplied by the unknown source-term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation also allows estimation of all tuning parameters from the measurements. The estimation procedure is based on the variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to also estimate all tuning parameters from the observations. The proposed algorithm is tested and compared with the standard methods on data from the European Tracer Experiment (ETEX) where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.

  10. H{sub 2}/H{infinity} control of flexible structures through linear matrix inequalities with pole placement

    Energy Technology Data Exchange (ETDEWEB)

    Lopes, Jean C. [PETROBRAS S.A., Rio de Janeiro, RJ (Brazil)

    2009-07-01

    The objective of this work is to apply the H2/H{infinity} control technique using linear matrix inequalities and pole placement constraints to the flexible structures control problem. The H2/H{infinity}control is a technique to design a controller with mixed features of the H2 and H{infinity} control formulations, such as, optimal dynamical performance and robust performance. The Linear Matrix Inequalities allow formulating the problem as a convex optimization problem, and additional constraints can be included such as the pole placement. The pole placement requirement comes from the necessity of adjusting the transient response of the plant and ensuring a specific behavior in terms of speed and damping responses. The mathematical model used for this study is related to a flexible beam, with an applied disturbance and an actuator in different positions. The state-space matrices of the structure were obtained using the finite element method with the Euler-Bernoulli formulation of beams. The results showed that the pole placement constraints can improve the performance of the controller H2/H{infinity}. The Matlab was used for the computational implementation. (author)

  11. Development of a Java Package for Matrix Programming

    OpenAIRE

    Lim, Ngee-Peng; Ling, Maurice HT; Lim, Shawn YC; Choi, Ji-Hee; Teo, Henry BK

    2003-01-01

    We had assembled a Java package, known as MatrixPak, of four classes for the purpose of numerical matrix computation. The classes are matrix, matrix_operations, StrToMatrix, and MatrixToStr; all of which are inherited from java.lang.Object class. Class matrix defines a matrix as a two-dimensional array of float types, and contains the following mathematical methods: transpose, adjoint, determinant, inverse, minor and cofactor. Class matrix_operations contains the following mathematical method...

  12. Minimal solution for inconsistent singular fuzzy matrix equations

    Directory of Open Access Journals (Sweden)

    M. Nikuie

    2013-10-01

    Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.

  13. On the calibration process of film dosimetry: OLS inverse regression versus WLS inverse prediction

    International Nuclear Information System (INIS)

    Crop, F; Thierens, H; Rompaye, B Van; Paelinck, L; Vakaet, L; Wagter, C De

    2008-01-01

    The purpose of this study was both putting forward a statistically correct model for film calibration and the optimization of this process. A reliable calibration is needed in order to perform accurate reference dosimetry with radiographic (Gafchromic) film. Sometimes, an ordinary least squares simple linear (in the parameters) regression is applied to the dose-optical-density (OD) curve with the dose as a function of OD (inverse regression) or sometimes OD as a function of dose (inverse prediction). The application of a simple linear regression fit is an invalid method because heteroscedasticity of the data is not taken into account. This could lead to erroneous results originating from the calibration process itself and thus to a lower accuracy. In this work, we compare the ordinary least squares (OLS) inverse regression method with the correct weighted least squares (WLS) inverse prediction method to create calibration curves. We found that the OLS inverse regression method could lead to a prediction bias of up to 7.3 cGy at 300 cGy and total prediction errors of 3% or more for Gafchromic EBT film. Application of the WLS inverse prediction method resulted in a maximum prediction bias of 1.4 cGy and total prediction errors below 2% in a 0-400 cGy range. We developed a Monte-Carlo-based process to optimize calibrations, depending on the needs of the experiment. This type of thorough analysis can lead to a higher accuracy for film dosimetry

  14. Bilinear Inverse Problems: Theory, Algorithms, and Applications

    Science.gov (United States)

    Ling, Shuyang

    We will discuss how several important real-world signal processing problems, such as self-calibration and blind deconvolution, can be modeled as bilinear inverse problems and solved by convex and nonconvex optimization approaches. In Chapter 2, we bring together three seemingly unrelated concepts, self-calibration, compressive sensing and biconvex optimization. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where the diagonal matrix D (which models the calibration error) is unknown and x is an unknown sparse signal. By "lifting" this biconvex inverse problem and exploiting sparsity in this model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently. In Chapter 3, we study the question of the joint blind deconvolution and blind demixing, i.e., extracting a sequence of functions [special characters omitted] from observing only the sum of their convolutions [special characters omitted]. In particular, for the special case s = 1, it becomes the well-known blind deconvolution problem. We present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. We discuss several applications of the proposed framework in image processing and wireless communications in connection with the Internet-of-Things. In Chapter 4, we consider three different self-calibration models of practical relevance. We show how their corresponding bilinear inverse problems can be solved by both the simple linear least squares approach and the SVD-based approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus allowing for real-time deployment. Explicit theoretical

  15. An approximate inversion method of geoelectrical sounding data using linear and bayesian statistical approaches. Examples of Tritrivakely volcanic lake and Mahitsy area (central part of Madagascar)

    International Nuclear Information System (INIS)

    Ranaivo Nomenjanahary, F.; Rakoto, H.; Ratsimbazafy, J.B.

    1994-08-01

    This paper is concerned with resistivity sounding measurements performed from single site (vertical sounding) or from several sites (profiles) within a bounded area. The objective is to present an accurate information about the study area and to estimate the likelihood of the produced quantitative models. The achievement of this objective obviously requires quite relevant data and processing methods. It also requires interpretation methods which should take into account the probable effect of an heterogeneous structure. In front of such difficulties, the interpretation of resistivity sounding data inevitably involves the use of inversion methods. We suggest starting the interpretation in simple situation (1-D approximation), and using the rough but correct model obtained as an a-priori model for any more refined interpretation. Related to this point of view, special attention should be paid for the inverse problem applied to the resistivity sounding data. This inverse problem is nonlinear, while linearity inherent in the functional response used to describe the physical experiment. Two different approaches are used to build an approximate but higher dimensional inversion of geoelectrical data: the linear approach and the bayesian statistical approach. Some illustrations of their application in resistivity sounding data acquired at Tritrivakely volcanic lake (single site) and at Mahitsy area (several sites) will be given. (author). 28 refs, 7 figs

  16. Matrix effect study in the determination of linear alkylbenzene sulfonates in sewage sludge samples.

    Science.gov (United States)

    Cantarero, Samuel; Zafra-Gómez, Alberto; Ballesteros, Oscar; Navalón, Alberto; Vílchez, José L; Verge, Coral; De Ferrer, Juan A

    2011-04-01

    We propose a study of the matrix effect in the determination of linear alkylbenzene sulfonates (LAS) in sewage sludge samples. First, a rapid, selective and sensitive method is proposed. The method involves two stages: the extraction of the compound from the samples and analysis by liquid chromatography with fluorescence detection (LC-FLD). Three different techniques of extraction (microwave-assisted extraction, Soxhlet, and ultrasounds) were compared, and microwave-assisted extraction was selected as the best suited for our purpose. Microwave-assisted extraction allows reducing the extraction time (25 min compared with 12 h for conventional Soxhlet extraction) and solvent waste (25 ml of methanol compared with 200 ml for Soxhlet or more than 50 ml for the ultrasonic procedure). Absence of matrix effect was evaluated with two standards (2ØC(8:0) and 2ØC(16:0) ) that are not commercial; therefore, neither of them was detected in sewage sludge samples and they showed similar environmental behavior (adsorption and precipitation) to LAS (C(11:0) -C(13.0) ), which allow us to evaluate the matrix effect. Validation was carried out by a recovery assay, and the method was applied to samples from different sources; therefore, they had different compositions. Copyright © 2011 SETAC.

  17. T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols

    Science.gov (United States)

    Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

    2013-07-01

    We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with ground-based, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.

  18. Frequency-domain elastic full waveform inversion using encoded simultaneous sources

    Science.gov (United States)

    Jeong, W.; Son, W.; Pyun, S.; Min, D.

    2011-12-01

    Currently, numerous studies have endeavored to develop robust full waveform inversion and migration algorithms. These processes require enormous computational costs, because of the number of sources in the survey. To avoid this problem, the phase encoding technique for prestack migration was proposed by Romero (2000) and Krebs et al. (2009) proposed the encoded simultaneous-source inversion technique in the time domain. On the other hand, Ben-Hadj-Ali et al. (2011) demonstrated the robustness of the frequency-domain full waveform inversion with simultaneous sources for noisy data changing the source assembling. Although several studies on simultaneous-source inversion tried to estimate P- wave velocity based on the acoustic wave equation, seismic migration and waveform inversion based on the elastic wave equations are required to obtain more reliable subsurface information. In this study, we propose a 2-D frequency-domain elastic full waveform inversion technique using phase encoding methods. In our algorithm, the random phase encoding method is employed to calculate the gradients of the elastic parameters, source signature estimation and the diagonal entries of approximate Hessian matrix. The crosstalk for the estimated source signature and the diagonal entries of approximate Hessian matrix are suppressed with iteration as for the gradients. Our 2-D frequency-domain elastic waveform inversion algorithm is composed using the back-propagation technique and the conjugate-gradient method. Source signature is estimated using the full Newton method. We compare the simultaneous-source inversion with the conventional waveform inversion for synthetic data sets of the Marmousi-2 model. The inverted results obtained by simultaneous sources are comparable to those obtained by individual sources, and source signature is successfully estimated in simultaneous source technique. Comparing the inverted results using the pseudo Hessian matrix with previous inversion results

  19. The Transmuted Generalized Inverse Weibull Distribution

    Directory of Open Access Journals (Sweden)

    Faton Merovci

    2014-05-01

    Full Text Available A generalization of the generalized inverse Weibull distribution the so-called transmuted generalized inverse Weibull distribution is proposed and studied. We will use the quadratic rank transmutation map (QRTM in order to generate a flexible family of probability distributions taking the generalized inverseWeibull distribution as the base value distribution by introducing a new parameter that would offer more distributional flexibility. Various structural properties including explicit expressions for the moments, quantiles, and moment generating function of the new distribution are derived. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set are used to compare the flexibility of the transmuted version versus the generalized inverse Weibull distribution.

  20. LS-APC v1.0: a tuning-free method for the linear inverse problem and its application to source-term determination

    Czech Academy of Sciences Publication Activity Database

    Tichý, Ondřej; Šmídl, Václav; Hofman, Radek; Stohl, A.

    2016-01-01

    Roč. 9, č. 11 (2016), s. 4297-4311 ISSN 1991-959X R&D Projects: GA MŠk(CZ) 7F14287 Institutional support: RVO:67985556 Keywords : Linear inverse problem * Bayesian regularization * Source-term determination * Variational Bayes method Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 3.458, year: 2016 http://library.utia.cas.cz/separaty/2016/AS/tichy-0466029.pdf

  1. Matrix theory selected topics and useful results

    CERN Document Server

    Mehta, Madan Lal

    1989-01-01

    Matrices and operations on matrices ; determinants ; elementary operations on matrices (continued) ; eigenvalues and eigenvectors, diagonalization of normal matrices ; functions of a matrix ; positive definiteness, various polar forms of a matrix ; special matrices ; matrices with quaternion elements ; inequalities ; generalised inverse of a matrix ; domain of values of a matrix, location and dispersion of eigenvalues ; symmetric functions ; integration over matrix variables ; permanents of doubly stochastic matrices ; infinite matrices ; Alexander matrices, knot polynomials, torsion numbers.

  2. Inverse LMI control design method and its application to position keeping system; Gyakumondai LMI seigyokei sekkeiho no kaihatsu to ichi hoji system eno oyo

    Energy Technology Data Exchange (ETDEWEB)

    Yamamoto, I; Hayashi, T [Mitsubishi Heavy Industries, Ltd., Tokyo (Japan)

    1997-10-01

    Recently, with a progress of robust control such as H{infinity} control, the application of a control system design considering a robustness of controlled system fluctuation to real machinery became possible. In addition, LMI (Linear Matrix Inequality) control system design method is superior to conventional H{infinity} control, although including various difficult elements. The design algorithm permitting the robust control system design of non-linear problems by giving controlled systems was thus developed by introducing an inverse LMI control design method. This design algorithm determines the solution of models outputting the deviation between a target value and controlled variables by solving the simultaneous equations composed of a linear matrix inequality under an impulse response constraint condition and that under an H{infinity} norm constraint condition. This technique allows to give a pending step response as control condition. The technique was confirmed to be effective by its application to the position keeping control problem of marine floating structures. 6 refs., 11 figs., 2 tabs.

  3. Finite-dimensional linear algebra

    CERN Document Server

    Gockenbach, Mark S

    2010-01-01

    Some Problems Posed on Vector SpacesLinear equationsBest approximationDiagonalizationSummaryFields and Vector SpacesFields Vector spaces Subspaces Linear combinations and spanning sets Linear independence Basis and dimension Properties of bases Polynomial interpolation and the Lagrange basis Continuous piecewise polynomial functionsLinear OperatorsLinear operatorsMore properties of linear operatorsIsomorphic vector spaces Linear operator equations Existence and uniqueness of solutions The fundamental theorem; inverse operatorsGaussian elimination Newton's method Linear ordinary differential eq

  4. Three-dimensional inversion of multisource array electromagnetic data

    Science.gov (United States)

    Tartaras, Efthimios

    Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM

  5. Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method

    Science.gov (United States)

    Kaporin, I. E.

    2012-02-01

    In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.

  6. The Relaxation Matrix for Symmetric Tops with Inversion Symmetry. II; Line Mixing Effects in the V1 Band of NH3

    Science.gov (United States)

    Boulet, C.; Ma, Q.

    2016-01-01

    Line mixing effects have been calculated in the ?1 parallel band of self-broadened NH3. The theoretical approach is an extension of a semi-classical model to symmetric-top molecules with inversion symmetry developed in the companion paper [Q. Ma and C. Boulet, J. Chem. Phys. 144, 224303 (2016)]. This model takes into account line coupling effects and hence enables the calculation of the entire relaxation matrix. A detailed analysis of the various coupling mechanisms is carried out for Q and R inversion doublets. The model has been applied to the calculation of the shape of the Q branch and of some R manifolds for which an obvious signature of line mixing effects has been experimentally demonstrated. Comparisons with measurements show that the present formalism leads to an accurate prediction of the available experimental line shapes. Discrepancies between the experimental and theoretical sets of first order mixing parameters are discussed as well as some extensions of both theory and experiment.

  7. Sheared Layers in the Continental Crust: Nonlinear and Linearized inversion for Ps receiver functions

    Science.gov (United States)

    Park, J. J.

    2017-12-01

    Sheared Layers in the Continental Crust: Nonlinear and Linearized inversion for Ps receiver functions Jeffrey Park, Yale University The interpretation of seismic receiver functions (RFs) in terms of isotropic and anisotropic layered structure can be complex. The relationship between structure and body-wave scattering is nonlinear. The anisotropy can involve more parameters than the observations can readily constrain. Finally, reflectivity-predicted layer reverberations are often not prominent in data, so that nonlinear waveform inversion can search in vain to match ghost signals. Multiple-taper correlation (MTC) receiver functions have uncertainties in the frequency domain that follow Gaussian statistics [Park and Levin, 2016a], so grid-searches for the best-fitting collections of interfaces can be performed rapidly to minimize weighted misfit variance. Tests for layer-reverberations can be performed in the frequency domain without reflectivity calculations, allowing flexible modelling of weak, but nonzero, reverberations. Park and Levin [2016b] linearized the hybridization of P and S body waves in an anisotropic layer to predict first-order Ps conversion amplitudes at crust and mantle interfaces. In an anisotropic layer, the P wave acquires small SV and SH components. To ensure continuity of displacement and traction at the top and bottom boundaries of the layer, shear waves are generated. Assuming hexagonal symmetry with an arbitrary symmetry axis, theory confirms the empirical stacking trick of phase-shifting transverse RFs by 90 degrees in back-azimuth [Shiomi and Park, 2008; Schulte-Pelkum and Mahan, 2014] to enhance 2-lobed and 4-lobed harmonic variation. Ps scattering is generated by sharp interfaces, so that RFs resemble the first derivative of the model. MTC RFs in the frequency domain can be manipulated to obtain a first-order reconstruction of the layered anisotropy, under the above modeling constraints and neglecting reverberations. Examples from long

  8. Full waveform inversion using envelope-based global correlation norm

    KAUST Repository

    Oh, Juwon

    2018-01-28

    Various parameterizations have been suggested to simplify inversions of first arrivals, or P −waves, in orthorhombic anisotropic media, but the number and type of retrievable parameters have not been decisively determined. We show that only six parameters can be retrieved from the dynamic linearized inversion of P −waves. These parameters are different from the six parameters needed to describe the kinematics of P −waves. Reflection-based radiation patterns from the P − P scattered waves are remapped into the spectral domain to allow for our resolution analysis based on the effective angle of illumination concept. Singular value decomposition of the spectral sensitivities from various azimuths, offset coverage scenarios, and data bandwidths allows us to quantify the resolution of different parameterizations, taking into account the signal-to-noise ratio in a given experiment. According to our singular value analysis, when the primary goal of inversion is determining the velocity of the P −waves, gradually adding anisotropy of lower orders (isotropic, vertically transversally isotropic, orthorhombic) in hierarchical parameterization is the best choice. Hierarchical parametrization reduces the tradeoff between the parameters and makes gradual introduction of lower anisotropy orders straightforward. When all the anisotropic parameters affecting P −wave propagation need to be retrieved simultaneously, the classic parameterization of orthorhombic medium with elastic stiffness matrix coefficients and density is a better choice for inversion. We provide estimates of the number and set of parameters that can be retrieved from surface seismic data in different acquisition scenarios. To set up an inversion process, the singular values determine the number of parameters that can be inverted and the resolution matrices from the parameterizations can be used to ascertain the set of parameters that can be resolved.

  9. Matrices and linear transformations

    CERN Document Server

    Cullen, Charles G

    1990-01-01

    ""Comprehensive . . . an excellent introduction to the subject."" - Electronic Engineer's Design Magazine.This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first

  10. Raney Distributions and Random Matrix Theory

    Science.gov (United States)

    Forrester, Peter J.; Liu, Dang-Zheng

    2015-03-01

    Recent works have shown that the family of probability distributions with moments given by the Fuss-Catalan numbers permit a simple parameterized form for their density. We extend this result to the Raney distribution which by definition has its moments given by a generalization of the Fuss-Catalan numbers. Such computations begin with an algebraic equation satisfied by the Stieltjes transform, which we show can be derived from the linear differential equation satisfied by the characteristic polynomial of random matrix realizations of the Raney distribution. For the Fuss-Catalan distribution, an equilibrium problem characterizing the density is identified. The Stieltjes transform for the limiting spectral density of the singular values squared of the matrix product formed from inverse standard Gaussian matrices, and standard Gaussian matrices, is shown to satisfy a variant of the algebraic equation relating to the Raney distribution. Supported on , we show that it too permits a simple functional form upon the introduction of an appropriate choice of parameterization. As an application, the leading asymptotic form of the density as the endpoints of the support are approached is computed, and is shown to have some universal features.

  11. Factorizable S-matrix for SO(D)/SO(2) circle times SO(D - 2) non-linear σ models with fermions

    International Nuclear Information System (INIS)

    Abdalla, E.; Lima-Santos, A.

    1988-01-01

    The authors compute the exact S matrix for the non-linear sigma model with symmetry SO(D)/SO(2) circle times SO(D-2) coupled to fermions in a minimal or supersymmetric way. The model has some relevance in string theory with non-zero external curvature

  12. Bayesian seismic AVO inversion

    Energy Technology Data Exchange (ETDEWEB)

    Buland, Arild

    2002-07-01

    A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P-wave velocity, S-wave velocity and density. Distributions for other elastic parameters can also be assessed, for example acoustic impedance, shear impedance and P-wave to S-wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance, hence exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3-D dataset from the Sleipner Field. The results show good agreement with well logs but the uncertainty is high. The stochastic model includes uncertainties of both the elastic parameters, the wavelet and the seismic and well log data. The posterior distribution is explored by Markov chain Monte Carlo simulation using the Gibbs sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The uncertainty of the estimated wavelet is low. In the Heidrun examples the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results. We have developed a 3-D linearized AVO inversion method with spatially coupled model parameters where the objective is to obtain posterior distributions for P-wave velocity, S

  13. Linear GPR inversion for lossy soil and a planar air-soil interface

    DEFF Research Database (Denmark)

    Meincke, Peter

    2001-01-01

    A three-dimensional inversion scheme for fixed-offset ground penetrating radar (GPR) is derived that takes into account the loss in the soil and the planar air-soil interface. The forward model of this inversion scheme is based upon the first Born approximation and the dyadic Green function...

  14. Matrix-Inversion-Free Compressed Sensing With Variable Orthogonal Multi-Matching Pursuit Based on Prior Information for ECG Signals.

    Science.gov (United States)

    Cheng, Yih-Chun; Tsai, Pei-Yun; Huang, Ming-Hao

    2016-05-19

    Low-complexity compressed sensing (CS) techniques for monitoring electrocardiogram (ECG) signals in wireless body sensor network (WBSN) are presented. The prior probability of ECG sparsity in the wavelet domain is first exploited. Then, variable orthogonal multi-matching pursuit (vOMMP) algorithm that consists of two phases is proposed. In the first phase, orthogonal matching pursuit (OMP) algorithm is adopted to effectively augment the support set with reliable indices and in the second phase, the orthogonal multi-matching pursuit (OMMP) is employed to rescue the missing indices. The reconstruction performance is thus enhanced with the prior information and the vOMMP algorithm. Furthermore, the computation-intensive pseudo-inverse operation is simplified by the matrix-inversion-free (MIF) technique based on QR decomposition. The vOMMP-MIF CS decoder is then implemented in 90 nm CMOS technology. The QR decomposition is accomplished by two systolic arrays working in parallel. The implementation supports three settings for obtaining 40, 44, and 48 coefficients in the sparse vector. From the measurement result, the power consumption is 11.7 mW at 0.9 V and 12 MHz. Compared to prior chip implementations, our design shows good hardware efficiency and is suitable for low-energy applications.

  15. The Modularized Software Package ASKI - Full Waveform Inversion Based on Waveform Sensitivity Kernels Utilizing External Seismic Wave Propagation Codes

    Science.gov (United States)

    Schumacher, F.; Friederich, W.

    2015-12-01

    We present the modularized software package ASKI which is a flexible and extendable toolbox for seismic full waveform inversion (FWI) as well as sensitivity or resolution analysis operating on the sensitivity matrix. It utilizes established wave propagation codes for solving the forward problem and offers an alternative to the monolithic, unflexible and hard-to-modify codes that have typically been written for solving inverse problems. It is available under the GPL at www.rub.de/aski. The Gauss-Newton FWI method for 3D-heterogeneous elastic earth models is based on waveform sensitivity kernels and can be applied to inverse problems at various spatial scales in both Cartesian and spherical geometries. The kernels are derived in the frequency domain from Born scattering theory as the Fréchet derivatives of linearized full waveform data functionals, quantifying the influence of elastic earth model parameters on the particular waveform data values. As an important innovation, we keep two independent spatial descriptions of the earth model - one for solving the forward problem and one representing the inverted model updates. Thereby we account for the independent needs of spatial model resolution of forward and inverse problem, respectively. Due to pre-integration of the kernels over the (in general much coarser) inversion grid, storage requirements for the sensitivity kernels are dramatically reduced.ASKI can be flexibly extended to other forward codes by providing it with specific interface routines that contain knowledge about forward code-specific file formats and auxiliary information provided by the new forward code. In order to sustain flexibility, the ASKI tools must communicate via file output/input, thus large storage capacities need to be accessible in a convenient way. Storing the complete sensitivity matrix to file, however, permits the scientist full manual control over each step in a customized procedure of sensitivity/resolution analysis and full

  16. A Joint Method of Envelope Inversion Combined with Hybrid-domain Full Waveform Inversion

    Science.gov (United States)

    CUI, C.; Hou, W.

    2017-12-01

    Full waveform inversion (FWI) aims to construct high-precision subsurface models by fully using the information in seismic records, including amplitude, travel time, phase and so on. However, high non-linearity and the absence of low frequency information in seismic data lead to the well-known cycle skipping problem and make inversion easily fall into local minima. In addition, those 3D inversion methods that are based on acoustic approximation ignore the elastic effects in real seismic field, and make inversion harder. As a result, the accuracy of final inversion results highly relies on the quality of initial model. In order to improve stability and quality of inversion results, multi-scale inversion that reconstructs subsurface model from low to high frequency are applied. But, the absence of very low frequencies (time domain and inversion in the frequency domain. To accelerate the inversion, we adopt CPU/GPU heterogeneous computing techniques. There were two levels of parallelism. In the first level, the inversion tasks are decomposed and assigned to each computation node by shot number. In the second level, GPU multithreaded programming is used for the computation tasks in each node, including forward modeling, envelope extraction, DFT (discrete Fourier transform) calculation and gradients calculation. Numerical tests demonstrated that the combined envelope inversion + hybrid-domain FWI could obtain much faithful and accurate result than conventional hybrid-domain FWI. The CPU/GPU heterogeneous parallel computation could improve the performance speed.

  17. Linear ketenimines. Variable structures of C,C-dicyanoketenimines and C,C-bis-sulfonylketenimines.

    Science.gov (United States)

    Finnerty, Justin; Mitschke, Ullrich; Wentrup, Curt

    2002-02-22

    C,C-dicyanoketenimines 10a-c were generated by flash vacuum thermolysis of ketene N,S-acetals 9a-c or by thermal or photochemical decomposition of alpha-azido-beta-cyanocinnamonitrile 11. In the latter reaction, 3,3-dicyano-2-phenyl-1-azirine 12 is also formed. IR spectroscopy of the keteniminines isolated in Ar matrixes or as neat films, NMR spectroscopy of 10c, and theoretical calculations (B3LYP/6-31G) demonstrate that these ketenimines have variable geometry, being essentially linear along the CCN-R framework in polar media (neat films and solution), but in the gas phase or Ar matrix they are bent, as is usual for ketenimines. Experiments and calculations agree that a single CN substituent as in 13 is not enough to enforce linearity, and sulfonyl groups are less effective that cyano groups in causing linearity. C,C-bis(methylsulfonyl)ketenimines 4-5 and a C-cyano-C-(methylsulfonyl)ketenimine 15 are not linear. The compound p-O2NC6H4N=C=C(COOMe)2 previously reported in the literature is probably somewhat linearized along the CCNR moiety. A computational survey (B3LYP/6-31G) of the inversion barrier at nitrogen indicates that electronegative C-substituents dramatically lower the barrier; this is also true of N-acyl substituents. Increasing polarity causes lower barriers. Although N-alkylbis(methylsulfonyl)ketenimines are not calculated to be linear, the barriers are so low that crystal lattice forces can induce planarity in N-methylbis(methylsulfonyl)ketenimine 3.

  18. Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix

    Directory of Open Access Journals (Sweden)

    Yanpeng Zheng

    2015-01-01

    Full Text Available The well known circulant matrices are applied to solve networked systems. In this paper, circulant and left circulant matrices with the Fermat and Mersenne numbers are considered. The nonsingularity of these special matrices is discussed. Meanwhile, the exact determinants and inverse matrices of these special matrices are presented.

  19. Massively parallel performance of neutron transport response matrix algorithms

    International Nuclear Information System (INIS)

    Hanebutte, U.R.; Lewis, E.E.

    1993-01-01

    Massively parallel red/black response matrix algorithms for the solution of within-group neutron transport problems are implemented on the Connection Machines-2, 200 and 5. The response matrices are dericed from the diamond-differences and linear-linear nodal discrete ordinate and variational nodal P 3 approximations. The unaccelerated performance of the iterative procedure is examined relative to the maximum rated performances of the machines. The effects of processor partitions size, of virtual processor ratio and of problems size are examined in detail. For the red/black algorithm, the ratio of inter-node communication to computing times is found to be quite small, normally of the order of ten percent or less. Performance increases with problems size and with virtual processor ratio, within the memeory per physical processor limitation. Algorithm adaptation to courser grain machines is straight-forward, with total computing time being virtually inversely proportional to the number of physical processors. (orig.)

  20. Inverse dose-rate-effects on the expressions of extra-cellular matrix-related genes in low-dose-rate γ-ray irradiated murine cells

    International Nuclear Information System (INIS)

    Sugihara, Takashi; Tanaka, Kimio; Oghiso, Yoichi; Murano, Hayato

    2008-01-01

    Based on the results of previous microarray analyses of murine NIH3T3/PG13Luc cells irradiated with continuous low-dose-rate (LDR) γ-ray or end-high-dose-rate-irradiations (end-HDR) at the end of the LDR-irradiation period, the inverse dose-rate-effects on gene expression levels were observed. To compare differences of the effects between LDR-irradiation and HDR-irradiation, HDR-irradiations at 2 different times, one (ini-HDR) at the same time at the start of LDR-irradiation and the other (end-HDR), were performed. The up-regulated genes were classified into two types, in which one was up-regulated in LDR-, ini-HDR-, and end-HDR irradiation such as Cdkn1a and Ccng1, which were reported as p53-dependent genes, and the other was up-regulated in LDR- and ini-HDR irradiations such as pro-collagen TypeIa2/Colla2, TenascinC/Tnc, and Fibulin5/Fbln5, which were reported as extra-cellular matrix-related (ECM) genes. The time dependent gene expression patterns in LDR-irradiation were also classified into two types, in which one was an early response such as in Cdkn1a and Ccng1 and the other was a delayed response such as the ECM genes which have no linearity to total dose. The protein expression pattern of Cdkn1a increased dose dependently in LDR- and end-HDR-irradiations, but those of p53Ser15/18 and MDM2 in LDR-irradiations were different from end-HDR-irradiations. Furthermore, the gene expression levels of the ECM genes in embryonic fibroblasts from p53-deficient mice were not increased by LDR- and end-HDR-irradiation, so the delayed expressions of the ECM genes seem to be regulated by p53. Consequently, the inverse dose-rate-effects on the expression levels of the ECM genes in LDR- and end-HDR-irradiations may be explained from different time responses by p53 status. (author)

  1. Probabilistic inversion in priority setting of emerging zoonoses.

    NARCIS (Netherlands)

    Kurowicka, D.; Bucura, C.; Cooke, R.; Havelaar, A.H.

    2010-01-01

    This article presents methodology of applying probabilistic inversion in combination with expert judgment in priority setting problem. Experts rank scenarios according to severity. A linear multi-criteria analysis model underlying the expert preferences is posited. Using probabilistic inversion, a

  2. Linear Algebraic Method for Non-Linear Map Analysis

    International Nuclear Information System (INIS)

    Yu, L.; Nash, B.

    2009-01-01

    We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.

  3. Pulsed laser deposition of the lysozyme protein: an unexpected “Inverse MAPLE” process

    DEFF Research Database (Denmark)

    Schou, Jørgen; Matei, Andreea; Constantinescu, Catalin

    2012-01-01

    Films of organic materials are commonly deposited by laser assisted methods, such as MAPLE (matrix-assisted pulsed laser evaporation), where a few percent of the film material in the target is protected by a light-absorbing volatile matrix. Another possibility is to irradiate the dry organic...... the ejection and deposition of lysozyme. This can be called an “inverse MAPLE” process, since the ratio of “matrix” to film material in the target is 10:90, which is inverse of the typical MAPLE process where the film material is dissolved in the matrix down to several wt.%. Lysozyme is a well-known protein...

  4. ITMETH, Iterative Routines for Linear System

    International Nuclear Information System (INIS)

    Greenbaum, A.

    1989-01-01

    1 - Description of program or function: ITMETH is a collection of iterative routines for solving large, sparse linear systems. 2 - Method of solution: ITMETH solves general linear systems of the form AX=B using a variety of methods: Jacobi iteration; Gauss-Seidel iteration; incomplete LU decomposition or matrix splitting with iterative refinement; diagonal scaling, matrix splitting, or incomplete LU decomposition with the conjugate gradient method for the problem AA'Y=B, X=A'Y; bi-conjugate gradient method with diagonal scaling, matrix splitting, or incomplete LU decomposition; and ortho-min method with diagonal scaling, matrix splitting, or incomplete LU decomposition. ITMETH also solves symmetric positive definite linear systems AX=B using the conjugate gradient method with diagonal scaling or matrix splitting, or the incomplete Cholesky conjugate gradient method

  5. Computer-Aided Numerical Inversion of Laplace Transform

    Directory of Open Access Journals (Sweden)

    Umesh Kumar

    2000-01-01

    Full Text Available This paper explores the technique for the computer aided numerical inversion of Laplace transform. The inversion technique is based on the properties of a family of three parameter exponential probability density functions. The only limitation in the technique is the word length of the computer being used. The Laplace transform has been used extensively in the frequency domain solution of linear, lumped time invariant networks but its application to the time domain has been limited, mainly because of the difficulty in finding the necessary poles and residues. The numerical inversion technique mentioned above does away with the poles and residues but uses precomputed numbers to find the time response. This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.

  6. Linear precoding based on polynomial expansion: reducing complexity in massive MIMO

    KAUST Repository

    Mueller, Axel

    2016-02-29

    Massive multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non-linear precoding are solved more or less automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the close-to-optimal and relatively “antenna-efficient” regularized zero-forcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion and multiplication by a truncated polynomial expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for real-time hardware implementation and significantly reduces the delay to the first transmitted symbol. The degree of the matrix polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission and more advanced RZF. By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.

  7. Stabilizing inverse problems by internal data. II: non-local internal data and generic linearized uniqueness

    KAUST Repository

    Kuchment, Peter

    2015-05-10

    © 2015, Springer Basel. In the previous paper (Kuchment and Steinhauer in Inverse Probl 28(8):084007, 2012), the authors introduced a simple procedure that allows one to detect whether and explain why internal information arising in several novel coupled physics (hybrid) imaging modalities could turn extremely unstable techniques, such as optical tomography or electrical impedance tomography, into stable, good-resolution procedures. It was shown that in all cases of interest, the Fréchet derivative of the forward mapping is a pseudo-differential operator with an explicitly computable principal symbol. If one can set up the imaging procedure in such a way that the symbol is elliptic, this would indicate that the problem was stabilized. In the cases when the symbol is not elliptic, the technique suggests how to change the procedure (e.g., by adding extra measurements) to achieve ellipticity. In this article, we consider the situation arising in acousto-optical tomography (also called ultrasound modulated optical tomography), where the internal data available involves the Green’s function, and thus depends globally on the unknown parameter(s) of the equation and its solution. It is shown that the technique of (Kuchment and Steinhauer in Inverse Probl 28(8):084007, 2012) can be successfully adopted to this situation as well. A significant part of the article is devoted to results on generic uniqueness for the linearized problem in a variety of situations, including those arising in acousto-electric and quantitative photoacoustic tomography.

  8. Approximation of the inverse G-frame operator

    Indian Academy of Sciences (India)

    ... projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we like using finite-dimensional linear algebra.

  9. Waveform inversion for orthorhombic anisotropy with P-waves: feasibility & resolution

    KAUST Repository

    Kazei, Vladimir

    2018-01-27

    Various parameterizations have been suggested to simplify inversions of first arrivals, or P −waves, in orthorhombic anisotropic media, but the number and type of retrievable parameters have not been decisively determined. We show that only six parameters can be retrieved from the dynamic linearized inversion of P −waves. These parameters are different from the six parameters needed to describe the kinematics of P −waves. Reflection-based radiation patterns from the P − P scattered waves are remapped into the spectral domain to allow for our resolution analysis based on the effective angle of illumination concept. Singular value decomposition of the spectral sensitivities from various azimuths, offset coverage scenarios, and data bandwidths allows us to quantify the resolution of different parameterizations, taking into account the signal-to-noise ratio in a given experiment. According to our singular value analysis, when the primary goal of inversion is determining the velocity of the P −waves, gradually adding anisotropy of lower orders (isotropic, vertically transversally isotropic, orthorhombic) in hierarchical parameterization is the best choice. Hierarchical parametrization reduces the tradeoff between the parameters and makes gradual introduction of lower anisotropy orders straightforward. When all the anisotropic parameters affecting P −wave propagation need to be retrieved simultaneously, the classic parameterization of orthorhombic medium with elastic stiffness matrix coefficients and density is a better choice for inversion. We provide estimates of the number and set of parameters that can be retrieved from surface seismic data in different acquisition scenarios. To set up an inversion process, the singular values determine the number of parameters that can be inverted and the resolution matrices from the parameterizations can be used to ascertain the set of parameters that can be resolved.

  10. Magnetotelluric inversion via reverse time migration algorithm of seismic data

    International Nuclear Information System (INIS)

    Ha, Taeyoung; Shin, Changsoo

    2007-01-01

    We propose a new algorithm for two-dimensional magnetotelluric (MT) inversion. Our algorithm is an MT inversion based on the steepest descent method, borrowed from the backpropagation technique of seismic inversion or reverse time migration, introduced in the middle 1980s by Lailly and Tarantola. The steepest descent direction can be calculated efficiently by using the symmetry of numerical Green's function derived from a mixed finite element method proposed by Nedelec for Maxwell's equation, without calculating the Jacobian matrix explicitly. We construct three different objective functions by taking the logarithm of the complex apparent resistivity as introduced in the recent waveform inversion algorithm by Shin and Min. These objective functions can be naturally separated into amplitude inversion, phase inversion and simultaneous inversion. We demonstrate our algorithm by showing three inversion results for synthetic data

  11. A cut-&-paste strategy for the 3-D inversion of helicopter-borne electromagnetic data - I. 3-D inversion using the explicit Jacobian and a tensor-based formulation

    Science.gov (United States)

    Scheunert, M.; Ullmann, A.; Afanasjew, M.; Börner, R.-U.; Siemon, B.; Spitzer, K.

    2016-06-01

    We present an inversion concept for helicopter-borne frequency-domain electromagnetic (HEM) data capable of reconstructing 3-D conductivity structures in the subsurface. Standard interpretation procedures often involve laterally constrained stitched 1-D inversion techniques to create pseudo-3-D models that are largely representative for smoothly varying conductivity distributions in the subsurface. Pronounced lateral conductivity changes may, however, produce significant artifacts that can lead to serious misinterpretation. Still, 3-D inversions of entire survey data sets are numerically very expensive. Our approach is therefore based on a cut-&-paste strategy whereupon the full 3-D inversion needs to be applied only to those parts of the survey where the 1-D inversion actually fails. The introduced 3-D Gauss-Newton inversion scheme exploits information given by a state-of-the-art (laterally constrained) 1-D inversion. For a typical HEM measurement, an explicit representation of the Jacobian matrix is inevitable which is caused by the unique transmitter-receiver relation. We introduce tensor quantities which facilitate the matrix assembly of the forward operator as well as the efficient calculation of the Jacobian. The finite difference forward operator incorporates the displacement currents because they may seriously affect the electromagnetic response at frequencies above 100. Finally, we deliver the proof of concept for the inversion using a synthetic data set with a noise level of up to 5%.

  12. Ground states of linear rotor chains via the density matrix renormalization group

    Science.gov (United States)

    Iouchtchenko, Dmitri; Roy, Pierre-Nicholas

    2018-04-01

    In recent years, experimental techniques have enabled the creation of ultracold optical lattices of molecules and endofullerene peapod nanomolecular assemblies. It was previously suggested that the rotor model resulting from the placement of dipolar linear rotors in one-dimensional lattices at low temperature has a transition between ordered and disordered phases. We use the density matrix renormalization group (DMRG) to compute ground states of chains of up to 100 rotors and provide further evidence of the phase transition in the form of a diverging entanglement entropy. We also propose two methods and present some first steps toward rotational spectra of such molecular assemblies using DMRG. The present work showcases the power of DMRG in this new context of interacting molecular rotors and opens the door to the study of fundamental questions regarding criticality in systems with continuous degrees of freedom.

  13. Optimized nonlinear inversion of surface-wave dispersion data

    International Nuclear Information System (INIS)

    Raykova, Reneta B.

    2014-01-01

    A new code for inversion of surface wave dispersion data is developed to obtain Earth’s crustal and upper mantle velocity structure. The author developed Optimized Non–Linear Inversion ( ONLI ) software, based on Monte-Carlo search. The values of S–wave velocity VS and thickness h for a number of horizontal homogeneous layers are parameterized. Velocity of P–wave VP and density ρ of relevant layers are calculated by empirical or theoretical relations. ONLI explores parameters space in two modes, selective and full search, and the main innovation of software is evaluation of tested models. Theoretical dispersion curves are calculated if tested model satisfied specific conditions only, reducing considerably the computation time. A number of tests explored impact of parameterization and proved the ability of ONLI approach to deal successfully with non–uniqueness of inversion problem. Key words: Earth’s structure, surface–wave dispersion, non–linear inversion, software

  14. Massively Parallel Geostatistical Inversion of Coupled Processes in Heterogeneous Porous Media

    Science.gov (United States)

    Ngo, A.; Schwede, R. L.; Li, W.; Bastian, P.; Ippisch, O.; Cirpka, O. A.

    2012-04-01

    The quasi-linear geostatistical approach is an inversion scheme that can be used to estimate the spatial distribution of a heterogeneous hydraulic conductivity field. The estimated parameter field is considered to be a random variable that varies continuously in space, meets the measurements of dependent quantities (such as the hydraulic head, the concentration of a transported solute or its arrival time) and shows the required spatial correlation (described by certain variogram models). This is a method of conditioning a parameter field to observations. Upon discretization, this results in as many parameters as elements of the computational grid. For a full three dimensional representation of the heterogeneous subsurface it is hardly sufficient to work with resolutions (up to one million parameters) of the model domain that can be achieved on a serial computer. The forward problems to be solved within the inversion procedure consists of the elliptic steady-state groundwater flow equation and the formally elliptic but nearly hyperbolic steady-state advection-dominated solute transport equation in a heterogeneous porous medium. Both equations are discretized by Finite Element Methods (FEM) using fully scalable domain decomposition techniques. Whereas standard conforming FEM is sufficient for the flow equation, for the advection dominated transport equation, which rises well known numerical difficulties at sharp fronts or boundary layers, we use the streamline diffusion approach. The arising linear systems are solved using efficient iterative solvers with an AMG (algebraic multigrid) pre-conditioner. During each iteration step of the inversion scheme one needs to solve a multitude of forward and adjoint problems in order to calculate the sensitivities of each measurement and the related cross-covariance matrix of the unknown parameters and the observations. In order to reduce interprocess communications and to improve the scalability of the code on larger clusters

  15. Green's matrix for a second-order self-adjoint matrix differential operator

    International Nuclear Information System (INIS)

    Sisman, Tahsin Cagri; Tekin, Bayram

    2010-01-01

    A systematic construction of the Green's matrix for a second-order self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the general approach of extracting the Green's matrix from the Green's matrix of the corresponding first-order system. This construction is required in the cases where the differential equation set cannot be turned to an algebraic equation set via transform techniques.

  16. Linear versus non-linear structural information limit in high-resolution transmission electron microscopy

    International Nuclear Information System (INIS)

    Van Aert, S.; Chen, J.H.; Van Dyck, D.

    2010-01-01

    A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has

  17. H{infinity} Filtering for Dynamic Compensation of Self-Powered Neutron Detectors - A Linear Matrix Inequality Based Method -

    Energy Technology Data Exchange (ETDEWEB)

    Park, M.G.; Kim, Y.H.; Cha, K.H.; Kim, M.K. [Korea Electric Power Research Institute, Taejon (Korea)

    1999-07-01

    A method is described to develop and H{infinity} filtering method for the dynamic compensation of self-powered neutron detectors normally used for fixed incore instruments. An H{infinity} norm of the filter transfer matrix is used as the optimization criteria in the worst-case estimation error sense. Filter modeling is performed for both continuous- and discrete-time models. The filter gains are optimized in the sense of noise attenuation level of H{infinity} setting. By introducing Bounded Real Lemma, the conventional algebraic Riccati inequalities are converted into Linear Matrix Inequalities (LMIs). Finally, the filter design problem is solved via the convex optimization framework using LMIs. The simulation results show that remarkable improvements are achieved in view of the filter response time and the filter design efficiency. (author). 15 refs., 4 figs., 3 tabs.

  18. Statistical perspectives on inverse problems

    DEFF Research Database (Denmark)

    Andersen, Kim Emil

    of the interior of an object from electrical boundary measurements. One part of this thesis concerns statistical approaches for solving, possibly non-linear, inverse problems. Thus inverse problems are recasted in a form suitable for statistical inference. In particular, a Bayesian approach for regularisation...... problem is given in terms of probability distributions. Posterior inference is obtained by Markov chain Monte Carlo methods and new, powerful simulation techniques based on e.g. coupled Markov chains and simulated tempering is developed to improve the computational efficiency of the overall simulation......Inverse problems arise in many scientific disciplines and pertain to situations where inference is to be made about a particular phenomenon from indirect measurements. A typical example, arising in diffusion tomography, is the inverse boundary value problem for non-invasive reconstruction...

  19. Viscoelastic material inversion using Sierra-SD and ROL

    Energy Technology Data Exchange (ETDEWEB)

    Walsh, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Aquino, Wilkins [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ridzal, Denis [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Kouri, Drew Philip [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); van Bloemen Waanders, Bart Gustaaf [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Urbina, Angel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2014-11-01

    In this report we derive frequency-domain methods for inverse characterization of the constitutive parameters of viscoelastic materials. The inverse problem is cast in a PDE-constrained optimization framework with efficient computation of gradients and Hessian vector products through matrix free operations. The abstract optimization operators for first and second derivatives are derived from first principles. Various methods from the Rapid Optimization Library (ROL) are tested on the viscoelastic inversion problem. The methods described herein are applied to compute the viscoelastic bulk and shear moduli of a foam block model, which was recently used in experimental testing for viscoelastic property characterization.

  20. Transfer matrix method for dynamics modeling and independent modal space vibration control design of linear hybrid multibody system

    Science.gov (United States)

    Rong, Bao; Rui, Xiaoting; Lu, Kun; Tao, Ling; Wang, Guoping; Ni, Xiaojun

    2018-05-01

    In this paper, an efficient method of dynamics modeling and vibration control design of a linear hybrid multibody system (MS) is studied based on the transfer matrix method. The natural vibration characteristics of a linear hybrid MS are solved by using low-order transfer equations. Then, by constructing the brand-new body dynamics equation, augmented operator and augmented eigenvector, the orthogonality of augmented eigenvector of a linear hybrid MS is satisfied, and its state space model expressed in each independent model space is obtained easily. According to this dynamics model, a robust independent modal space-fuzzy controller is designed for vibration control of a general MS, and the genetic optimization of some critical control parameters of fuzzy tuners is also presented. Two illustrative examples are performed, which results show that this method is computationally efficient and with perfect control performance.

  1. Support Minimized Inversion of Acoustic and Elastic Wave Scattering

    Science.gov (United States)

    Safaeinili, Ali

    Inversion of limited data is common in many areas of NDE such as X-ray Computed Tomography (CT), Ultrasonic and eddy current flaw characterization and imaging. In many applications, it is common to have a bias toward a solution with minimum (L^2)^2 norm without any physical justification. When it is a priori known that objects are compact as, say, with cracks and voids, by choosing "Minimum Support" functional instead of the minimum (L^2)^2 norm, an image can be obtained that is equally in agreement with the available data, while it is more consistent with what is most probably seen in the real world. We have utilized a minimum support functional to find a solution with the smallest volume. This inversion algorithm is most successful in reconstructing objects that are compact like voids and cracks. To verify this idea, we first performed a variational nonlinear inversion of acoustic backscatter data using minimum support objective function. A full nonlinear forward model was used to accurately study the effectiveness of the minimized support inversion without error due to the linear (Born) approximation. After successful inversions using a full nonlinear forward model, a linearized acoustic inversion was developed to increase speed and efficiency in imaging process. The results indicate that by using minimum support functional, we can accurately size and characterize voids and/or cracks which otherwise might be uncharacterizable. An extremely important feature of support minimized inversion is its ability to compensate for unknown absolute phase (zero-of-time). Zero-of-time ambiguity is a serious problem in the inversion of the pulse-echo data. The minimum support inversion was successfully used for the inversion of acoustic backscatter data due to compact scatterers without the knowledge of the zero-of-time. The main drawback to this type of inversion is its computer intensiveness. In order to make this type of constrained inversion available for common use, work

  2. Anisotropic magnetotelluric inversion using a mutual information constraint

    Science.gov (United States)

    Mandolesi, E.; Jones, A. G.

    2012-12-01

    In recent years, several authors pointed that the electrical conductivity of many subsurface structures cannot be described properly by a scalar field. With the development of field devices and techniques, data quality improved to the point that the anisotropy in conductivity of rocks (microscopic anisotropy) and tectonic structures (macroscopic anisotropy) cannot be neglected. Therefore a correct use of high quality data has to include electrical anisotropy and a correct interpretation of anisotropic data characterizes directly a non-negligible part of the subsurface. In this work we test an inversion routine that takes advantage of the classic Levenberg-Marquardt (LM) algorithm to invert magnetotelluric (MT) data generated from a bi-dimensional (2D) anisotropic domain. The LM method is routinely used in inverse problems due its performance and robustness. In non-linear inverse problems -such the MT problem- the LM method provides a spectacular compromise betwee quick and secure convergence at the price of the explicit computation and storage of the sensitivity matrix. Regularization in inverse MT problems has been used extensively, due to the necessity to constrain model space and to reduce the ill-posedness of the anisotropic MT problem, which makes MT inversions extremely challenging. In order to reduce non-uniqueness of the MT problem and to reach a model compatible with other different tomographic results from the same target region, we used a mutual information (MI) based constraint. MI is a basic quantity in information theory that can be used to define a metric between images, and it is routinely used in fields as computer vision, image registration and medical tomography, to cite some applications. We -thus- inverted for the model that best fits the anisotropic data and that is the closest -in a MI sense- to a tomographic model of the target area. The advantage of this technique is that the tomographic model of the studied region may be produced by any

  3. Geostatistical regularization operators for geophysical inverse problems on irregular meshes

    Science.gov (United States)

    Jordi, C.; Doetsch, J.; Günther, T.; Schmelzbach, C.; Robertsson, J. OA

    2018-05-01

    Irregular meshes allow to include complicated subsurface structures into geophysical modelling and inverse problems. The non-uniqueness of these inverse problems requires appropriate regularization that can incorporate a priori information. However, defining regularization operators for irregular discretizations is not trivial. Different schemes for calculating smoothness operators on irregular meshes have been proposed. In contrast to classical regularization constraints that are only defined using the nearest neighbours of a cell, geostatistical operators include a larger neighbourhood around a particular cell. A correlation model defines the extent of the neighbourhood and allows to incorporate information about geological structures. We propose an approach to calculate geostatistical operators for inverse problems on irregular meshes by eigendecomposition of a covariance matrix that contains the a priori geological information. Using our approach, the calculation of the operator matrix becomes tractable for 3-D inverse problems on irregular meshes. We tested the performance of the geostatistical regularization operators and compared them against the results of anisotropic smoothing in inversions of 2-D surface synthetic electrical resistivity tomography (ERT) data as well as in the inversion of a realistic 3-D cross-well synthetic ERT scenario. The inversions of 2-D ERT and seismic traveltime field data with geostatistical regularization provide results that are in good accordance with the expected geology and thus facilitate their interpretation. In particular, for layered structures the geostatistical regularization provides geologically more plausible results compared to the anisotropic smoothness constraints.

  4. Treatment of pauli exclusion operator in G-matrix calculations for hypernuclei

    International Nuclear Information System (INIS)

    Kuo, T.T.S.; Hao, Jifa

    1995-01-01

    We discuss a matrix-inversion method for treating the Pauli exclusion operator Q in the hyperon-nucleon G-matrix equation for hypernuclei such as Λ 16 O. A model space consisted of shell-model wave functions is employed. We discuss that it is preferable to employ a free-particle spectrum for the intermediate states of the G matrix. This leads to the difficulty that the G-matrix intermediate states are plane waves and on this representation the Pauli operator Q has a rather complicated structure. A matrix-inversion method for over-coming this difficulty is examined. To implement this method it is necessary to employ a so-called n 3Λ truncation approximation. Numerical calculations using the Juelich B tilde and A tilde potentials have been performed to study the accuracy of this approximation. (author)

  5. Eikonal-Based Inversion of GPR Data from the Vaucluse Karst Aquifer

    Science.gov (United States)

    Yedlin, M. J.; van Vorst, D.; Guglielmi, Y.; Cappa, F.; Gaffet, S.

    2009-12-01

    In this paper, we present an easy-to-implement eikonal-based travel time inversion algorithm and apply it to borehole GPR measurement data obtained from a karst aquifer located in the Vaucluse in Provence. The boreholes are situated with a fault zone deep inside the aquifer, in the Laboratoire Souterrain à Bas Bruit (LSBB). The measurements were made using 250 MHz MALA RAMAC borehole GPR antennas. The inversion formulation is unique in its application of a fast-sweeping eikonal solver (Zhao [1]) to the minimization of an objective functional that is composed of a travel time misfit and a model-based regularization [2]. The solver is robust in the presence of large velocity contrasts, efficient, easy to implement, and does not require the use of a sorting algorithm. The computation of sensitivities, which are required for the inversion process, is achieved by tracing rays backward from receiver to source following the gradient of the travel time field [2]. A user wishing to implement this algorithm can opt to avoid the ray tracing step and simply perturb the model to obtain the required sensitivities. Despite the obvious computational inefficiency of such an approach, it is acceptable for 2D problems. The relationship between travel time and the velocity profile is non-linear, requiring an iterative approach to be used. At each iteration, a set of matrix equations is solved to determine the model update. As the inversion continues, the weighting of the regularization parameter is adjusted until an appropriate data misfit is obtained. The inversion results, shown in the attached image, are consistent with previously obtained geological structure. Future work will look at improving inversion resolution and incorporating other measurement methodologies, with the goal of providing useful data for groundwater analysis. References: [1] H. Zhao, “A fast sweeping method for Eikonal equations,” Mathematics of Computation, vol. 74, no. 250, pp. 603-627, 2004. [2] D

  6. A Reduced-Order Successive Linear Estimator for Geostatistical Inversion and its Application in Hydraulic Tomography

    Science.gov (United States)

    Zha, Yuanyuan; Yeh, Tian-Chyi J.; Illman, Walter A.; Zeng, Wenzhi; Zhang, Yonggen; Sun, Fangqiang; Shi, Liangsheng

    2018-03-01

    Hydraulic tomography (HT) is a recently developed technology for characterizing high-resolution, site-specific heterogeneity using hydraulic data (nd) from a series of cross-hole pumping tests. To properly account for the subsurface heterogeneity and to flexibly incorporate additional information, geostatistical inverse models, which permit a large number of spatially correlated unknowns (ny), are frequently used to interpret the collected data. However, the memory storage requirements for the covariance of the unknowns (ny × ny) in these models are prodigious for large-scale 3-D problems. Moreover, the sensitivity evaluation is often computationally intensive using traditional difference method (ny forward runs). Although employment of the adjoint method can reduce the cost to nd forward runs, the adjoint model requires intrusive coding effort. In order to resolve these issues, this paper presents a Reduced-Order Successive Linear Estimator (ROSLE) for analyzing HT data. This new estimator approximates the covariance of the unknowns using Karhunen-Loeve Expansion (KLE) truncated to nkl order, and it calculates the directional sensitivities (in the directions of nkl eigenvectors) to form the covariance and cross-covariance used in the Successive Linear Estimator (SLE). In addition, the covariance of unknowns is updated every iteration by updating the eigenvalues and eigenfunctions. The computational advantages of the proposed algorithm are demonstrated through numerical experiments and a 3-D transient HT analysis of data from a highly heterogeneous field site.

  7. Analog fault diagnosis by inverse problem technique

    KAUST Repository

    Ahmed, Rania F.

    2011-12-01

    A novel algorithm for detecting soft faults in linear analog circuits based on the inverse problem concept is proposed. The proposed approach utilizes optimization techniques with the aid of sensitivity analysis. The main contribution of this work is to apply the inverse problem technique to estimate the actual parameter values of the tested circuit and so, to detect and diagnose single fault in analog circuits. The validation of the algorithm is illustrated through applying it to Sallen-Key second order band pass filter and the results show that the detecting percentage efficiency was 100% and also, the maximum error percentage of estimating the parameter values is 0.7%. This technique can be applied to any other linear circuit and it also can be extended to be applied to non-linear circuits. © 2011 IEEE.

  8. On the joint inversion of SGG and SST data from the GOCE mission

    Directory of Open Access Journals (Sweden)

    P. Ditmar

    2003-01-01

    Full Text Available The computation of spherical harmonic coefficients of the Earth’s gravity field from satellite-to-satellite tracking (SST data and satellite gravity gradiometry (SGG data is considered. As long as the functional model related to SST data contains nuisance parameters (e.g. unknown initial state vectors, assembling of the corresponding normal matrix must be supplied with the back-substitution operation, so that the nuisance parameters are excluded from consideration. The traditional back-substitution algorithm, however, may result in large round-off errors. Hence an alternative approach, back-substitution at the level of the design matrix, is implemented. Both a stand-alone inversion of either type of data and a joint inversion of both types are considered. The conclusion drawn is that the joint inversion results in a much better model of the Earth’s gravity field than a standalone inversion. Furthermore, two numerical techniques for solving the joint system of normal equations are compared: (i the Cholesky method based on an explicit computation of the normal matrix, and (ii the pre-conditioned conjugate gradient method (PCCG, for which an explicit computation of the entire normal matrix is not needed. The comparison shows that the PCCG method is much faster than the Cholesky method.Key words. Earth’s gravity field, GOCE, satellite-tosatellite tracking, satellite gravity gradiometry, backsubstitution

  9. On the Resolution of Inversion for Orthorhombic Anisotropy

    KAUST Repository

    Kazei, Vladimir

    2017-05-26

    We investigate the resolution of elastic anisotropic inversion for orthorhombic media with P-waves by remapping classic radiation patterns into the wavenumber domain. We show analytically that dynamic linearized inversion (linearized reverse-time migration and full-waveform inversion) for orthorhombic anisotropy based on longitudinal waves is fundamentally sensitive to emph{six} parameters only and density, in which the perturbing effects can be represented by particular anisotropy configuration. Singular value decomposition of spectral sensitivities allows us to provide estimates of the number of parameters one could invert in specific acquisition settings, and with certain parametrization. In most acquisition scenarios, a hierarchical parameterization based on the $P$, and $S$-wave velocities, along with dimensionless parameters that describe the anisotropy as velocity ratio in the radial and azimuthal directions, minimizes the tradeoff and increases the sensitivity of the data to velocity compared to the standard (stiffness, density) parametrization. These features yield more robust velocity estimation, by focusing the inversion on a subset of invertible parameters.

  10. On the Resolution of Inversion for Orthorhombic Anisotropy

    KAUST Repository

    Kazei, Vladimir; Alkhalifah, Tariq Ali

    2017-01-01

    We investigate the resolution of elastic anisotropic inversion for orthorhombic media with P-waves by remapping classic radiation patterns into the wavenumber domain. We show analytically that dynamic linearized inversion (linearized reverse-time migration and full-waveform inversion) for orthorhombic anisotropy based on longitudinal waves is fundamentally sensitive to emph{six} parameters only and density, in which the perturbing effects can be represented by particular anisotropy configuration. Singular value decomposition of spectral sensitivities allows us to provide estimates of the number of parameters one could invert in specific acquisition settings, and with certain parametrization. In most acquisition scenarios, a hierarchical parameterization based on the $P$, and $S$-wave velocities, along with dimensionless parameters that describe the anisotropy as velocity ratio in the radial and azimuthal directions, minimizes the tradeoff and increases the sensitivity of the data to velocity compared to the standard (stiffness, density) parametrization. These features yield more robust velocity estimation, by focusing the inversion on a subset of invertible parameters.

  11. Minimization of Linear Functionals Defined on| Solutions of Large-Scale Discrete Ill-Posed Problems

    DEFF Research Database (Denmark)

    Elden, Lars; Hansen, Per Christian; Rojas, Marielba

    2003-01-01

    The minimization of linear functionals de ned on the solutions of discrete ill-posed problems arises, e.g., in the computation of con dence intervals for these solutions. In 1990, Elden proposed an algorithm for this minimization problem based on a parametric-programming reformulation involving...... the solution of a sequence of trust-region problems, and using matrix factorizations. In this paper, we describe MLFIP, a large-scale version of this algorithm where a limited-memory trust-region solver is used on the subproblems. We illustrate the use of our algorithm in connection with an inverse heat...

  12. Introduction to computational linear algebra

    CERN Document Server

    Nassif, Nabil; Erhel, Jocelyne

    2015-01-01

    Introduction to Computational Linear Algebra introduces the reader with a background in basic mathematics and computer programming to the fundamentals of dense and sparse matrix computations with illustrating examples. The textbook is a synthesis of conceptual and practical topics in ""Matrix Computations."" The book's learning outcomes are twofold: to understand state-of-the-art computational tools to solve matrix computations problems (BLAS primitives, MATLAB® programming) as well as essential mathematical concepts needed to master the topics of numerical linear algebra. It is suitable for s

  13. Matrix with Prescribed Eigenvectors

    Science.gov (United States)

    Ahmad, Faiz

    2011-01-01

    It is a routine matter for undergraduates to find eigenvalues and eigenvectors of a given matrix. But the converse problem of finding a matrix with prescribed eigenvalues and eigenvectors is rarely discussed in elementary texts on linear algebra. This problem is related to the "spectral" decomposition of a matrix and has important technical…

  14. Inverse scattering with supersymmetric quantum mechanics

    International Nuclear Information System (INIS)

    Baye, Daniel; Sparenberg, Jean-Marc

    2004-01-01

    The application of supersymmetric quantum mechanics to the inverse scattering problem is reviewed. The main difference with standard treatments of the inverse problem lies in the simple and natural extension to potentials with singularities at the origin and with a Coulomb behaviour at infinity. The most general form of potentials which are phase-equivalent to a given potential is discussed. The use of singular potentials allows adding or removing states from the bound spectrum without contradicting the Levinson theorem. Physical applications of phase-equivalent potentials in nuclear reactions and in three-body systems are described. Derivation of a potential from the phase shift at fixed orbital momentum can also be performed with the supersymmetric inversion by using a Bargmann-type approximation of the scattering matrix or phase shift. A unique singular potential without bound states can be obtained from any phase shift. A limited number of bound states depending on the singularity can then be added. This inversion procedure is illustrated with nucleon-nucleon scattering

  15. Efficient generalized Golub-Kahan based methods for dynamic inverse problems

    Science.gov (United States)

    Chung, Julianne; Saibaba, Arvind K.; Brown, Matthew; Westman, Erik

    2018-02-01

    We consider efficient methods for computing solutions to and estimating uncertainties in dynamic inverse problems, where the parameters of interest may change during the measurement procedure. Compared to static inverse problems, incorporating prior information in both space and time in a Bayesian framework can become computationally intensive, in part, due to the large number of unknown parameters. In these problems, explicit computation of the square root and/or inverse of the prior covariance matrix is not possible, so we consider efficient, iterative, matrix-free methods based on the generalized Golub-Kahan bidiagonalization that allow automatic regularization parameter and variance estimation. We demonstrate that these methods for dynamic inversion can be more flexible than standard methods and develop efficient implementations that can exploit structure in the prior, as well as possible structure in the forward model. Numerical examples from photoacoustic tomography, space-time deblurring, and passive seismic tomography demonstrate the range of applicability and effectiveness of the described approaches. Specifically, in passive seismic tomography, we demonstrate our approach on both synthetic and real data. To demonstrate the scalability of our algorithm, we solve a dynamic inverse problem with approximately 43 000 measurements and 7.8 million unknowns in under 40 s on a standard desktop.

  16. Efficient Brownian Dynamics of rigid colloids in linear flow fields based on the grand mobility matrix

    Science.gov (United States)

    Palanisamy, Duraivelan; den Otter, Wouter K.

    2018-05-01

    We present an efficient general method to simulate in the Stokesian limit the coupled translational and rotational dynamics of arbitrarily shaped colloids subject to external potential forces and torques, linear flow fields, and Brownian motion. The colloid's surface is represented by a collection of spherical primary particles. The hydrodynamic interactions between these particles, here approximated at the Rotne-Prager-Yamakawa level, are evaluated only once to generate the body's (11 × 11) grand mobility matrix. The constancy of this matrix in the body frame, combined with the convenient properties of quaternions in rotational Brownian Dynamics, enables an efficient simulation of the body's motion. Simulations in quiescent fluids yield correct translational and rotational diffusion behaviour and sample Boltzmann's equilibrium distribution. Simulations of ellipsoids and spherical caps under shear, in the absence of thermal fluctuations, yield periodic orbits in excellent agreement with the theories by Jeffery and Dorrepaal. The time-varying stress tensors provide the Einstein coefficient and viscosity of dilute suspensions of these bodies.

  17. Reactivity-induced time-dependencies of EBR-II linear and non-linear feedbacks

    International Nuclear Information System (INIS)

    Grimm, K.N.; Meneghetti, D.

    1988-01-01

    Time-dependent linear feedback reactivities are calculated for stereotypical subassemblies in the EBR-II reactor. These quantities are calculated from nodal reactivities obtained from a kinetic code analysis of an experiment in which the change in power resulted from the dropping of a control rod. Shown with these linear reactivities are the reactivity associated with the control-rod shaft contraction and also time-dependent non-linear (mainly bowing) component deduced from the inverse kinetics of the experimentally measured fission power and the calculated linear reactivities. (author)

  18. Waveform inversion for orthorhombic anisotropy with P waves: feasibility and resolution

    Science.gov (United States)

    Kazei, Vladimir; Alkhalifah, Tariq

    2018-05-01

    Various parametrizations have been suggested to simplify inversions of first arrivals, or P waves, in orthorhombic anisotropic media, but the number and type of retrievable parameters have not been decisively determined. We show that only six parameters can be retrieved from the dynamic linearized inversion of P waves. These parameters are different from the six parameters needed to describe the kinematics of P waves. Reflection-based radiation patterns from the P-P scattered waves are remapped into the spectral domain to allow for our resolution analysis based on the effective angle of illumination concept. Singular value decomposition of the spectral sensitivities from various azimuths, offset coverage scenarios and data bandwidths allows us to quantify the resolution of different parametrizations, taking into account the signal-to-noise ratio in a given experiment. According to our singular value analysis, when the primary goal of inversion is determining the velocity of the P waves, gradually adding anisotropy of lower orders (isotropic, vertically transversally isotropic and orthorhombic) in hierarchical parametrization is the best choice. Hierarchical parametrization reduces the trade-off between the parameters and makes gradual introduction of lower anisotropy orders straightforward. When all the anisotropic parameters affecting P-wave propagation need to be retrieved simultaneously, the classic parametrization of orthorhombic medium with elastic stiffness matrix coefficients and density is a better choice for inversion. We provide estimates of the number and set of parameters that can be retrieved from surface seismic data in different acquisition scenarios. To set up an inversion process, the singular values determine the number of parameters that can be inverted and the resolution matrices from the parametrizations can be used to ascertain the set of parameters that can be resolved.

  19. Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules.

    Science.gov (United States)

    Marrero-Ponce, Yovani; Martínez-Albelo, Eugenio R; Casañola-Martín, Gerardo M; Castillo-Garit, Juan A; Echevería-Díaz, Yunaimy; Zaldivar, Vicente Romero; Tygat, Jan; Borges, José E Rodriguez; García-Domenech, Ramón; Torrens, Francisco; Pérez-Giménez, Facundo

    2010-11-01

    Novel bond-level molecular descriptors are proposed, based on linear maps similar to the ones defined in algebra theory. The kth edge-adjacency matrix (E(k)) denotes the matrix of bond linear indices (non-stochastic) with regard to canonical basis set. The kth stochastic edge-adjacency matrix, ES(k), is here proposed as a new molecular representation easily calculated from E(k). Then, the kth stochastic bond linear indices are calculated using ES(k) as operators of linear transformations. In both cases, the bond-type formalism is developed. The kth non-stochastic and stochastic total linear indices are calculated by adding the kth non-stochastic and stochastic bond linear indices, respectively, of all bonds in molecule. First, the new bond-based molecular descriptors (MDs) are tested for suitability, for the QSPRs, by analyzing regressions of novel indices for selected physicochemical properties of octane isomers (first round). General performance of the new descriptors in this QSPR studies is evaluated with regard to the well-known sets of 2D/3D MDs. From the analysis, we can conclude that the non-stochastic and stochastic bond-based linear indices have an overall good modeling capability proving their usefulness in QSPR studies. Later, the novel bond-level MDs are also used for the description and prediction of the boiling point of 28 alkyl-alcohols (second round), and to the modeling of the specific rate constant (log k), partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (third round). The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) exposes a good behavior of our method in this QSPR studies. Finally, the approach described in this study appears to be a very promising structural invariant, useful not only for QSPR studies but also for similarity

  20. Introduction of a priori information in the elastic linearized inversion of seismic data before stacking; Introduction d'informations a priori dans l'inversion linearisee elastique de donnees sismiques de surface avant sommation

    Energy Technology Data Exchange (ETDEWEB)

    Tonellot, Th.L.

    2000-03-24

    In this thesis, we propose a method which takes into account a priori information (geological, diagraphic and stratigraphic knowledge) in linearized pre-stack seismic data inversion. The approach is based on a formalism in which the a priori information is incorporated in an a priori model of elastic parameters - density, P and S impedances - and a model covariance operator which describes the uncertainties in the model. The first part of the thesis is dedicated to the study of this covariance operator and to the norm associated to its inverse. We have generalized the exponential covariance operator in order to describe the uncertainties in the a priori model elastic parameters and their correlations at each location. We give the analytical expression of the covariance operator inverse in 1-D, 2-D, and 3-D, and we discretized the associated norm with a finite element method. The second part is dedicated to synthetic and real examples. In a preliminary step, we have developed a pre-stack data well calibration method which allows the estimation of the source signal. The impact of different a priori information is then demonstrated on synthetic and real data. (author)

  1. Approximate Solution of LR Fuzzy Sylvester Matrix Equations

    Directory of Open Access Journals (Sweden)

    Xiaobin Guo

    2013-01-01

    Full Text Available The fuzzy Sylvester matrix equation AX~+X~B=C~ in which A,B are m×m and n×n crisp matrices, respectively, and C~ is an m×n LR fuzzy numbers matrix is investigated. Based on the Kronecker product of matrices, we convert the fuzzy Sylvester matrix equation into an LR fuzzy linear system. Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. The existence condition of the LR fuzzy solution is also discussed. Some examples are given to illustrate the proposed method.

  2. Time-lapse three-dimensional inversion of complex conductivity data using an active time constrained (ATC) approach

    Science.gov (United States)

    Karaoulis, M.; Revil, A.; Werkema, D.D.; Minsley, B.J.; Woodruff, W.F.; Kemna, A.

    2011-01-01

    Induced polarization (more precisely the magnitude and phase of impedance of the subsurface) is measured using a network of electrodes located at the ground surface or in boreholes. This method yields important information related to the distribution of permeability and contaminants in the shallow subsurface. We propose a new time-lapse 3-D modelling and inversion algorithm to image the evolution of complex conductivity over time. We discretize the subsurface using hexahedron cells. Each cell is assigned a complex resistivity or conductivity value. Using the finite-element approach, we model the in-phase and out-of-phase (quadrature) electrical potentials on the 3-D grid, which are then transformed into apparent complex resistivity. Inhomogeneous Dirichlet boundary conditions are used at the boundary of the domain. The calculation of the Jacobian matrix is based on the principles of reciprocity. The goal of time-lapse inversion is to determine the change in the complex resistivity of each cell of the spatial grid as a function of time. Each model along the time axis is called a 'reference space model'. This approach can be simplified into an inverse problem looking for the optimum of several reference space models using the approximation that the material properties vary linearly in time between two subsequent reference models. Regularizations in both space domain and time domain reduce inversion artefacts and improve the stability of the inversion problem. In addition, the use of the time-lapse equations allows the simultaneous inversion of data obtained at different times in just one inversion step (4-D inversion). The advantages of this new inversion algorithm are demonstrated on synthetic time-lapse data resulting from the simulation of a salt tracer test in a heterogeneous random material described by an anisotropic semi-variogram. ?? 2011 The Authors Geophysical Journal International ?? 2011 RAS.

  3. ANNIT - An Efficient Inversion Algorithm based on Prediction Principles

    Science.gov (United States)

    Růžek, B.; Kolář, P.

    2009-04-01

    Solution of inverse problems represents meaningful job in geophysics. The amount of data is continuously increasing, methods of modeling are being improved and the computer facilities are also advancing great technical progress. Therefore the development of new and efficient algorithms and computer codes for both forward and inverse modeling is still up to date. ANNIT is contributing to this stream since it is a tool for efficient solution of a set of non-linear equations. Typical geophysical problems are based on parametric approach. The system is characterized by a vector of parameters p, the response of the system is characterized by a vector of data d. The forward problem is usually represented by unique mapping F(p)=d. The inverse problem is much more complex and the inverse mapping p=G(d) is available in an analytical or closed form only exceptionally and generally it may not exist at all. Technically, both forward and inverse mapping F and G are sets of non-linear equations. ANNIT solves such situation as follows: (i) joint subspaces {pD, pM} of original data and model spaces D, M, resp. are searched for, within which the forward mapping F is sufficiently smooth that the inverse mapping G does exist, (ii) numerical approximation of G in subspaces {pD, pM} is found, (iii) candidate solution is predicted by using this numerical approximation. ANNIT is working in an iterative way in cycles. The subspaces {pD, pM} are searched for by generating suitable populations of individuals (models) covering data and model spaces. The approximation of the inverse mapping is made by using three methods: (a) linear regression, (b) Radial Basis Function Network technique, (c) linear prediction (also known as "Kriging"). The ANNIT algorithm has built in also an archive of already evaluated models. Archive models are re-used in a suitable way and thus the number of forward evaluations is minimized. ANNIT is now implemented both in MATLAB and SCILAB. Numerical tests show good

  4. Linear analysis of rotationally invariant, radially variant tomographic imaging systems

    International Nuclear Information System (INIS)

    Huesmann, R.H.

    1990-01-01

    This paper describes a method to analyze the linear imaging characteristics of rotationally invariant, radially variant tomographic imaging systems using singular value decomposition (SVD). When the projection measurements from such a system are assumed to be samples from independent and identically distributed multi-normal random variables, the best estimate of the emission intensity is given by the unweighted least squares estimator. The noise amplification of this estimator is inversely proportional to the singular values of the normal matrix used to model projection and backprojection. After choosing an acceptable noise amplification, the new method can determine the number of parameters and hence the number of pixels that should be estimated from data acquired from an existing system with a fixed number of angles and projection bins. Conversely, for the design of a new system, the number of angles and projection bins necessary for a given number of pixels and noise amplification can be determined. In general, computing the SVD of the projection normal matrix has cubic computational complexity. However, the projection normal matrix for this class of rotationally invariant, radially variant systems has a block circulant form. A fast parallel algorithm to compute the SVD of this block circulant matrix makes the singular value analysis practical by asymptotically reducing the computation complexity of the method by a multiplicative factor equal to the number of angles squared

  5. Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems

    DEFF Research Database (Denmark)

    Adegas, Fabiano Daher; Stoustrup, Jakob

    2015-01-01

    the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems......SUMMARY Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between....... The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form. Copyright © 2014 John Wiley & Sons, Ltd....

  6. Numerical linear algebra theory and applications

    CERN Document Server

    Beilina, Larisa; Karchevskii, Mikhail

    2017-01-01

    This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

  7. Inverse scattering scheme for the Dirac equation at fixed energy

    International Nuclear Information System (INIS)

    Leeb, H.; Lehninger, H.; Schilder, C.

    2001-01-01

    Full text: Based on the concept of generalized transformation operators a new hierarchy of Dirac equations with spherical symmetric scalar and fourth component vector potentials is presented. Within this hierarchy closed form expressions for the solutions, the potentials and the S-matrix can be given in terms of solutions of the original Dirac equation. Using these transformations an inverse scattering scheme has been constructed for the Dirac equation which is the analog to the rational scheme in the non-relativistic case. The given method provides for the first time an inversion scheme with closed form expressions for the S-matrix for non-relativistic scattering problems with central and spin-orbit potentials. (author)

  8. On the inversion of geodetic integrals defined over the sphere using 1-D FFT

    Science.gov (United States)

    García, R. V.; Alejo, C. A.

    2005-08-01

    An iterative method is presented which performs inversion of integrals defined over the sphere. The method is based on one-dimensional fast Fourier transform (1-D FFT) inversion and is implemented with the projected Landweber technique, which is used to solve constrained least-squares problems reducing the associated 1-D cyclic-convolution error. The results obtained are as precise as the direct matrix inversion approach, but with better computational efficiency. A case study uses the inversion of Hotine’s integral to obtain gravity disturbances from geoid undulations. Numerical convergence is also analyzed and comparisons with respect to the direct matrix inversion method using conjugate gradient (CG) iteration are presented. Like the CG method, the number of iterations needed to get the optimum (i.e., small) error decreases as the measurement noise increases. Nevertheless, for discrete data given over a whole parallel band, the method can be applied directly without implementing the projected Landweber method, since no cyclic convolution error exists.

  9. Linear analysis near a steady-state of biochemical networks: control analysis, correlation metrics and circuit theory

    Directory of Open Access Journals (Sweden)

    Qian Hong

    2008-05-01

    Full Text Available Abstract Background: Several approaches, including metabolic control analysis (MCA, flux balance analysis (FBA, correlation metric construction (CMC, and biochemical circuit theory (BCT, have been developed for the quantitative analysis of complex biochemical networks. Here, we present a comprehensive theory of linear analysis for nonequilibrium steady-state (NESS biochemical reaction networks that unites these disparate approaches in a common mathematical framework and thermodynamic basis. Results: In this theory a number of relationships between key matrices are introduced: the matrix A obtained in the standard, linear-dynamic-stability analysis of the steady-state can be decomposed as A = SRT where R and S are directly related to the elasticity-coefficient matrix for the fluxes and chemical potentials in MCA, respectively; the control-coefficients for the fluxes and chemical potentials can be written in terms of RT BS and ST BS respectively where matrix B is the inverse of A; the matrix S is precisely the stoichiometric matrix in FBA; and the matrix eAt plays a central role in CMC. Conclusion: One key finding that emerges from this analysis is that the well-known summation theorems in MCA take different forms depending on whether metabolic steady-state is maintained by flux injection or concentration clamping. We demonstrate that if rate-limiting steps exist in a biochemical pathway, they are the steps with smallest biochemical conductances and largest flux control-coefficients. We hypothesize that biochemical networks for cellular signaling have a different strategy for minimizing energy waste and being efficient than do biochemical networks for biosynthesis. We also discuss the intimate relationship between MCA and biochemical systems analysis (BSA.

  10. Inverse scale space decomposition

    DEFF Research Database (Denmark)

    Schmidt, Marie Foged; Benning, Martin; Schönlieb, Carola-Bibiane

    2018-01-01

    We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and even and positively one-homogeneous regularisation functionals, can decompose data represented...... by the application of a forward operator to a linear combination of generalised singular vectors into its individual singular vectors. We verify that for this decomposition to hold true, two additional conditions on the singular vectors are sufficient: orthogonality in the data space and inclusion of partial sums...... of the subgradients of the singular vectors in the subdifferential of the regularisation functional at zero. We also address the converse question of when the inverse scale space flow returns a generalised singular vector given that the initial data is arbitrary (and therefore not necessarily in the range...

  11. Retrieval of collision kernels from the change of droplet size distributions with linear inversion

    Energy Technology Data Exchange (ETDEWEB)

    Onishi, Ryo; Takahashi, Keiko [Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology, 3173-25 Showa-machi, Kanazawa-ku, Yokohama Kanagawa 236-0001 (Japan); Matsuda, Keigo; Kurose, Ryoichi; Komori, Satoru [Department of Mechanical Engineering and Science, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)], E-mail: onishi.ryo@jamstec.go.jp, E-mail: matsuda.keigo@t03.mbox.media.kyoto-u.ac.jp, E-mail: takahasi@jamstec.go.jp, E-mail: kurose@mech.kyoto-u.ac.jp, E-mail: komori@mech.kyoto-u.ac.jp

    2008-12-15

    We have developed a new simple inversion scheme for retrieving collision kernels from the change of droplet size distribution due to collision growth. Three-dimensional direct numerical simulations (DNS) of steady isotropic turbulence with colliding droplets are carried out in order to investigate the validity of the developed inversion scheme. In the DNS, air turbulence is calculated using a quasi-spectral method; droplet motions are tracked in a Lagrangian manner. The initial droplet size distribution is set to be equivalent to that obtained in a wind tunnel experiment. Collision kernels retrieved by the developed inversion scheme are compared to those obtained by the DNS. The comparison shows that the collision kernels can be retrieved within 15% error. This verifies the feasibility of retrieving collision kernels using the present inversion scheme.

  12. Matrix-based image reconstruction methods for tomography

    International Nuclear Information System (INIS)

    Llacer, J.; Meng, J.D.

    1984-10-01

    Matrix methods of image reconstruction have not been used, in general, because of the large size of practical matrices, ill condition upon inversion and the success of Fourier-based techniques. An exception is the work that has been done at the Lawrence Berkeley Laboratory for imaging with accelerated radioactive ions. An extension of that work into more general imaging problems shows that, with a correct formulation of the problem, positron tomography with ring geometries results in well behaved matrices which can be used for image reconstruction with no distortion of the point response in the field of view and flexibility in the design of the instrument. Maximum Likelihood Estimator methods of reconstruction, which use the system matrices tailored to specific instruments and do not need matrix inversion, are shown to result in good preliminary images. A parallel processing computer structure based on multiple inexpensive microprocessors is proposed as a system to implement the matrix-MLE methods. 14 references, 7 figures

  13. Discriminative Elastic-Net Regularized Linear Regression.

    Science.gov (United States)

    Zhang, Zheng; Lai, Zhihui; Xu, Yong; Shao, Ling; Wu, Jian; Xie, Guo-Sen

    2017-03-01

    In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zero-one matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.

  14. A linear programming manual

    Science.gov (United States)

    Tuey, R. C.

    1972-01-01

    Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.

  15. Triangularization of a Matrix

    Indian Academy of Sciences (India)

    Much of linear algebra is devoted to reducing a matrix (via similarity or unitary similarity) to another that has lots of zeros. The simplest such theorem is the Schur triangularization theorem. This says that every matrix is unitarily similar to an upper triangular matrix. Our aim here is to show that though it is very easy to prove it ...

  16. Optimal Inversion Parameters for Full Waveform Inversion using OBS Data Set

    Science.gov (United States)

    Kim, S.; Chung, W.; Shin, S.; Kim, D.; Lee, D.

    2017-12-01

    In recent years, full Waveform Inversion (FWI) has been the most researched technique in seismic data processing. It uses the residuals between observed and modeled data as an objective function; thereafter, the final subsurface velocity model is generated through a series of iterations meant to minimize the residuals.Research on FWI has expanded from acoustic media to elastic media. In acoustic media, the subsurface property is defined by P-velocity; however, in elastic media, properties are defined by multiple parameters, such as P-velocity, S-velocity, and density. Further, the elastic media can also be defined by Lamé constants, density or impedance PI, SI; consequently, research is being carried out to ascertain the optimal parameters.From results of advanced exploration equipment and Ocean Bottom Seismic (OBS) survey, it is now possible to obtain multi-component seismic data. However, to perform FWI on these data and generate an accurate subsurface model, it is important to determine optimal inversion parameters among (Vp, Vs, ρ), (λ, μ, ρ), and (PI, SI) in elastic media. In this study, staggered grid finite difference method was applied to simulate OBS survey. As in inversion, l2-norm was set as objective function. Further, the accurate computation of gradient direction was performed using the back-propagation technique and its scaling was done using the Pseudo-hessian matrix.In acoustic media, only Vp is used as the inversion parameter. In contrast, various sets of parameters, such as (Vp, Vs, ρ) and (λ, μ, ρ) can be used to define inversion in elastic media. Therefore, it is important to ascertain the parameter that gives the most accurate result for inversion with OBS data set.In this study, we generated Vp and Vs subsurface models by using (λ, μ, ρ) and (Vp, Vs, ρ) as inversion parameters in every iteration, and compared the final two FWI results.This research was supported by the Basic Research Project(17-3312) of the Korea Institute of

  17. Radii of Solvability and Unsolvability of Linear Systems

    Czech Academy of Sciences Publication Activity Database

    Hladík, M.; Rohn, Jiří

    2016-01-01

    Roč. 503, 15 August (2016), s. 120-134 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * linear equations * linear inequalities * matrix norm Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016

  18. Stochastic Gabor reflectivity and acoustic impedance inversion

    Science.gov (United States)

    Hariri Naghadeh, Diako; Morley, Christopher Keith; Ferguson, Angus John

    2018-02-01

    To delineate subsurface lithology to estimate petrophysical properties of a reservoir, it is possible to use acoustic impedance (AI) which is the result of seismic inversion. To change amplitude to AI, removal of wavelet effects from the seismic signal in order to get a reflection series, and subsequently transforming those reflections to AI, is vital. To carry out seismic inversion correctly it is important to not assume that the seismic signal is stationary. However, all stationary deconvolution methods are designed following that assumption. To increase temporal resolution and interpretation ability, amplitude compensation and phase correction are inevitable. Those are pitfalls of stationary reflectivity inversion. Although stationary reflectivity inversion methods are trying to estimate reflectivity series, because of incorrect assumptions their estimations will not be correct, but may be useful. Trying to convert those reflection series to AI, also merging with the low frequency initial model, can help us. The aim of this study was to apply non-stationary deconvolution to eliminate time variant wavelet effects from the signal and to convert the estimated reflection series to the absolute AI by getting bias from well logs. To carry out this aim, stochastic Gabor inversion in the time domain was used. The Gabor transform derived the signal’s time-frequency analysis and estimated wavelet properties from different windows. Dealing with different time windows gave an ability to create a time-variant kernel matrix, which was used to remove matrix effects from seismic data. The result was a reflection series that does not follow the stationary assumption. The subsequent step was to convert those reflections to AI using well information. Synthetic and real data sets were used to show the ability of the introduced method. The results highlight that the time cost to get seismic inversion is negligible related to general Gabor inversion in the frequency domain. Also

  19. Linear matrix inequality approach to exponential synchronization of a class of chaotic neural networks with time-varying delays

    Science.gov (United States)

    Wu, Wei; Cui, Bao-Tong

    2007-07-01

    In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented. This class of chaotic neural networks covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.

  20. Imaging linear and circular polarization features in leaves with complete Mueller matrix polarimetry.

    Science.gov (United States)

    Patty, C H Lucas; Luo, David A; Snik, Frans; Ariese, Freek; Buma, Wybren Jan; Ten Kate, Inge Loes; van Spanning, Rob J M; Sparks, William B; Germer, Thomas A; Garab, Győző; Kudenov, Michael W

    2018-06-01

    Spectropolarimetry of intact plant leaves allows to probe the molecular architecture of vegetation photosynthesis in a non-invasive and non-destructive way and, as such, can offer a wealth of physiological information. In addition to the molecular signals due to the photosynthetic machinery, the cell structure and its arrangement within a leaf can create and modify polarization signals. Using Mueller matrix polarimetry with rotating retarder modulation, we have visualized spatial variations in polarization in transmission around the chlorophyll a absorbance band from 650 nm to 710 nm. We show linear and circular polarization measurements of maple leaves and cultivated maize leaves and discuss the corresponding Mueller matrices and the Mueller matrix decompositions, which show distinct features in diattenuation, polarizance, retardance and depolarization. Importantly, while normal leaf tissue shows a typical split signal with both a negative and a positive peak in the induced fractional circular polarization and circular dichroism, the signals close to the veins only display a negative band. The results are similar to the negative band as reported earlier for single macrodomains. We discuss the possible role of the chloroplast orientation around the veins as a cause of this phenomenon. Systematic artefacts are ruled out as three independent measurements by different instruments gave similar results. These results provide better insight into circular polarization measurements on whole leaves and options for vegetation remote sensing using circular polarization. Copyright © 2018 The Author(s). Published by Elsevier B.V. All rights reserved.

  1. Optimized simultaneous inversion of primary and multiple reflections; Inversion linearisee simultanee des reflexions primaires et des reflexions multiples

    Energy Technology Data Exchange (ETDEWEB)

    Pelle, L.

    2003-12-01

    The removal of multiple reflections remains a real problem in seismic imaging. Many preprocessing methods have been developed to attenuate multiples in seismic data but none of them is satisfactory in 3D. The objective of this thesis is to develop a new method to remove multiples, extensible in 3D. Contrary to the existing methods, our approach is not a preprocessing step: we directly include the multiple removal in the imaging process by means of a simultaneous inversion of primaries and multiples. We then propose to improve the standard linearized inversion so as to make it insensitive to the presence of multiples in the data. We exploit kinematics differences between primaries and multiples. We propose to pick in the data the kinematics of the multiples we want to remove. The wave field is decomposed into primaries and multiples. Primaries are modeled by the Ray+Born operator from perturbations of the logarithm of impedance, given the velocity field. Multiples are modeled by the Transport operator from an initial trace, given the picking. The inverse problem simultaneously fits primaries and multiples to the data. To solve this problem with two unknowns, we take advantage of the isometric nature of the Transport operator, which allows to drastically reduce the CPU time: this simultaneous inversion is this almost as fast as the standard linearized inversion. This gain of time opens the way to different applications to multiple removal and in particular, allows to foresee the straightforward 3D extension. (author)

  2. Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

    Science.gov (United States)

    Gnoffo, Peter A.

    2015-01-01

    Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

  3. A fully general and adaptive inverse analysis method for cementitious materials

    DEFF Research Database (Denmark)

    Jepsen, Michael S.; Damkilde, Lars; Lövgren, Ingemar

    2016-01-01

    The paper presents an adaptive method for inverse determination of the tensile σ - w relationship, direct tensile strength and Young’s modulus of cementitious materials. The method facilitates an inverse analysis with a multi-linear σ - w function. Usually, simple bi- or tri-linear functions...... are applied when modeling the fracture mechanisms in cementitious materials, but the vast development of pseudo-strain hardening, fiber reinforced cementitious materials require inverse methods, capable of treating multi-linear σ - w functions. The proposed method is fully general in the sense that it relies...... of notched specimens and simulated data from a nonlinear hinge model. The paper shows that the results obtained by means of the proposed method is independent on the initial shape of the σ - w function and the initial guess of the tensile strength. The method provides very accurate fits, and the increased...

  4. Porting of the DBCSR library for Sparse Matrix-Matrix Multiplications to Intel Xeon Phi systems

    OpenAIRE

    Bethune, Iain; Gloess, Andeas; Hutter, Juerg; Lazzaro, Alfio; Pabst, Hans; Reid, Fiona

    2017-01-01

    Multiplication of two sparse matrices is a key operation in the simulation of the electronic structure of systems containing thousands of atoms and electrons. The highly optimized sparse linear algebra library DBCSR (Distributed Block Compressed Sparse Row) has been specifically designed to efficiently perform such sparse matrix-matrix multiplications. This library is the basic building block for linear scaling electronic structure theory and low scaling correlated methods in CP2K. It is para...

  5. Parallel Programming Application to Matrix Algebra in the Spectral Method for Control Systems Analysis, Synthesis and Identification

    Directory of Open Access Journals (Sweden)

    V. Yu. Kleshnin

    2016-01-01

    Full Text Available The article describes the matrix algebra libraries based on the modern technologies of parallel programming for the Spectrum software, which can use a spectral method (in the spectral form of mathematical description to analyse, synthesise and identify deterministic and stochastic dynamical systems. The developed matrix algebra libraries use the following technologies for the GPUs: OmniThreadLibrary, OpenMP, Intel Threading Building Blocks, Intel Cilk Plus for CPUs nVidia CUDA, OpenCL, and Microsoft Accelerated Massive Parallelism.The developed libraries support matrices with real elements (single and double precision. The matrix dimensions are limited by 32-bit or 64-bit memory model and computer configuration. These libraries are general-purpose and can be used not only for the Spectrum software. They can also find application in the other projects where there is a need to perform operations with large matrices.The article provides a comparative analysis of the libraries developed for various matrix operations (addition, subtraction, scalar multiplication, multiplication, powers of matrices, tensor multiplication, transpose, inverse matrix, finding a solution of the system of linear equations through the numerical experiments using different CPU and GPU. The article contains sample programs and performance test results for matrix multiplication, which requires most of all computational resources in regard to the other operations.

  6. Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs

    OpenAIRE

    Zuidwijk, Rob

    2005-01-01

    textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an optimal solution are investigated, and the optimal solution is studied on a so-called critical range of the initial data, in which certain properties such as the optimal basis in linear programming are ...

  7. ARMA Cholesky Factor Models for the Covariance Matrix of Linear Models.

    Science.gov (United States)

    Lee, Keunbaik; Baek, Changryong; Daniels, Michael J

    2017-11-01

    In longitudinal studies, serial dependence of repeated outcomes must be taken into account to make correct inferences on covariate effects. As such, care must be taken in modeling the covariance matrix. However, estimation of the covariance matrix is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcomes these limitations, two Cholesky decomposition approaches have been proposed: modified Cholesky decomposition for autoregressive (AR) structure and moving average Cholesky decomposition for moving average (MA) structure, respectively. However, the correlations of repeated outcomes are often not captured parsimoniously using either approach separately. In this paper, we propose a class of flexible, nonstationary, heteroscedastic models that exploits the structure allowed by combining the AR and MA modeling of the covariance matrix that we denote as ARMACD. We analyze a recent lung cancer study to illustrate the power of our proposed methods.

  8. The effect of averaging adjacent planes for artifact reduction in matrix inversion tomosynthesis

    Energy Technology Data Exchange (ETDEWEB)

    Godfrey, Devon J. [Department of Radiation Oncology, Duke University Medical Center, Durham, North Carolina 27705 (United States); Page McAdams, H. [Carl E. Ravin Advanced Imaging Laboratories, Department of Radiology, Duke University Medical Center, Durham, North Carolina 27705 (United States); Dobbins, James T. III [Carl E. Ravin Advanced Imaging Laboratories, Department of Radiology, Department of Biomedical Engineering, Department of Physics, and Medical Physics Graduate Program, Duke University Medical Center, Durham, North Carolina 27705 (United States)

    2013-02-15

    Purpose: Matrix inversion tomosynthesis (MITS) uses linear systems theory and knowledge of the imaging geometry to remove tomographic blur that is present in conventional backprojection tomosynthesis reconstructions, leaving in-plane detail rendered clearly. The use of partial-pixel interpolation during the backprojection process introduces imprecision in the MITS modeling of tomographic blur, and creates low-contrast artifacts in some MITS planes. This paper examines the use of MITS slabs, created by averaging several adjacent MITS planes, as a method for suppressing partial-pixel artifacts. Methods: Human chest tomosynthesis projection data, acquired as part of an IRB-approved pilot study, were used to generate MITS planes, three-plane MITS slabs (MITSa3), five-plane MITS slabs (MITSa5), and seven-plane MITS slabs (MITSa7). These were qualitatively examined for partial-pixel artifacts and the visibility of normal and abnormal anatomy. Additionally, small (5 mm) subtle pulmonary nodules were simulated and digitally superimposed upon human chest tomosynthesis projection images, and their visibility was qualitatively assessed in the different reconstruction techniques. Simulated images of a thin wire were used to generate modulation transfer function (MTF) and slice-sensitivity profile curves for the different MITS and MITS slab techniques, and these were examined for indications of partial-pixel artifacts and frequency response uniformity. Finally, mean-subtracted, exposure-normalized noise power spectra (ENNPS) estimates were computed and compared for MITS and MITS slab reconstructions, generated from 10 sets of tomosynthesis projection data of an acrylic slab. The simulated in-plane MTF response of each technique was also combined with the square root of the ENNPS estimate to yield stochastic signal-to-noise ratio (SNR) information about the different reconstruction techniques. Results: For scan angles of 20 Degree-Sign and 5 mm plane separation, seven MITS

  9. The effect of averaging adjacent planes for artifact reduction in matrix inversion tomosynthesis

    Science.gov (United States)

    Godfrey, Devon J.; Page McAdams, H.; Dobbins, James T.

    2013-01-01

    Purpose: Matrix inversion tomosynthesis (MITS) uses linear systems theory and knowledge of the imaging geometry to remove tomographic blur that is present in conventional backprojection tomosynthesis reconstructions, leaving in-plane detail rendered clearly. The use of partial-pixel interpolation during the backprojection process introduces imprecision in the MITS modeling of tomographic blur, and creates low-contrast artifacts in some MITS planes. This paper examines the use of MITS slabs, created by averaging several adjacent MITS planes, as a method for suppressing partial-pixel artifacts. Methods: Human chest tomosynthesis projection data, acquired as part of an IRB-approved pilot study, were used to generate MITS planes, three-plane MITS slabs (MITSa3), five-plane MITS slabs (MITSa5), and seven-plane MITS slabs (MITSa7). These were qualitatively examined for partial-pixel artifacts and the visibility of normal and abnormal anatomy. Additionally, small (5 mm) subtle pulmonary nodules were simulated and digitally superimposed upon human chest tomosynthesis projection images, and their visibility was qualitatively assessed in the different reconstruction techniques. Simulated images of a thin wire were used to generate modulation transfer function (MTF) and slice-sensitivity profile curves for the different MITS and MITS slab techniques, and these were examined for indications of partial-pixel artifacts and frequency response uniformity. Finally, mean-subtracted, exposure-normalized noise power spectra (ENNPS) estimates were computed and compared for MITS and MITS slab reconstructions, generated from 10 sets of tomosynthesis projection data of an acrylic slab. The simulated in-plane MTF response of each technique was also combined with the square root of the ENNPS estimate to yield stochastic signal-to-noise ratio (SNR) information about the different reconstruction techniques. Results: For scan angles of 20° and 5 mm plane separation, seven MITS planes must be

  10. The effect of averaging adjacent planes for artifact reduction in matrix inversion tomosynthesis.

    Science.gov (United States)

    Godfrey, Devon J; McAdams, H Page; Dobbins, James T

    2013-02-01

    Matrix inversion tomosynthesis (MITS) uses linear systems theory and knowledge of the imaging geometry to remove tomographic blur that is present in conventional backprojection tomosynthesis reconstructions, leaving in-plane detail rendered clearly. The use of partial-pixel interpolation during the backprojection process introduces imprecision in the MITS modeling of tomographic blur, and creates low-contrast artifacts in some MITS planes. This paper examines the use of MITS slabs, created by averaging several adjacent MITS planes, as a method for suppressing partial-pixel artifacts. Human chest tomosynthesis projection data, acquired as part of an IRB-approved pilot study, were used to generate MITS planes, three-plane MITS slabs (MITSa3), five-plane MITS slabs (MITSa5), and seven-plane MITS slabs (MITSa7). These were qualitatively examined for partial-pixel artifacts and the visibility of normal and abnormal anatomy. Additionally, small (5 mm) subtle pulmonary nodules were simulated and digitally superimposed upon human chest tomosynthesis projection images, and their visibility was qualitatively assessed in the different reconstruction techniques. Simulated images of a thin wire were used to generate modulation transfer function (MTF) and slice-sensitivity profile curves for the different MITS and MITS slab techniques, and these were examined for indications of partial-pixel artifacts and frequency response uniformity. Finally, mean-subtracted, exposure-normalized noise power spectra (ENNPS) estimates were computed and compared for MITS and MITS slab reconstructions, generated from 10 sets of tomosynthesis projection data of an acrylic slab. The simulated in-plane MTF response of each technique was also combined with the square root of the ENNPS estimate to yield stochastic signal-to-noise ratio (SNR) information about the different reconstruction techniques. For scan angles of 20° and 5 mm plane separation, seven MITS planes must be averaged to sufficiently

  11. The effect of averaging adjacent planes for artifact reduction in matrix inversion tomosynthesis

    International Nuclear Information System (INIS)

    Godfrey, Devon J.; Page McAdams, H.; Dobbins, James T. III

    2013-01-01

    Purpose: Matrix inversion tomosynthesis (MITS) uses linear systems theory and knowledge of the imaging geometry to remove tomographic blur that is present in conventional backprojection tomosynthesis reconstructions, leaving in-plane detail rendered clearly. The use of partial-pixel interpolation during the backprojection process introduces imprecision in the MITS modeling of tomographic blur, and creates low-contrast artifacts in some MITS planes. This paper examines the use of MITS slabs, created by averaging several adjacent MITS planes, as a method for suppressing partial-pixel artifacts. Methods: Human chest tomosynthesis projection data, acquired as part of an IRB-approved pilot study, were used to generate MITS planes, three-plane MITS slabs (MITSa3), five-plane MITS slabs (MITSa5), and seven-plane MITS slabs (MITSa7). These were qualitatively examined for partial-pixel artifacts and the visibility of normal and abnormal anatomy. Additionally, small (5 mm) subtle pulmonary nodules were simulated and digitally superimposed upon human chest tomosynthesis projection images, and their visibility was qualitatively assessed in the different reconstruction techniques. Simulated images of a thin wire were used to generate modulation transfer function (MTF) and slice-sensitivity profile curves for the different MITS and MITS slab techniques, and these were examined for indications of partial-pixel artifacts and frequency response uniformity. Finally, mean-subtracted, exposure-normalized noise power spectra (ENNPS) estimates were computed and compared for MITS and MITS slab reconstructions, generated from 10 sets of tomosynthesis projection data of an acrylic slab. The simulated in-plane MTF response of each technique was also combined with the square root of the ENNPS estimate to yield stochastic signal-to-noise ratio (SNR) information about the different reconstruction techniques. Results: For scan angles of 20° and 5 mm plane separation, seven MITS planes must be

  12. Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis.

    Science.gov (United States)

    Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping

    2015-10-01

    We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.

  13. A companion matrix for 2-D polynomials

    International Nuclear Information System (INIS)

    Boudellioua, M.S.

    1995-08-01

    In this paper, a matrix form analogous to the companion matrix which is often encountered in the theory of one dimensional (1-D) linear systems is suggested for a class of polynomials in two indeterminates and real coefficients, here referred to as two dimensional (2-D) polynomials. These polynomials arise in the context of 2-D linear systems theory. Necessary and sufficient conditions are also presented under which a matrix is equivalent to this companion form. (author). 6 refs

  14. Closed-form solutions for linear regulator-design of mechanical systems including optimal weighting matrix selection

    Science.gov (United States)

    Hanks, Brantley R.; Skelton, Robert E.

    1991-01-01

    This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.

  15. An inverse method for non linear ablative thermics with experimentation of automatic differentiation

    Energy Technology Data Exchange (ETDEWEB)

    Alestra, S [Simulation Information Technology and Systems Engineering, EADS IW Toulouse (France); Collinet, J [Re-entry Systems and Technologies, EADS ASTRIUM ST, Les Mureaux (France); Dubois, F [Professor of Applied Mathematics, Conservatoire National des Arts et Metiers Paris (France)], E-mail: stephane.alestra@eads.net, E-mail: jean.collinet@astrium.eads.net, E-mail: fdubois@cnam.fr

    2008-11-01

    Thermal Protection System is a key element for atmospheric re-entry missions of aerospace vehicles. The high level of heat fluxes encountered in such missions has a direct effect on mass balance of the heat shield. Consequently, the identification of heat fluxes is of great industrial interest but is in flight only available by indirect methods based on temperature measurements. This paper is concerned with inverse analyses of highly evolutive heat fluxes. An inverse problem is used to estimate transient surface heat fluxes (convection coefficient), for degradable thermal material (ablation and pyrolysis), by using time domain temperature measurements on thermal protection. The inverse problem is formulated as a minimization problem involving an objective functional, through an optimization loop. An optimal control formulation (Lagrangian, adjoint and gradient steepest descent method combined with quasi-Newton method computations) is then developed and applied, using Monopyro, a transient one-dimensional thermal model with one moving boundary (ablative surface) that has been developed since many years by ASTRIUM-ST. To compute numerically the adjoint and gradient quantities, for the inverse problem in heat convection coefficient, we have used both an analytical manual differentiation and an Automatic Differentiation (AD) engine tool, Tapenade, developed at INRIA Sophia-Antipolis by the TROPICS team. Several validation test cases, using synthetic temperature measurements are carried out, by applying the results of the inverse method with minimization algorithm. Accurate results of identification on high fluxes test cases, and good agreement for temperatures restitutions, are obtained, without and with ablation and pyrolysis, using bad fluxes initial guesses. First encouraging results with an automatic differentiation procedure are also presented in this paper.

  16. Linearized image reconstruction method for ultrasound modulated electrical impedance tomography based on power density distribution

    International Nuclear Information System (INIS)

    Song, Xizi; Xu, Yanbin; Dong, Feng

    2017-01-01

    Electrical resistance tomography (ERT) is a promising measurement technique with important industrial and clinical applications. However, with limited effective measurements, it suffers from poor spatial resolution due to the ill-posedness of the inverse problem. Recently, there has been an increasing research interest in hybrid imaging techniques, utilizing couplings of physical modalities, because these techniques obtain much more effective measurement information and promise high resolution. Ultrasound modulated electrical impedance tomography (UMEIT) is one of the newly developed hybrid imaging techniques, which combines electric and acoustic modalities. A linearized image reconstruction method based on power density is proposed for UMEIT. The interior data, power density distribution, is adopted to reconstruct the conductivity distribution with the proposed image reconstruction method. At the same time, relating the power density change to the change in conductivity, the Jacobian matrix is employed to make the nonlinear problem into a linear one. The analytic formulation of this Jacobian matrix is derived and its effectiveness is also verified. In addition, different excitation patterns are tested and analyzed, and opposite excitation provides the best performance with the proposed method. Also, multiple power density distributions are combined to implement image reconstruction. Finally, image reconstruction is implemented with the linear back-projection (LBP) algorithm. Compared with ERT, with the proposed image reconstruction method, UMEIT can produce reconstructed images with higher quality and better quantitative evaluation results. (paper)

  17. Handbook of linear algebra

    CERN Document Server

    Hogben, Leslie

    2013-01-01

    With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.New to the Second EditionSeparate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of

  18. Linear data mining the Wichita clinical matrix suggests sleep and allostatic load involvement in chronic fatigue syndrome.

    Science.gov (United States)

    Gurbaxani, Brian M; Jones, James F; Goertzel, Benjamin N; Maloney, Elizabeth M

    2006-04-01

    To provide a mathematical introduction to the Wichita (KS, USA) clinical dataset, which is all of the nongenetic data (no microarray or single nucleotide polymorphism data) from the 2-day clinical evaluation, and show the preliminary findings and limitations, of popular, matrix algebra-based data mining techniques. An initial matrix of 440 variables by 227 human subjects was reduced to 183 variables by 164 subjects. Variables were excluded that strongly correlated with chronic fatigue syndrome (CFS) case classification by design (for example, the multidimensional fatigue inventory [MFI] data), that were otherwise self reporting in nature and also tended to correlate strongly with CFS classification, or were sparse or nonvarying between case and control. Subjects were excluded if they did not clearly fall into well-defined CFS classifications, had comorbid depression with melancholic features, or other medical or psychiatric exclusions. The popular data mining techniques, principle components analysis (PCA) and linear discriminant analysis (LDA), were used to determine how well the data separated into groups. Two different feature selection methods helped identify the most discriminating parameters. Although purely biological features (variables) were found to separate CFS cases from controls, including many allostatic load and sleep-related variables, most parameters were not statistically significant individually. However, biological correlates of CFS, such as heart rate and heart rate variability, require further investigation. Feature selection of a limited number of variables from the purely biological dataset produced better separation between groups than a PCA of the entire dataset. Feature selection highlighted the importance of many of the allostatic load variables studied in more detail by Maloney and colleagues in this issue [1] , as well as some sleep-related variables. Nonetheless, matrix linear algebra-based data mining approaches appeared to be of

  19. H-/H∞ structural damage detection filter design using an iterative linear matrix inequality approach

    International Nuclear Information System (INIS)

    Chen, B; Nagarajaiah, S

    2008-01-01

    The existence of damage in different members of a structure can be posed as a fault detection problem. It is also necessary to isolate structural members in which damage exists, which can be posed as a fault isolation problem. It is also important to detect the time instants of occurrence of the faults/damage. The structural damage detection filter developed in this paper is a model-based fault detection and isolation (FDI) observer suitable for detecting and isolating structural damage. In systems, possible faults, disturbances and noise are coupled together. When system disturbances and sensor noise cannot be decoupled from faults/damage, the detection filter needs to be designed to be robust to disturbances as well as sensitive to faults/damage. In this paper, a new H - /H ∞ and iterative linear matrix inequality (LMI) technique is developed and a new stabilizing FDI filter is proposed, which bounds the H ∞ norm of the transfer function from disturbances to the output residual and simultaneously does not degrade the component of the output residual due to damage. The reduced-order error dynamic system is adopted to form bilinear matrix inequalities (BMIs), then an iterative LMI algorithm is developed to solve the BMIs. The numerical example and experimental verification demonstrate that the proposed algorithm can successfully detect and isolate structural damage in the presence of measurement noise

  20. Linear Models

    CERN Document Server

    Searle, Shayle R

    2012-01-01

    This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.

  1. Solution of the scattering T matrix equation in discrete complex momentum space

    International Nuclear Information System (INIS)

    Rawitscher, G.H.; Delic, G.

    1984-01-01

    The scattering solution to the Lippmann-Schwinger equation is expanded into a set of spherical Bessel functions of complex wave numbers, K/sub j/, with j = 1,2 , . . . , M. The value of each K/sub j/ is determined from the condition that the spherical Bessel function smoothly matches onto an asymptotically outgoing spherical Hankel (or Coulomb) function of the correct physical wave number at a matching point R. The spherical Bessel functions thus determined are Sturmian functions, and they form a complete set in the interval 0 to R. The coefficients of the expansion of the scattering function are determined by matrix inversion of a linear set of algebraic equations, which are equivalent to the solution of the T-matrix equation in complex momentum space. In view of the presence of a matching radius, no singularities are encountered for the Green's functions, and the inclusion of Coulomb potentials offers no computational difficulties. Three numerical examples are performed in order to illustrate the convergence of the elastic scattering matrix S with M. One of these consists of a set of coupled equations which describe the breakup of a deuteron as it scatters from the nucleus on 58 Ni. A value of M of 15 or less is found sufficient to reproduce the exact S matrix element to an accuracy of four figures after the decimal point

  2. Efficient Monte Carlo sampling of inverse problems using a neural network-based forward—applied to GPR crosshole traveltime inversion

    Science.gov (United States)

    Hansen, T. M.; Cordua, K. S.

    2017-12-01

    Probabilistically formulated inverse problems can be solved using Monte Carlo-based sampling methods. In principle, both advanced prior information, based on for example, complex geostatistical models and non-linear forward models can be considered using such methods. However, Monte Carlo methods may be associated with huge computational costs that, in practice, limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical forward response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival traveltime inversion of crosshole ground penetrating radar data. An accurate forward model, based on 2-D full-waveform modeling followed by automatic traveltime picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the accurate and computationally expensive forward model, and also considerably faster and more accurate (i.e. with better resolution), than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of non-linear and non-Gaussian inverse problems that have to be solved using Monte Carlo sampling techniques.

  3. Inverse modeling of the terrestrial carbon flux in China with flux covariance among inverted regions

    Science.gov (United States)

    Wang, H.; Jiang, F.; Chen, J. M.; Ju, W.; Wang, H.

    2011-12-01

    Quantitative understanding of the role of ocean and terrestrial biosphere in the global carbon cycle, their response and feedback to climate change is required for the future projection of the global climate. China has the largest amount of anthropogenic CO2 emission, diverse terrestrial ecosystems and an unprecedented rate of urbanization. Thus information on spatial and temporal distributions of the terrestrial carbon flux in China is of great importance in understanding the global carbon cycle. We developed a nested inversion with focus in China. Based on Transcom 22 regions for the globe, we divide China and its neighboring countries into 17 regions, making 39 regions in total for the globe. A Bayesian synthesis inversion is made to estimate the terrestrial carbon flux based on GlobalView CO2 data. In the inversion, GEOS-Chem is used as the transport model to develop the transport matrix. A terrestrial ecosystem model named BEPS is used to produce the prior surface flux to constrain the inversion. However, the sparseness of available observation stations in Asia poses a challenge to the inversion for the 17 small regions. To obtain additional constraint on the inversion, a prior flux covariance matrix is constructed using the BEPS model through analyzing the correlation in the net carbon flux among regions under variable climate conditions. The use of the covariance among different regions in the inversion effectively extends the information content of CO2 observations to more regions. The carbon flux over the 39 land and ocean regions are inverted for the period from 2004 to 2009. In order to investigate the impact of introducing the covariance matrix with non-zero off-diagonal values to the inversion, the inverted terrestrial carbon flux over China is evaluated against ChinaFlux eddy-covariance observations after applying an upscaling methodology.

  4. On the quantum inverse scattering problem

    International Nuclear Information System (INIS)

    Maillet, J.M.; Terras, V.

    2000-01-01

    A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an R-matrix) for a large class of lattice quantum integrable models is given. The principal requirement being the initial condition (R(0)=P, the permutation operator) for the quantum R-matrix solving the Yang-Baxter equation, it applies not only to most known integrable fundamental lattice models (such as Heisenberg spin chains) but also to lattice models with arbitrary number of impurities and to the so-called fused lattice models (including integrable higher spin generalizations of Heisenberg chains). Our method is then applied to several important examples like the sl n XXZ model, the XYZ spin-((1)/(2)) chain and also to the spin-s Heisenberg chains

  5. Energy conserving, linear scaling Born-Oppenheimer molecular dynamics.

    Science.gov (United States)

    Cawkwell, M J; Niklasson, Anders M N

    2012-10-07

    Born-Oppenheimer molecular dynamics simulations with long-term conservation of the total energy and a computational cost that scales linearly with system size have been obtained simultaneously. Linear scaling with a low pre-factor is achieved using density matrix purification with sparse matrix algebra and a numerical threshold on matrix elements. The extended Lagrangian Born-Oppenheimer molecular dynamics formalism [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] yields microcanonical trajectories with the approximate forces obtained from the linear scaling method that exhibit no systematic drift over hundreds of picoseconds and which are indistinguishable from trajectories computed using exact forces.

  6. Improved L-BFGS diagonal preconditioners for a large-scale 4D-Var inversion system: application to CO2 flux constraints and analysis error calculation

    Science.gov (United States)

    Bousserez, Nicolas; Henze, Daven; Bowman, Kevin; Liu, Junjie; Jones, Dylan; Keller, Martin; Deng, Feng

    2013-04-01

    This work presents improved analysis error estimates for 4D-Var systems. From operational NWP models to top-down constraints on trace gas emissions, many of today's data assimilation and inversion systems in atmospheric science rely on variational approaches. This success is due to both the mathematical clarity of these formulations and the availability of computationally efficient minimization algorithms. However, unlike Kalman Filter-based algorithms, these methods do not provide an estimate of the analysis or forecast error covariance matrices, these error statistics being propagated only implicitly by the system. From both a practical (cycling assimilation) and scientific perspective, assessing uncertainties in the solution of the variational problem is critical. For large-scale linear systems, deterministic or randomization approaches can be considered based on the equivalence between the inverse Hessian of the cost function and the covariance matrix of analysis error. For perfectly quadratic systems, like incremental 4D-Var, Lanczos/Conjugate-Gradient algorithms have proven to be most efficient in generating low-rank approximations of the Hessian matrix during the minimization. For weakly non-linear systems though, the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), a quasi-Newton descent algorithm, is usually considered the best method for the minimization. Suitable for large-scale optimization, this method allows one to generate an approximation to the inverse Hessian using the latest m vector/gradient pairs generated during the minimization, m depending upon the available core memory. At each iteration, an initial low-rank approximation to the inverse Hessian has to be provided, which is called preconditioning. The ability of the preconditioner to retain useful information from previous iterations largely determines the efficiency of the algorithm. Here we assess the performance of different preconditioners to estimate the inverse Hessian of a

  7. Inverse scattering and solitons in An-1 affine Toda field theories

    International Nuclear Information System (INIS)

    Beggs, E.J.; Johnson, P.R.

    1997-01-01

    We implement the inverse scattering method in the case of the A n affine Toda field theories, by studying the space-time evolution of simple poles in the underlying loop group. We find the known single-soliton solutions, as well as additional solutions with non-linear modes of oscillation around the standard solution, by studying the particularly simple case where the residue at the pole is a rank-one projection. We show that these solutions with extra modes have the same mass and topological charges as the standard solutions, so we do not shed any light on the missing topological charge problem in these models. From the monodromy matrix it is shown that these solutions have the same higher conserved charges as the standard solutions. We also show that the integrated energy-momentum density can be calculated from the central extension of the loop group. (orig.)

  8. Bayesian inversion of refraction seismic traveltime data

    Science.gov (United States)

    Ryberg, T.; Haberland, Ch

    2018-03-01

    We apply a Bayesian Markov chain Monte Carlo (McMC) formalism to the inversion of refraction seismic, traveltime data sets to derive 2-D velocity models below linear arrays (i.e. profiles) of sources and seismic receivers. Typical refraction data sets, especially when using the far-offset observations, are known as having experimental geometries which are very poor, highly ill-posed and far from being ideal. As a consequence, the structural resolution quickly degrades with depth. Conventional inversion techniques, based on regularization, potentially suffer from the choice of appropriate inversion parameters (i.e. number and distribution of cells, starting velocity models, damping and smoothing constraints, data noise level, etc.) and only local model space exploration. McMC techniques are used for exhaustive sampling of the model space without the need of prior knowledge (or assumptions) of inversion parameters, resulting in a large number of models fitting the observations. Statistical analysis of these models allows to derive an average (reference) solution and its standard deviation, thus providing uncertainty estimates of the inversion result. The highly non-linear character of the inversion problem, mainly caused by the experiment geometry, does not allow to derive a reference solution and error map by a simply averaging procedure. We present a modified averaging technique, which excludes parts of the prior distribution in the posterior values due to poor ray coverage, thus providing reliable estimates of inversion model properties even in those parts of the models. The model is discretized by a set of Voronoi polygons (with constant slowness cells) or a triangulated mesh (with interpolation within the triangles). Forward traveltime calculations are performed by a fast, finite-difference-based eikonal solver. The method is applied to a data set from a refraction seismic survey from Northern Namibia and compared to conventional tomography. An inversion test

  9. Inverse Schroedinger equation and the exact wave function

    International Nuclear Information System (INIS)

    Nakatsuji, Hiroshi

    2002-01-01

    Using the inverse of the Hamiltonian, we introduce the inverse Schroedinger equation (ISE) that is equivalent to the ordinary Schroedinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem

  10. Minimal-Inversion Feedforward-And-Feedback Control System

    Science.gov (United States)

    Seraji, Homayoun

    1990-01-01

    Recent developments in theory of control systems support concept of minimal-inversion feedforward-and feedback control system consisting of three independently designable control subsystems. Applicable to the control of linear, time-invariant plant.

  11. Information matrix estimation procedures for cognitive diagnostic models.

    Science.gov (United States)

    Liu, Yanlou; Xin, Tao; Andersson, Björn; Tian, Wei

    2018-03-06

    Two new methods to estimate the asymptotic covariance matrix for marginal maximum likelihood estimation of cognitive diagnosis models (CDMs), the inverse of the observed information matrix and the sandwich-type estimator, are introduced. Unlike several previous covariance matrix estimators, the new methods take into account both the item and structural parameters. The relationships between the observed information matrix, the empirical cross-product information matrix, the sandwich-type covariance matrix and the two approaches proposed by de la Torre (2009, J. Educ. Behav. Stat., 34, 115) are discussed. Simulation results show that, for a correctly specified CDM and Q-matrix or with a slightly misspecified probability model, the observed information matrix and the sandwich-type covariance matrix exhibit good performance with respect to providing consistent standard errors of item parameter estimates. However, with substantial model misspecification only the sandwich-type covariance matrix exhibits robust performance. © 2018 The British Psychological Society.

  12. Robust Model Predictive Control Using Linear Matrix Inequalities for the Treatment of Asymmetric Output Constraints

    Directory of Open Access Journals (Sweden)

    Mariana Santos Matos Cavalca

    2012-01-01

    Full Text Available One of the main advantages of predictive control approaches is the capability of dealing explicitly with constraints on the manipulated and output variables. However, if the predictive control formulation does not consider model uncertainties, then the constraint satisfaction may be compromised. A solution for this inconvenience is to use robust model predictive control (RMPC strategies based on linear matrix inequalities (LMIs. However, LMI-based RMPC formulations typically consider only symmetric constraints. This paper proposes a method based on pseudoreferences to treat asymmetric output constraints in integrating SISO systems. Such technique guarantees robust constraint satisfaction and convergence of the state to the desired equilibrium point. A case study using numerical simulation indicates that satisfactory results can be achieved.

  13. Remote and Local Influences in Forecasting Pacific SST: a Linear Inverse Model and a Multimodel Ensemble Study

    Science.gov (United States)

    Faggiani Dias, D.; Subramanian, A. C.; Zanna, L.; Miller, A. J.

    2017-12-01

    Sea surface temperature (SST) in the Pacific sector is well known to vary on time scales from seasonal to decadal, and the ability to predict these SST fluctuations has many societal and economical benefits. Therefore, we use a suite of statistical linear inverse models (LIMs) to understand the remote and local SST variability that influences SST predictions over the North Pacific region and further improve our understanding on how the long-observed SST record can help better guide multi-model ensemble forecasts. Observed monthly SST anomalies in the Pacific sector (between 15oS and 60oN) are used to construct different regional LIMs for seasonal to decadal prediction. The forecast skills of the LIMs are compared to that from two operational forecast systems in the North American Multi-Model Ensemble (NMME) revealing that the LIM has better skill in the Northeastern Pacific than NMME models. The LIM is also found to have comparable forecast skill for SST in the Tropical Pacific with NMME models. This skill, however, is highly dependent on the initialization month, with forecasts initialized during the summer having better skill than those initialized during the winter. The forecast skill with LIM is also influenced by the verification period utilized to make the predictions, likely due to the changing character of El Niño in the 20th century. The North Pacific seems to be a source of predictability for the Tropics on seasonal to interannual time scales, while the Tropics act to worsen the skill for the forecast in the North Pacific. The data were also bandpassed into seasonal, interannual and decadal time scales to identify the relationships between time scales using the structure of the propagator matrix. For the decadal component, this coupling occurs the other way around: Tropics seem to be a source of predictability for the Extratropics, but the Extratropics don't improve the predictability for the Tropics. These results indicate the importance of temporal

  14. Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski Space

    Directory of Open Access Journals (Sweden)

    Hanifa Zekraoui

    2013-01-01

    Full Text Available We introduce some new algebraic and topological properties of the Minkowski inverse A⊕ of an arbitrary matrix A∈Mm,n (including singular and rectangular in a Minkowski space μ. Furthermore, we show that the Minkowski inverse A⊕ in a Minkowski space and the Moore-Penrose inverse A+ in a Hilbert space are different in many properties such as the existence, continuity, norm, and SVD. New conditions of the Minkowski inverse are also given. These conditions are related to the existence, continuity, and reverse order law. Finally, a new representation of the Minkowski inverse A⊕ is also derived.

  15. Observer-dependent sign inversions of polarization singularities.

    Science.gov (United States)

    Freund, Isaac

    2014-10-15

    We describe observer-dependent sign inversions of the topological charges of vector field polarization singularities: C points (points of circular polarization), L points (points of linear polarization), and two virtually unknown singularities we call γ(C) and α(L) points. In all cases, the sign of the charge seen by an observer can change as she changes the direction from which she views the singularity. Analytic formulas are given for all C and all L point sign inversions.

  16. Physics-based models for measurement correlations: application to an inverse Sturm–Liouville problem

    International Nuclear Information System (INIS)

    Bal, Guillaume; Ren Kui

    2009-01-01

    In many inverse problems, the measurement operator, which maps objects of interest to available measurements, is a smoothing (regularizing) operator. Its inverse is therefore unbounded and as a consequence, only the low-frequency component of the object of interest is accessible from inevitably noisy measurements. In many inverse problems however, the neglected high-frequency component may significantly affect the measured data. Using simple scaling arguments, we characterize the influence of the high-frequency component. We then consider situations where the correlation function of such an influence may be estimated by asymptotic expansions, for instance as a random corrector in homogenization theory. This allows us to consistently eliminate the high-frequency component and derive a closed form, more accurate, inverse problem for the low-frequency component of the object of interest. We present the asymptotic expression of the correlation matrix of the eigenvalues in a Sturm–Liouville problem with unknown potential. We propose an iterative algorithm for the reconstruction of the potential from knowledge of the eigenvalues and show that using the approximate correlation matrix significantly improves the reconstructions

  17. Inverse Higgs effect in nonlinear realizations

    International Nuclear Information System (INIS)

    Ivanov, E.A.; Ogievetskij, V.I.

    1975-01-01

    In theories with nonlinearly realized symmetry it is possible in a number of cases to eliminate some initial Goldstone and gauge fields by means of putting appropriate Cartan forms equal to zero. This is called the inverse Higgs phenomenon. We give a general treatment of the inverse Higgs phenomenon for gauge and space-time symmetries and consider four instructive examples which are the elimination of unessential gauge fields in chiral symmetry and in non-linearly realized supersymmetry and also the elimination of unessential Goldstone fields in the spontaneously broken conformal and projective symmetries

  18. Linear reversible second-order cellular automata and their first-order matrix equivalents

    International Nuclear Information System (INIS)

    Macfarlane, A J

    2004-01-01

    Linear or one-dimensional reversible second-order cellular automata, exemplified by three cases named as RCA1-3, are introduced. Displays of their evolution in discrete time steps, t=0, 1, 2, ..., from their simplest initial states and on the basis of updating rules in modulo 2 arithmetic, are presented. In these, shaded and unshaded squares denote cells whose cell variables are equal to one and zero respectively. This paper is devoted to finding general formulas for, and explicit numerical evaluations of, the weights N(t) of the states or configurations of RCA1-3, i.e. the total number of shaded cells in tth line of their displays. This is achieved by means of the replacement of RCA1-3 by the equivalent linear first-order matrix automata MCA1-3, for which the cell variables are 2x2 matrices, instead of just numbers (element of Z 2 ) as for RCA1-3. MCA1-3 are tractable because it has been possible to generalize to them the heavy duty methods already well-developed for ordinary first-order cellular automata like those of Wolfram's Rules 90 and 150. While the automata MCA1-3 are thought to be of genuine interest in their own right, with untapped further mathematical potential, their treatment has been applied here to expediting derivation of a large body of general and explicit results for N(t) for RCA1-3. Amongst explicit results obtained are formulas also for each of RCA1-3 for the total weight of the configurations of the first 2 M times, M=0, 1, 2, ..

  19. General inverse problems for regular variation

    DEFF Research Database (Denmark)

    Damek, Ewa; Mikosch, Thomas Valentin; Rosinski, Jan

    2014-01-01

    Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed random object is caused by regular variation of components ...

  20. Visualizing phase transition behavior of dilute stimuli responsive polymer solutions via Mueller matrix polarimetry.

    Science.gov (United States)

    Narayanan, Amal; Chandel, Shubham; Ghosh, Nirmalya; De, Priyadarsi

    2015-09-15

    Probing volume phase transition behavior of superdiluted polymer solutions both micro- and macroscopically still persists as an outstanding challenge. In this regard, we have explored 4 × 4 spectral Mueller matrix measurement and its inverse analysis for excavating the microarchitectural facts about stimuli responsiveness of "smart" polymers. Phase separation behavior of thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) and pH responsive poly(N,N-(dimethylamino)ethyl methacrylate) (PDMAEMA) and their copolymers were analyzed in terms of Mueller matrix derived polarization parameters, namely, depolarization (Δ), diattenuation (d), and linear retardance (δ). The Δ, d, and δ parameters provided useful information on both macro- and microstructural alterations during the phase separation. Additionally, the two step action ((i) breakage of polymer-water hydrogen bonding and (ii) polymer-polymer aggregation) at the molecular microenvironment during the cloud point generation was successfully probed via these parameters. It is demonstrated that, in comparison to the present techniques available for assessing the hydrophobic-hydrophilic switch over of simple stimuli-responsive polymers, Mueller matrix polarimetry offers an important advantage requiring a few hundred times dilute polymer solution (0.01 mg/mL, 1.1-1.4 μM) at a low-volume format.

  1. A comparative study of Kalman filter and Linear Matrix Inequality based H infinity filter for SPND delay compensation

    International Nuclear Information System (INIS)

    Tamboli, P.K.; Duttagupta, Siddhartha P.; Roy, Kallol

    2016-01-01

    Highlights: • Derivation for delay compensation algorithm using recursive Kalman filter. • Derivation for delay compensation algorithm using Linear Matrix Inequality based H infinity filter. • Process modeling suitable for delay compensation. • Dynamic tuning of the delay compensation algorithm for both Kalman and H infinity filter. • Simulations and trade-off curve for Kalman and H infinity filter. - Abstract: This paper deals with delay compensation of vanadium Self Powered Neutron Detectors (SPNDs) using Linear Matrix Inequality (LMI) based H-infinity filtering method and compares the results with Kalman filtering method. The entire study is established upon the framework of neutron flux estimation in large core Pressurized Heavy Water Reactor (PHWR) in which delayed SPNDs such as vanadium SPNDs are used as in-core flux monitoring detectors. The use of vanadium SPNDs are limited to 3-D flux mapping despite of providing better Signal to Noise Ratio as compared to other prompt SPNDs, due to their small prompt component in the signal. The use of an appropriate delay compensation technique has been always considered to be an effective strategy to build a prompt and accurate estimate of the neutron flux. We also indicate the noise-response trade-off curve for both the techniques. Since all the delay compensation algorithms always suffer from noise amplification, we propose an efficient adaptive parameter tuning technique for improving performance of the filtering algorithm against noise in the measurement.

  2. Relative sensitivity of depth discrimination for ankle inversion and plantar flexion movements.

    Science.gov (United States)

    Black, Georgia; Waddington, Gordon; Adams, Roger

    2014-02-01

    25 participants (20 women, 5 men) were tested for sensitivity in discrimination between sets of six movements centered on 8 degrees, 11 degrees, and 14 degrees, and separated by 0.3 degrees. Both inversion and plantar flexion movements were tested. Discrimination of the extent of inversion movement was observed to decline linearly with increasing depth; however, for plantar flexion, the discrimination function for movement extent was found to be non-linear. The relatively better discrimination of plantar flexion movements than inversion movements at around 11 degrees from horizontal is interpreted as an effect arising from differential amounts of practice through use, because this position is associated with the plantar flexion movement made in normal walking. The fact that plantar flexion movements are discriminated better than inversion at one region but not others argues against accounts of superior proprioceptive sensitivity for plantar flexion compared to inversion that are based on general properties of plantar flexion such as the number of muscle fibres on stretch.

  3. The Cauchy problem for non-linear Klein-Gordon equations

    International Nuclear Information System (INIS)

    Simon, J.C.H.; Taflin, E.

    1993-01-01

    We consider in R n+1 , n≥2, the non-linear Klein-Gordon equation. We prove for such an equation that there is neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincare covariant then the non-linear representation of the Poincare-Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincare group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the wave operator. The Hilbert space is, in both cases, the closure of the space of the differentiable vectors for the linear representation of the Poincare group, associated with the Klein-Gordon equation, with respect to a norm defined by the representation of the enveloping algebra. (orig.)

  4. Particles geometry influence in the thermal stress level in an SiC reinforced aluminum matrix composite considering the material non-linear behavior

    International Nuclear Information System (INIS)

    Miranda, Carlos A. de J.; Libardi, Rosani M.P.; Boari, Zoroastro de M.

    2009-01-01

    An analytical methodology was developed to predict the thermal stress level that occurs in a metallic matrix composite reinforced with SiC particles, when the temperature decreases from 600 deg C to 20 deg C during the fabrication process. This analytical development is based on the Eshelby method, dislocation mechanisms, and the Maxwell-Boltzmann distribution model. The material was assumed to have a linear elastic behavior. The analytical results from this formulation were verified against numerical linear analyses that were performed over a set of random non-uniform distribution of particles that covers a wide range of volumetric ratios. To stick with the analytical hypothesis, particles with round geometry were used. Each stress distribution, represented by the isostress curves at ΔT=-580 deg C, was analyzed with an image analyzer. A statistical procedure was applied to obtain the most probable thermal stress level. Analytical and numerical results compared very well. Plastic deformation as well as particle geometry can alter significantly the stress field in the material. To account for these effects, in this work, several numerical analyses were performed considering the non-linear behavior for the aluminum matrix and distinct particle geometries. Two distinct sets of data with were used. To allow a direct comparison, the first set has the same models (particle form, size and distribution) as used previously. The second set analyze quadrilateral particles and present very tight range of volumetric ratio, closer to what is found in actual SiC composites. A simple and fast algorithm was developed to analyze the new results. The comparison of these results with the previous ones shows, as expected, the strong influence of the elastic-plastic behavior of the aluminum matrix on the composite thermal stress distribution due to its manufacturing process and shows, also, a small influence of the particles geometry and volumetric ratio. (author)

  5. A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesis

    Science.gov (United States)

    Landi, G.; Loli Piccolomini, E.; Nagy, J. G.

    2017-09-01

    Digital breast tomosynthesis (DBT) is an imaging technique that allows the reconstruction of a pseudo three-dimensional image of the breast from a finite number of low-dose two-dimensional projections obtained by different x-ray tube angles. An issue that is often ignored in DBT is the fact that an x-ray beam is polyenergetic, i.e. it is composed of photons with different levels of energy. The polyenergetic model requires solving a large-scale, nonlinear inverse problem, which is more expensive than the typically used simplified, linear monoenergetic model. However, the polyenergetic model is much less susceptible to beam hardening artifacts, which show up as dark streaks and cupping (i.e. background nonuniformities) in the reconstructed image. In addition, it has been shown that the polyenergetic model can be exploited to obtain additional quantitative information about the material of the object being imaged. In this paper we consider the multimaterial polyenergetic DBT model, and solve the nonlinear inverse problem with a limited memory BFGS quasi-Newton method. Regularization is enforced at each iteration using a diagonally modified approximation of the Hessian matrix, and by truncating the iterations.

  6. Accelerating atomic orbital-based electronic structure calculation via pole expansion and selected inversion

    International Nuclear Information System (INIS)

    Lin, Lin; Yang, Chao; Chen, Mohan; He, Lixin

    2013-01-01

    We describe how to apply the recently developed pole expansion and selected inversion (PEXSI) technique to Kohn–Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating the charge density, the total energy, the Helmholtz free energy and the atomic forces (including both the Hellmann–Feynman force and the Pulay force) without using the eigenvalues and eigenvectors of the Kohn–Sham Hamiltonian. We also show how to update the chemical potential without using Kohn–Sham eigenvalues. The advantage of using PEXSI is that it has a computational complexity much lower than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEXSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEXSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEXSI are modest. This even makes it possible to perform Kohn–Sham DFT calculations for 10 000-atom nanotubes with a sequential implementation of the selected inversion algorithm. We also perform an accurate geometry optimization calculation on a truncated (8, 0) boron nitride nanotube system containing 1024 atoms. Numerical results indicate that the use of PEXSI does not lead to loss of the accuracy required in a practical DFT calculation. (paper)

  7. Modeling and inverse feedforward control for conducting polymer actuators with hysteresis

    International Nuclear Information System (INIS)

    Wang, Xiangjiang; Alici, Gursel; Tan, Xiaobo

    2014-01-01

    Conducting polymer actuators are biocompatible with a small footprint, and operate in air or liquid media under low actuation voltages. This makes them excellent actuators for macro- and micro-manipulation devices, however, their positioning ability or accuracy is adversely affected by their hysteresis non-linearity under open-loop control strategies. In this paper, we establish a hysteresis model for conducting polymer actuators, based on a rate-independent hysteresis model known as the Duhem model. The hysteresis model is experimentally identified and integrated with the linear dynamics of the actuator. This combined model is inverted to control the displacement of the tri-layer actuators considered in this study, without using any external feedback. The inversion requires an inverse hysteresis model which was experimentally identified using an inverse neural network model. Experimental results show that the position tracking errors are reduced by more than 50% when the hysteresis inverse model is incorporated into an inversion-based feedforward controller, indicating the potential of the proposed method in enabling wider use of such smart actuators. (paper)

  8. Scilab software as an alternative low-cost computing in solving the linear equations problem

    Science.gov (United States)

    Agus, Fahrul; Haviluddin

    2017-02-01

    Numerical computation packages are widely used both in teaching and research. These packages consist of license (proprietary) and open source software (non-proprietary). One of the reasons to use the package is a complexity of mathematics function (i.e., linear problems). Also, number of variables in a linear or non-linear function has been increased. The aim of this paper was to reflect on key aspects related to the method, didactics and creative praxis in the teaching of linear equations in higher education. If implemented, it could be contribute to a better learning in mathematics area (i.e., solving simultaneous linear equations) that essential for future engineers. The focus of this study was to introduce an additional numerical computation package of Scilab as an alternative low-cost computing programming. In this paper, Scilab software was proposed some activities that related to the mathematical models. In this experiment, four numerical methods such as Gaussian Elimination, Gauss-Jordan, Inverse Matrix, and Lower-Upper Decomposition (LU) have been implemented. The results of this study showed that a routine or procedure in numerical methods have been created and explored by using Scilab procedures. Then, the routine of numerical method that could be as a teaching material course has exploited.

  9. Inverse Faraday Effect Revisited

    Science.gov (United States)

    Mendonça, J. T.; Ali, S.; Davies, J. R.

    2010-11-01

    The inverse Faraday effect is usually associated with circularly polarized laser beams. However, it was recently shown that it can also occur for linearly polarized radiation [1]. The quasi-static axial magnetic field by a laser beam propagating in plasma can be calculated by considering both the spin and the orbital angular momenta of the laser pulse. A net spin is present when the radiation is circularly polarized and a net orbital angular momentum is present if there is any deviation from perfect rotational symmetry. This orbital angular momentum has recently been discussed in the plasma context [2], and can give an additional contribution to the axial magnetic field, thus enhancing or reducing the inverse Faraday effect. As a result, this effect that is usually attributed to circular polarization can also be excited by linearly polarized radiation, if the incident laser propagates in a Laguerre-Gauss mode carrying a finite amount of orbital angular momentum.[4pt] [1] S. ALi, J.R. Davies and J.T. Mendonca, Phys. Rev. Lett., 105, 035001 (2010).[0pt] [2] J. T. Mendonca, B. Thidé, and H. Then, Phys. Rev. Lett. 102, 185005 (2009).

  10. Inverse planning and optimization: a comparison of solutions

    Energy Technology Data Exchange (ETDEWEB)

    Ringor, Michael [School of Health Sciences, Purdue University, West Lafayette, IN (United States); Papiez, Lech [Department of Radiation Oncology, Indiana University, Indianapolis, IN (United States)

    1998-09-01

    The basic problem in radiation therapy treatment planning is to determine an appropriate set of treatment parameters that would induce an effective dose distribution inside a patient. One can approach this task as an inverse problem, or as an optimization problem. In this presentation, we compare both approaches. The inverse problem is presented as a dose reconstruction problem similar to tomography reconstruction. We formulate the optimization problem as linear and quadratic programs. Explicit comparisons are made between the solutions obtained by inversion and those obtained by optimization for the case in which scatter and attenuation are ignored (the NS-NA approximation)

  11. Two linearization methods for atmospheric remote sensing

    International Nuclear Information System (INIS)

    Doicu, A.; Trautmann, T.

    2009-01-01

    We present two linearization methods for a pseudo-spherical atmosphere and general viewing geometries. The first approach is based on an analytical linearization of the discrete ordinate method with matrix exponential and incorporates two models for matrix exponential calculation: the matrix eigenvalue method and the Pade approximation. The second method referred to as the forward-adjoint approach is based on the adjoint radiative transfer for a pseudo-spherical atmosphere. We provide a compact description of the proposed methods as well as a numerical analysis of their accuracy and efficiency.

  12. Three Interpretations of the Matrix Equation Ax = b

    Science.gov (United States)

    Larson, Christine; Zandieh, Michelle

    2013-01-01

    Many of the central ideas in an introductory undergraduate linear algebra course are closely tied to a set of interpretations of the matrix equation Ax = b (A is a matrix, x and b are vectors): linear combination interpretations, systems interpretations, and transformation interpretations. We consider graphic and symbolic representations for each,…

  13. Inverse problem in nuclear physics

    International Nuclear Information System (INIS)

    Zakhariev, B.N.

    1976-01-01

    The method of reconstruction of interaction from the scattering data is formulated in the frame of the R-matrix theory in which the potential is determined by position of resonance Esub(lambda) and their reduced widths γ 2 lambda. In finite difference approximation for the Schroedinger equation this new approach allows to make the logics of the inverse problem IP more clear. A possibility of applications of IP formalism to various nuclear systems is discussed. (author)

  14. Blocky inversion of multichannel elastic impedance for elastic parameters

    Science.gov (United States)

    Mozayan, Davoud Karami; Gholami, Ali; Siahkoohi, Hamid Reza

    2018-04-01

    Petrophysical description of reservoirs requires proper knowledge of elastic parameters like P- and S-wave velocities (Vp and Vs) and density (ρ), which can be retrieved from pre-stack seismic data using the concept of elastic impedance (EI). We propose an inversion algorithm which recovers elastic parameters from pre-stack seismic data in two sequential steps. In the first step, using the multichannel blind seismic inversion method (exploited recently for recovering acoustic impedance from post-stack seismic data), high-resolution blocky EI models are obtained directly from partial angle-stacks. Using an efficient total-variation (TV) regularization, each angle-stack is inverted independently in a multichannel form without prior knowledge of the corresponding wavelet. The second step involves inversion of the resulting EI models for elastic parameters. Mathematically, under some assumptions, the EI's are linearly described by the elastic parameters in the logarithm domain. Thus a linear weighted least squares inversion is employed to perform this step. Accuracy of the concept of elastic impedance in predicting reflection coefficients at low and high angles of incidence is compared with that of exact Zoeppritz elastic impedance and the role of low frequency content in the problem is discussed. The performance of the proposed inversion method is tested using synthetic 2D data sets obtained from the Marmousi model and also 2D field data sets. The results confirm the efficiency and accuracy of the proposed method for inversion of pre-stack seismic data.

  15. Optimization for nonlinear inverse problem

    International Nuclear Information System (INIS)

    Boyadzhiev, G.; Brandmayr, E.; Pinat, T.; Panza, G.F.

    2007-06-01

    The nonlinear inversion of geophysical data in general does not yield a unique solution, but a single model, representing the investigated field, is preferred for an easy geological interpretation of the observations. The analyzed region is constituted by a number of sub-regions where the multi-valued nonlinear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper are presented new methodologies, capable to select one model, among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface waves dispersion curves, which gives structural models of shear-wave velocity versus depth, but the basic concepts have a general validity. (author)

  16. Source-independent elastic waveform inversion using a logarithmic wavefield

    KAUST Repository

    Choi, Yun Seok

    2012-01-01

    The logarithmic waveform inversion has been widely developed and applied to some synthetic and real data. In most logarithmic waveform inversion algorithms, the subsurface velocities are updated along with the source estimation. To avoid estimating the source wavelet in the logarithmic waveform inversion, we developed a source-independent logarithmic waveform inversion algorithm. In this inversion algorithm, we first normalize the wavefields with the reference wavefield to remove the source wavelet, and then take the logarithm of the normalized wavefields. Based on the properties of the logarithm, we define three types of misfit functions using the following methods: combination of amplitude and phase, amplitude-only, and phase-only. In the inversion, the gradient is computed using the back-propagation formula without directly calculating the Jacobian matrix. We apply our algorithm to noise-free and noise-added synthetic data generated for the modified version of elastic Marmousi2 model, and compare the results with those of the source-estimation logarithmic waveform inversion. For the noise-free data, the source-independent algorithms yield velocity models close to true velocity models. For random-noise data, the source-estimation logarithmic waveform inversion yields better results than the source-independent method, whereas for coherent-noise data, the results are reversed. Numerical results show that the source-independent and source-estimation logarithmic waveform inversion methods have their own merits for random- and coherent-noise data. © 2011.

  17. Non-linear sliding mode control of the lower extremity exoskeleton based on human–robot cooperation

    Directory of Open Access Journals (Sweden)

    Shiqiang Zhu

    2016-10-01

    Full Text Available This article presents a human–robot cooperation controller towards the lower extremity exoskeleton which aims to improve the tracking performance of the exoskeleton and reduce the human–robot interaction force. Radial basis function neural network is introduced to model the human–machine interaction which can better approximate the non-linear relationship than the general impedance model. A new method to calculate the inverse Jacobian matrix is presented. Compared to traditional damped least squares method, the novel method is proved to be able to avoid the orientation change of the velocity of the human–robot interaction point by the simulation result. This feature is very important in human–robot system. Then, an improved non-linear robust sliding mode controller is designed to promote the tracking performance considering system uncertainties and model errors, where a new non-linear integral sliding surface is given. The stability analysis of the proposed controller is performed using Lyapunov stability theory. Finally, the novel methods are applied to the swing leg control of the lower extremity exoskeleton, its effectiveness is validated by simulation and comparative experiments.

  18. Embedded Lattice and Properties of Gram Matrix

    Directory of Open Access Journals (Sweden)

    Futa Yuichi

    2017-03-01

    Full Text Available In this article, we formalize in Mizar [14] the definition of embedding of lattice and its properties. We formally define an inner product on an embedded module. We also formalize properties of Gram matrix. We formally prove that an inverse of Gram matrix for a rational lattice exists. Lattice of Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz base reduction algorithm [16] and cryptographic systems with lattice [17].

  19. Inverse radiative transfer problems in two-dimensional heterogeneous media

    International Nuclear Information System (INIS)

    Tito, Mariella Janette Berrocal

    2001-01-01

    The analysis of inverse problems in participating media where emission, absorption and scattering take place has several relevant applications in engineering and medicine. Some of the techniques developed for the solution of inverse problems have as a first step the solution of the direct problem. In this work the discrete ordinates method has been used for the solution of the linearized Boltzmann equation in two dimensional cartesian geometry. The Levenberg - Marquardt method has been used for the solution of the inverse problem of internal source and absorption and scattering coefficient estimation. (author)

  20. Guidance for the utility of linear models in meta-analysis of genetic association studies of binary phenotypes.

    Science.gov (United States)

    Cook, James P; Mahajan, Anubha; Morris, Andrew P

    2017-02-01

    Linear mixed models are increasingly used for the analysis of genome-wide association studies (GWAS) of binary phenotypes because they can efficiently and robustly account for population stratification and relatedness through inclusion of random effects for a genetic relationship matrix. However, the utility of linear (mixed) models in the context of meta-analysis of GWAS of binary phenotypes has not been previously explored. In this investigation, we present simulations to compare the performance of linear and logistic regression models under alternative weighting schemes in a fixed-effects meta-analysis framework, considering designs that incorporate variable case-control imbalance, confounding factors and population stratification. Our results demonstrate that linear models can be used for meta-analysis of GWAS of binary phenotypes, without loss of power, even in the presence of extreme case-control imbalance, provided that one of the following schemes is used: (i) effective sample size weighting of Z-scores or (ii) inverse-variance weighting of allelic effect sizes after conversion onto the log-odds scale. Our conclusions thus provide essential recommendations for the development of robust protocols for meta-analysis of binary phenotypes with linear models.

  1. Inverse scattering problems with multi-frequencies

    International Nuclear Information System (INIS)

    Bao, Gang; Li, Peijun; Lin, Junshan; Triki, Faouzi

    2015-01-01

    This paper is concerned with computational approaches and mathematical analysis for solving inverse scattering problems in the frequency domain. The problems arise in a diverse set of scientific areas with significant industrial, medical, and military applications. In addition to nonlinearity, there are two common difficulties associated with the inverse problems: ill-posedness and limited resolution (diffraction limit). Due to the diffraction limit, for a given frequency, only a low spatial frequency part of the desired parameter can be observed from measurements in the far field. The main idea developed here is that if the reconstruction is restricted to only the observable part, then the inversion will become stable. The challenging task is how to design stable numerical methods for solving these inverse scattering problems inspired by the diffraction limit. Recently, novel recursive linearization based algorithms have been presented in an attempt to answer the above question. These methods require multi-frequency scattering data and proceed via a continuation procedure with respect to the frequency from low to high. The objective of this paper is to give a brief review of these methods, their error estimates, and the related mathematical analysis. More attention is paid to the inverse medium and inverse source problems. Numerical experiments are included to illustrate the effectiveness of these methods. (topical review)

  2. Generalized Uncertainty Quantification for Linear Inverse Problems in X-ray Imaging

    Energy Technology Data Exchange (ETDEWEB)

    Fowler, Michael James [Clarkson Univ., Potsdam, NY (United States)

    2014-04-25

    In industrial and engineering applications, X-ray radiography has attained wide use as a data collection protocol for the assessment of material properties in cases where direct observation is not possible. The direct measurement of nuclear materials, particularly when they are under explosive or implosive loading, is not feasible, and radiography can serve as a useful tool for obtaining indirect measurements. In such experiments, high energy X-rays are pulsed through a scene containing material of interest, and a detector records a radiograph by measuring the radiation that is not attenuated in the scene. One approach to the analysis of these radiographs is to model the imaging system as an operator that acts upon the object being imaged to produce a radiograph. In this model, the goal is to solve an inverse problem to reconstruct the values of interest in the object, which are typically material properties such as density or areal density. The primary objective in this work is to provide quantitative solutions with uncertainty estimates for three separate applications in X-ray radiography: deconvolution, Abel inversion, and radiation spot shape reconstruction. For each problem, we introduce a new hierarchical Bayesian model for determining a posterior distribution on the unknowns and develop efficient Markov chain Monte Carlo (MCMC) methods for sampling from the posterior. A Poisson likelihood, based on a noise model for photon counts at the detector, is combined with a prior tailored to each application: an edge-localizing prior for deconvolution; a smoothing prior with non-negativity constraints for spot reconstruction; and a full covariance sampling prior based on a Wishart hyperprior for Abel inversion. After developing our methods in a general setting, we demonstrate each model on both synthetically generated datasets, including those from a well known radiation transport code, and real high energy radiographs taken at two U. S. Department of Energy

  3. Sparsity Prevention Pivoting Method for Linear Programming

    DEFF Research Database (Denmark)

    Li, Peiqiang; Li, Qiyuan; Li, Canbing

    2018-01-01

    When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper....... The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...

  4. Sparsity Prevention Pivoting Method for Linear Programming

    DEFF Research Database (Denmark)

    Li, Peiqiang; Li, Qiyuan; Li, Canbing

    2018-01-01

    . The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following......When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...

  5. Mathematical investigation of one-way transform matrix options

    International Nuclear Information System (INIS)

    Cooper, James Arlin

    2006-01-01

    One-way transforms have been used in weapon systems processors since the mid- to late-1970s in order to help recognize insertion of correct pre-arm information while maintaining abnormal-environment safety. Level-One, Level-Two, and Level-Three transforms have been designed. The Level-One and Level-Two transforms have been implemented in weapon systems, and both of these transforms are equivalent to matrix multiplication applied to the inserted information. The Level-Two transform, utilizing a 6 x 6 matrix, provided the basis for the ''System 2'' interface definition for Unique-Signal digital communication between aircraft and attached weapons. The investigation described in this report was carried out to find out if there were other size matrices that would be equivalent to the 6 x 6 Level-Two matrix. One reason for the investigation was to find out whether or not other dimensions were possible, and if so, to derive implementation options. Another important reason was to more fully explore the potential for inadvertent inversion. The results were that additional implementation methods were discovered, but no inversion weaknesses were revealed

  6. Full Waveform Inversion Using Oriented Time Migration Method

    KAUST Repository

    Zhang, Zhendong

    2016-04-12

    Full waveform inversion (FWI) for reflection events is limited by its linearized update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate the resulting gradient can have an inaccurate update direction leading the inversion to converge into what we refer to as local minima of the objective function. In this thesis, I first look into the subject of full model wavenumber to analysis the root of local minima and suggest the possible ways to avoid this problem. And then I analysis the possibility of recovering the corresponding wavenumber components through the existing inversion and migration algorithms. Migration can be taken as a generalized inversion method which mainly retrieves the high wavenumber part of the model. Conventional impedance inversion method gives a mapping relationship between the migration image (high wavenumber) and model parameters (full wavenumber) and thus provides a possible cascade inversion strategy to retrieve the full wavenumber components from seismic data. In the proposed approach, consider a mild lateral variation in the model, I find an analytical Frechet derivation corresponding to the new objective function. In the proposed approach, the gradient is given by the oriented time-domain imaging method. This is independent of the background velocity. Specifically, I apply the oriented time-domain imaging (which depends on the reflection slope instead of a background velocity) on the data residual to obtain the geometrical features of the velocity perturbation. Assuming that density is constant, the conventional 1D impedance inversion method is also applicable for 2D or 3D velocity inversion within the process of FWI. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearized representations of the reflection response. To eliminate the cross-talk artifacts between different parameters, I

  7. Recurrent Neural Network Approach Based on the Integral Representation of the Drazin Inverse.

    Science.gov (United States)

    Stanimirović, Predrag S; Živković, Ivan S; Wei, Yimin

    2015-10-01

    In this letter, we present the dynamical equation and corresponding artificial recurrent neural network for computing the Drazin inverse for arbitrary square real matrix, without any restriction on its eigenvalues. Conditions that ensure the stability of the defined recurrent neural network as well as its convergence toward the Drazin inverse are considered. Several illustrative examples present the results of computer simulations.

  8. Continuity of the direct and inverse problems in one-dimensional scattering theory and numerical solution of the inverse problem

    International Nuclear Information System (INIS)

    Moura, C.A. de.

    1976-09-01

    We propose an algorithm for computing the potential V(x) associated to the one-dimensional Schroedinger operator E identical to - d 2 /dx 2 + V(x) -infinite < x< infinite from knowledge of the S.matrix, more exactly, of one of the reelection coefficients. The convergence of the algorithm is guaranteed by the stability results obtained for both the direct and inverse problems

  9. Solution of the point kinetics equations in the presence of Newtonian temperature feedback by Pade approximations via the analytical inversion method

    International Nuclear Information System (INIS)

    Aboanber, A E; Nahla, A A

    2002-01-01

    A method based on the Pade approximations is applied to the solution of the point kinetics equations with a time varying reactivity. The technique consists of treating explicitly the roots of the inhour formula. A significant improvement has been observed by treating explicitly the most dominant roots of the inhour equation, which usually would make the Pade approximation inaccurate. Also the analytical inversion method which permits a fast inversion of polynomials of the point kinetics matrix is applied to the Pade approximations. Results are presented for several cases of Pade approximations using various options of the method with different types of reactivity. The formalism is applicable equally well to non-linear problems, where the reactivity depends on the neutron density through temperature feedback. It was evident that the presented method is particularly good for cases in which the reactivity can be represented by a series of steps and performed quite well for more general cases

  10. On a quadratic inverse eigenvalue problem

    International Nuclear Information System (INIS)

    Cai, Yunfeng; Xu, Shufang

    2009-01-01

    This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable

  11. Model study of the compact gravity reconstruction; Juryoku inversion `CGR` no model kento

    Energy Technology Data Exchange (ETDEWEB)

    Ishii, Y; Muraoka, A [Sogo Geophysical Exploration Co. Ltd., Tokyo (Japan)

    1996-05-01

    An examination was made on gravity inversion using a compact gravity reconstruction (CGR) method in gravity tomography analysis. In a model analysis, an analytical region of 100m{times}50m was divided into cells of 10m{times}10m, on the assumption that two density anomalous bodies with a density difference of 1.0g/cm{sup 3} existed with one shallow and the other deep density distribution. The result of the analysis revealed that, in a linear analysis by a general inverse matrix, blurs and blotting were plenty with a tendency of making gravity anomaly attributable to an anomalous distribution of shallow density; that CGR provided a large effect in making a clear contrast of an anomalous part; that, where structures of shallow and deep density anomalies existed, the analysis by CGR was inferior in the restoration of a deep structure with errors enlarged; that, if a gravity traverse was taken long compared with the distribution depth of density anomalies, the analytical precision of a deep part was improved; that an analytical convergence was better with the restriction of density difference given on the large side than on the small side; and so on. 3 refs., 10 figs.

  12. Matrix transformations and sequence spaces

    International Nuclear Information System (INIS)

    Nanda, S.

    1983-06-01

    In most cases the most general linear operator from one sequence space into another is actually given by an infinite matrix and therefore the theory of matrix transformations has always been of great interest in the study of sequence spaces. The study of general theory of matrix transformations was motivated by the special results in summability theory. This paper is a review article which gives almost all known results on matrix transformations. This also suggests a number of open problems for further study and will be very useful for research workers. (author)

  13. Handling of computational in vitro/in vivo correlation problems by Microsoft Excel: IV. Generalized matrix analysis of linear compartment systems.

    Science.gov (United States)

    Langenbucher, Frieder

    2005-01-01

    A linear system comprising n compartments is completely defined by the rate constants between any of the compartments and the initial condition in which compartment(s) the drug is present at the beginning. The generalized solution is the time profiles of drug amount in each compartment, described by polyexponential equations. Based on standard matrix operations, an Excel worksheet computes the rate constants and the coefficients, finally the full time profiles for a specified range of time values.

  14. Kelvin Notation for Stabilizing Elastic-Constant Inversion Notation Kelvin pour stabiliser l'inversion de constantes élastiques

    Directory of Open Access Journals (Sweden)

    Dellinger J.

    2006-12-01

    Full Text Available Inverting a set of core-sample traveltime measurements for a complete set of 21 elastic constants is a difficult problem. If the 21 elastic constants are directly used as the inversion parameters, a few bad measurements or an unfortunate starting guess may result in the inversion converging to a physically impossible solution . Even given perfect data, multiple solutions may exist that predict the observed traveltimes equally well. We desire the inversion algorithm to converge not just to a physically possible solution, but to the best(i. e. most physically likely solution of all those allowed. We present a new parameterization that attempts to solve these difficulties. The search space is limited to physically realizable media by making use of the Kelvin eigenstiffness-eigentensor representation of the 6 x 6 elastic stiffness matrix. Instead of 21 stiffnesses, there are 6 eigenstiffness parametersand 15 rotational parameters . The rotational parameters are defined using a Lie-algebra representation that avoids the artificial degeneracies and coordinate-system bias that can occur with standard polar representations. For any choice of these 21 real parameters, the corresponding stiffness matrix is guaranteed to be physically realizable. Furthermore, all physically realizable matrices can be represented in this way. This new parameterization still leaves considerable latitude as to which linear combinations of the Kelvin parameters to use, and how they should be ordered. We demonstrate that by careful choice and ordering of the parameters, the inversion can be relaxedfrom higher to lower symmetry simply by adding a few more parameters at a time. By starting from isotropy and relaxing to the general result in stages (isotropy, transverse isotropy, orthorhombic, general, we expect that the method should find the solution that is closest to isotropy of all those that fit the data. L'inversion d'un ensemble de mesures du temps de parcours d

  15. Incorporating modelled subglacial hydrology into inversions for basal drag

    Directory of Open Access Journals (Sweden)

    C. P. Koziol

    2017-12-01

    Full Text Available A key challenge in modelling coupled ice-flow–subglacial hydrology is initializing the state and parameters of the system. We address this problem by presenting a workflow for initializing these values at the start of a summer melt season. The workflow depends on running a subglacial hydrology model for the winter season, when the system is not forced by meltwater inputs, and ice velocities can be assumed constant. Key parameters of the winter run of the subglacial hydrology model are determined from an initial inversion for basal drag using a linear sliding law. The state of the subglacial hydrology model at the end of winter is incorporated into an inversion of basal drag using a non-linear sliding law which is a function of water pressure. We demonstrate this procedure in the Russell Glacier area and compare the output of the linear sliding law with two non-linear sliding laws. Additionally, we compare the modelled winter hydrological state to radar observations and find that it is in line with summer rather than winter observations.

  16. Tsunami waveform inversion by numerical finite-elements Green’s functions

    Directory of Open Access Journals (Sweden)

    A. Piatanesi

    2001-01-01

    Full Text Available During the last few years, the steady increase in the quantity and quality of the data concerning tsunamis has led to an increasing interest in the inversion problem for tsunami data. This work addresses the usually ill-posed problem of the hydrodynamical inversion of tsunami tide-gage records to infer the initial sea perturbation. We use an inversion method for which the data space consists of a given number of waveforms and the model parameter space is represented by the values of the initial water elevation field at a given number of points. The forward model, i.e. the calculation of the synthetic tide-gage records from an initial water elevation field, is based on the linear shallow water equations and is simply solved by applying the appropriate Green’s functions to the known initial state. The inversion of tide-gage records to determine the initial state results in the least square inversion of a rectangular system of linear equations. When the inversions are unconstrained, we found that in order to attain good results, the dimension of the data space has to be much larger than that of the model space parameter. We also show that a large number of waveforms is not sufficient to ensure a good inversion if the corresponding stations do not have a good azimuthal coverage with respect to source directivity. To improve the inversions we use the available a priori information on the source, generally coming from the inversion of seismological data. In this paper we show how to implement very common information about a tsunamigenic seismic source, i.e. the earthquake source region, as a set of spatial constraints. The results are very satisfactory, since even a rough localisation of the source enables us to invert correctly the initial elevation field.

  17. Full Waveform Inversion Using Oriented Time Migration Method

    KAUST Repository

    Zhang, Zhendong

    2016-01-01

    Full waveform inversion (FWI) for reflection events is limited by its linearized update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate the resulting gradient can have

  18. Two-step algorithm of generalized PAPA method applied to linear programming solution of dynamic matrix control

    International Nuclear Information System (INIS)

    Shimizu, Yoshiaki

    1991-01-01

    In recent complicated nuclear systems, there are increasing demands for developing highly advanced procedures for various problems-solvings. Among them keen interests have been paid on man-machine communications to improve both safety and economy factors. Many optimization methods have been good enough to elaborate on these points. In this preliminary note, we will concern with application of linear programming (LP) for this purpose. First we will present a new superior version of the generalized PAPA method (GEPAPA) to solve LP problems. We will then examine its effectiveness when applied to derive dynamic matrix control (DMC) as the LP solution. The approach is to aim at the above goal through a quality control of process that will appear in the system. (author)

  19. Matrix groups for undergraduates

    CERN Document Server

    Tapp, Kristopher

    2005-01-01

    Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori.

  20. Efficient parallel iterative solvers for the solution of large dense linear systems arising from the boundary element method in electromagnetism

    International Nuclear Information System (INIS)

    Alleon, G.; Carpentieri, B.; Du, I.S.; Giraud, L.; Langou, J.; Martin, E.

    2003-01-01

    The boundary element method has become a popular tool for the solution of Maxwell's equations in electromagnetism. It discretizes only the surface of the radiating object and gives rise to linear systems that are smaller in size compared to those arising from finite element or finite difference discretizations. However, these systems are prohibitively demanding in terms of memory for direct methods and challenging to solve by iterative methods. In this paper we address the iterative solution via preconditioned Krylov methods of electromagnetic scattering problems expressed in an integral formulation, with main focus on the design of the pre-conditioner. We consider an approximate inverse method based on the Frobenius-norm minimization with a pattern prescribed in advance. The pre-conditioner is constructed from a sparse approximation of the dense coefficient matrix, and the patterns both for the pre-conditioner and for the coefficient matrix are computed a priori using geometric information from the mesh. We describe the implementation of the approximate inverse in an out-of-core parallel code that uses multipole techniques for the matrix-vector products, and show results on the numerical scalability of our method on systems of size up to one million unknowns. We propose an embedded iterative scheme based on the GMRES method and combined with multipole techniques, aimed at improving the robustness of the approximate inverse for large problems. We prove by numerical experiments that the proposed scheme enables the solution of very large and difficult problems efficiently at reduced computational and memory cost. Finally we perform a preliminary study on a spectral two-level pre-conditioner to enhance the robustness of our method. This numerical technique exploits spectral information of the preconditioned systems to build a low rank-update of the pre-conditioner. (authors)

  1. Efficient parallel iterative solvers for the solution of large dense linear systems arising from the boundary element method in electromagnetism

    Energy Technology Data Exchange (ETDEWEB)

    Alleon, G. [EADS-CCR, 31 - Blagnac (France); Carpentieri, B.; Du, I.S.; Giraud, L.; Langou, J.; Martin, E. [Cerfacs, 31 - Toulouse (France)

    2003-07-01

    The boundary element method has become a popular tool for the solution of Maxwell's equations in electromagnetism. It discretizes only the surface of the radiating object and gives rise to linear systems that are smaller in size compared to those arising from finite element or finite difference discretizations. However, these systems are prohibitively demanding in terms of memory for direct methods and challenging to solve by iterative methods. In this paper we address the iterative solution via preconditioned Krylov methods of electromagnetic scattering problems expressed in an integral formulation, with main focus on the design of the pre-conditioner. We consider an approximate inverse method based on the Frobenius-norm minimization with a pattern prescribed in advance. The pre-conditioner is constructed from a sparse approximation of the dense coefficient matrix, and the patterns both for the pre-conditioner and for the coefficient matrix are computed a priori using geometric information from the mesh. We describe the implementation of the approximate inverse in an out-of-core parallel code that uses multipole techniques for the matrix-vector products, and show results on the numerical scalability of our method on systems of size up to one million unknowns. We propose an embedded iterative scheme based on the GMRES method and combined with multipole techniques, aimed at improving the robustness of the approximate inverse for large problems. We prove by numerical experiments that the proposed scheme enables the solution of very large and difficult problems efficiently at reduced computational and memory cost. Finally we perform a preliminary study on a spectral two-level pre-conditioner to enhance the robustness of our method. This numerical technique exploits spectral information of the preconditioned systems to build a low rank-update of the pre-conditioner. (authors)

  2. International Conference on Matrix Analysis and its Applications 2015

    CERN Document Server

    2017-01-01

    This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference. Topics covered include interval linear algebra and computational complexity, Birkhoff polynomial basis, tensors, graphs, linear pencils, K-theory and statistic inference, showing the ubiquity of matrices in different mathematical areas. With a particular focus on matrix and operator theory, statistical models and computation, the International Conference on Matrix Analysis and its Applications 2015, held in Coimbra, Portugal, was the sixth in a series of conferences. Applied and Computational Matrix Analysis will appeal to graduate students and researchers in theoretical and applied mathematics, physics and engineering who are seeking an overview of recent problems and methods in matrix analysis.

  3. Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

    Energy Technology Data Exchange (ETDEWEB)

    Agaltsov, A. D., E-mail: agalets@gmail.com [Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow (Russian Federation); Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr [CNRS (UMR 7641), Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau (France); IEPT RAS, 117997 Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny (Russian Federation)

    2014-10-15

    We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

  4. Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

    International Nuclear Information System (INIS)

    Agaltsov, A. D.; Novikov, R. G.

    2014-01-01

    We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given

  5. Inverse Scattering Method and Soliton Solution Family for String Effective Action

    International Nuclear Information System (INIS)

    Ya-Jun, Gao

    2009-01-01

    A modified Hauser–Ernst-type linear system is established and used to develop an inverse scattering method for solving the motion equations of the string effective action describing the coupled gravity, dilaton and Kalb–Ramond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the proposed inverse scattering method applied fine and effective. As an application, a concrete family of soliton solutions for the considered theory is obtained

  6. Linear methods in band theory

    DEFF Research Database (Denmark)

    Andersen, O. Krogh

    1975-01-01

    of Korringa-Kohn-Rostoker, linear-combination-of-atomic-orbitals, and cellular methods; the secular matrix is linear in energy, the overlap integrals factorize as potential parameters and structure constants, the latter are canonical in the sense that they neither depend on the energy nor the cell volume...

  7. On a finite moment perturbation of linear functionals and the inverse Szegö transformation

    Directory of Open Access Journals (Sweden)

    Edinson Fuentes

    2016-05-01

    Full Text Available Given a sequence of moments $\\{c_{n}\\}_{n\\in\\ze}$ associated with an Hermitian linear functional $\\mathcal{L}$ defined in the space of Laurent polynomials, we study a new functional $\\mathcal{L}_{\\Omega}$ which is a perturbation of $\\mathcal{L}$ in such a way that a finite number of moments are perturbed. Necessary and sufficient conditions are given for the regularity of $\\mathcal{L}_{\\Omega}$, and a connection formula between the corresponding families of orthogonal polynomials is obtained. On the other hand, assuming $\\mathcal{L}_{\\Omega}$ is positive definite, the perturbation is analyzed through the inverse Szegö transformation. Resumen. Dada una sucesión de momentos $\\{c_{n}\\}_{n\\in\\ze}$ asociada a un funcional lineal hermitiano $\\mathcal{L}$ definido en el espacio de los polinomios de Laurent, estudiamos un nuevo funcional $\\mathcal{L}_{\\Omega}$ que consiste en una perturbación de $\\mathcal{L}$ de tal forma que se perturba un número finito de momentos de la sucesión. Se encuentran condiciones necesarias y suficientes para la regularidad de $\\mathcal{L}_{\\Omega}$, y se obtiene una fórmula de conexión que relaciona las familias de polinomios ortogonales correspondientes. Por otro lado, suponiendo que $\\mathcal{L}_{\\Omega}$ es definido positivo, se analiza la perturbación mediante de la transformación inversa de Szegö.

  8. Performance evaluation of matrix gradient coils.

    Science.gov (United States)

    Jia, Feng; Schultz, Gerrit; Testud, Frederik; Welz, Anna Masako; Weber, Hans; Littin, Sebastian; Yu, Huijun; Hennig, Jürgen; Zaitsev, Maxim

    2016-02-01

    In this paper, we present a new performance measure of a matrix coil (also known as multi-coil) from the perspective of efficient, local, non-linear encoding without explicitly considering target encoding fields. An optimization problem based on a joint optimization for the non-linear encoding fields is formulated. Based on the derived objective function, a figure of merit of a matrix coil is defined, which is a generalization of a previously known resistive figure of merit for traditional gradient coils. A cylindrical matrix coil design with a high number of elements is used to illustrate the proposed performance measure. The results are analyzed to reveal novel features of matrix coil designs, which allowed us to optimize coil parameters, such as number of coil elements. A comparison to a scaled, existing multi-coil is also provided to demonstrate the use of the proposed performance parameter. The assessment of a matrix gradient coil profits from using a single performance parameter that takes the local encoding performance of the coil into account in relation to the dissipated power.

  9. Generalised Assignment Matrix Methodology in Linear Programming

    Science.gov (United States)

    Jerome, Lawrence

    2012-01-01

    Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

  10. Sorting signed permutations by inversions in O(nlogn) time.

    Science.gov (United States)

    Swenson, Krister M; Rajan, Vaibhav; Lin, Yu; Moret, Bernard M E

    2010-03-01

    The study of genomic inversions (or reversals) has been a mainstay of computational genomics for nearly 20 years. After the initial breakthrough of Hannenhalli and Pevzner, who gave the first polynomial-time algorithm for sorting signed permutations by inversions, improved algorithms have been designed, culminating with an optimal linear-time algorithm for computing the inversion distance and a subquadratic algorithm for providing a shortest sequence of inversions--also known as sorting by inversions. Remaining open was the question of whether sorting by inversions could be done in O(nlogn) time. In this article, we present a qualified answer to this question, by providing two new sorting algorithms, a simple and fast randomized algorithm and a deterministic refinement. The deterministic algorithm runs in time O(nlogn + kn), where k is a data-dependent parameter. We provide the results of extensive experiments showing that both the average and the standard deviation for k are small constants, independent of the size of the permutation. We conclude (but do not prove) that almost all signed permutations can be sorted by inversions in O(nlogn) time.

  11. The inverse method parametric verification of real-time embedded systems

    CERN Document Server

    André , Etienne

    2013-01-01

    This book introduces state-of-the-art verification techniques for real-time embedded systems, based on the inverse method for parametric timed automata. It reviews popular formalisms for the specification and verification of timed concurrent systems and, in particular, timed automata as well as several extensions such as timed automata equipped with stopwatches, linear hybrid automata and affine hybrid automata.The inverse method is introduced, and its benefits for guaranteeing robustness in real-time systems are shown. Then, it is shown how an iteration of the inverse method can solv

  12. Homogenization of linear viscoelastic three phase media: internal variable formulation versus full-field computation

    International Nuclear Information System (INIS)

    Blanc, V.; Barbie, L.; Masson, R.

    2011-01-01

    Homogenization of linear viscoelastic heterogeneous media is here extended from two phase inclusion-matrix media to three phase inclusion-matrix media. Each phase obeying to a compressible Maxwellian behaviour, this analytic method leads to an equivalent elastic homogenization problem in the Laplace-Carson space. For some particular microstructures, such as the Hashin composite sphere assemblage, an exact solution is obtained. The inversion of the Laplace-Carson transforms of the overall stress-strain behaviour gives in such cases an internal variable formulation. As expected, the number of these internal variables and their evolution laws are modified to take into account the third phase. Moreover, evolution laws of averaged stresses and strains per phase can still be derived for three phase media. Results of this model are compared to full fields computations of representative volume elements using finite element method, for various concentrations and sizes of inclusion. Relaxation and creep test cases are performed in order to compare predictions of the effective response. The internal variable formulation is shown to yield accurate prediction in both cases. (authors)

  13. An Explicit Consistent Geometric Stiffness Matrix for the DKT Element

    Directory of Open Access Journals (Sweden)

    Eliseu Lucena Neto

    Full Text Available Abstract A large number of references dealing with the geometric stiffness matrix of the DKT finite element exist in the literature, where nearly all of them adopt an inconsistent form. While such a matrix may be part of the element to treat nonlinear problems in general, it is of crucial importance for linearized buckling analysis. The present work seems to be the first to obtain an explicit expression for this matrix in a consistent way. Numerical results on linear buckling of plates assess the element performance either with the proposed explicit consistent matrix, or with the most commonly used inconsistent matrix.

  14. Nonlinear inversion of resistivity sounding data for 1-D earth models using the Neighbourhood Algorithm

    Science.gov (United States)

    Ojo, A. O.; Xie, Jun; Olorunfemi, M. O.

    2018-01-01

    To reduce ambiguity related to nonlinearities in the resistivity model-data relationships, an efficient direct-search scheme employing the Neighbourhood Algorithm (NA) was implemented to solve the 1-D resistivity problem. In addition to finding a range of best-fit models which are more likely to be global minimums, this method investigates the entire multi-dimensional model space and provides additional information about the posterior model covariance matrix, marginal probability density function and an ensemble of acceptable models. This provides new insights into how well the model parameters are constrained and make assessing trade-offs between them possible, thus avoiding some common interpretation pitfalls. The efficacy of the newly developed program is tested by inverting both synthetic (noisy and noise-free) data and field data from other authors employing different inversion methods so as to provide a good base for comparative performance. In all cases, the inverted model parameters were in good agreement with the true and recovered model parameters from other methods and remarkably correlate with the available borehole litho-log and known geology for the field dataset. The NA method has proven to be useful whilst a good starting model is not available and the reduced number of unknowns in the 1-D resistivity inverse problem makes it an attractive alternative to the linearized methods. Hence, it is concluded that the newly developed program offers an excellent complementary tool for the global inversion of the layered resistivity structure.

  15. A convex optimization approach for solving large scale linear systems

    Directory of Open Access Journals (Sweden)

    Debora Cores

    2017-01-01

    Full Text Available The well-known Conjugate Gradient (CG method minimizes a strictly convex quadratic function for solving large-scale linear system of equations when the coefficient matrix is symmetric and positive definite. In this work we present and analyze a non-quadratic convex function for solving any large-scale linear system of equations regardless of the characteristics of the coefficient matrix. For finding the global minimizers, of this new convex function, any low-cost iterative optimization technique could be applied. In particular, we propose to use the low-cost globally convergent Spectral Projected Gradient (SPG method, which allow us to extend this optimization approach for solving consistent square and rectangular linear system, as well as linear feasibility problem, with and without convex constraints and with and without preconditioning strategies. Our numerical results indicate that the new scheme outperforms state-of-the-art iterative techniques for solving linear systems when the symmetric part of the coefficient matrix is indefinite, and also for solving linear feasibility problems.

  16. Acoustic 2D full waveform inversion to solve gas cloud challenges

    Directory of Open Access Journals (Sweden)

    Srichand Prajapati

    2015-09-01

    Full Text Available The existing conventional inversion algorithm does not provide satisfactory results due to the complexity of propagated wavefield though the gas cloud. Acoustic full waveform inversion has been developed and applied to a realistic synthetic offshore shallow gas cloud feature with Student-t approach, with and without simultaneous sources encoding. As a modeling operator, we implemented the grid based finite-difference method in frequency domain using second order elastic wave equation. Jacobin operator and its adjoint provide a necessary platform for solving full waveform inversion problem in a reduced Hessian matrix. We invert gas cloud model in 5 frequency band selected from 1 to 12 Hz, each band contains 3 frequencies. The inversion results are highly sensitive to the misfit. The model allows better convergence and recovery of amplitude losses. This approach gives better resolution then the existing least-squares approach. In this paper, we implement the full waveform inversion for low frequency model with minimum number of iteration providing a better resolution of inversion results.

  17. Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs

    NARCIS (Netherlands)

    R.A. Zuidwijk (Rob)

    2005-01-01

    textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an

  18. Representations for the generalized Drazin inverse of the sum in a Banach algebra and its application for some operator matrices.

    Science.gov (United States)

    Liu, Xiaoji; Qin, Xiaolan

    2015-01-01

    We investigate additive properties of the generalized Drazin inverse in a Banach algebra A. We find explicit expressions for the generalized Drazin inverse of the sum a + b, under new conditions on a, b ∈ A. As an application we give some new representations for the generalized Drazin inverse of an operator matrix.

  19. An MCMC method for the evaluation of the Fisher information matrix for non-linear mixed effect models.

    Science.gov (United States)

    Riviere, Marie-Karelle; Ueckert, Sebastian; Mentré, France

    2016-10-01

    Non-linear mixed effect models (NLMEMs) are widely used for the analysis of longitudinal data. To design these studies, optimal design based on the expected Fisher information matrix (FIM) can be used instead of performing time-consuming clinical trial simulations. In recent years, estimation algorithms for NLMEMs have transitioned from linearization toward more exact higher-order methods. Optimal design, on the other hand, has mainly relied on first-order (FO) linearization to calculate the FIM. Although efficient in general, FO cannot be applied to complex non-linear models and with difficulty in studies with discrete data. We propose an approach to evaluate the expected FIM in NLMEMs for both discrete and continuous outcomes. We used Markov Chain Monte Carlo (MCMC) to integrate the derivatives of the log-likelihood over the random effects, and Monte Carlo to evaluate its expectation w.r.t. the observations. Our method was implemented in R using Stan, which efficiently draws MCMC samples and calculates partial derivatives of the log-likelihood. Evaluated on several examples, our approach showed good performance with relative standard errors (RSEs) close to those obtained by simulations. We studied the influence of the number of MC and MCMC samples and computed the uncertainty of the FIM evaluation. We also compared our approach to Adaptive Gaussian Quadrature, Laplace approximation, and FO. Our method is available in R-package MIXFIM and can be used to evaluate the FIM, its determinant with confidence intervals (CIs), and RSEs with CIs. © The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

  20. Factorizations of rational matrix functions with application to discrete isomonodromic transformations and difference Painleve equations

    International Nuclear Information System (INIS)

    Dzhamay, Anton

    2009-01-01

    We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this space is given by a mix of residue eigenvectors of the matrix and its inverse. Our approach is motivated by the theory of discrete isomonodromic transformations and their relationship with difference Painleve equations. In particular, in these coordinates, basic isomonodromic transformations take the form of the discrete Euler-Lagrange equations. Secondly we show that dPV equations, previously obtained in this context by D Arinkin and A Borodin, can be understood as simple relationships between the residues of such matrices and their inverses.

  1. ORACLS: A system for linear-quadratic-Gaussian control law design

    Science.gov (United States)

    Armstrong, E. S.

    1978-01-01

    A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

  2. The Growing Importance of Linear Algebra in Undergraduate Mathematics.

    Science.gov (United States)

    Tucker, Alan

    1993-01-01

    Discusses the theoretical and practical importance of linear algebra. Presents a brief history of linear algebra and matrix theory and describes the place of linear algebra in the undergraduate curriculum. (MDH)

  3. The effect of dendrimer charge inversion in complexes with linear polyelectrolytes

    NARCIS (Netherlands)

    Lyulin, S.V.; Lyulin, A.V.; Darinskii, A.A.; Emri, I.

    2005-01-01

    The structure of complexes formed by charged dendrimers and oppositely charged linear chains with a charge of at least the same as that of dendrimers was studied by computer simulation using the Brownian dynamics method. The freely jointed, free-draining model of the dendrimer and the linear chain

  4. Geodynamic inversion to constrain the non-linear rheology of the lithosphere

    Science.gov (United States)

    Baumann, T. S.; Kaus, Boris J. P.

    2015-08-01

    One of the main methods to determine the strength of the lithosphere is by estimating it's effective elastic thickness. This method assumes that the lithosphere is a thin elastic plate that floats on the mantle and uses both topography and gravity anomalies to estimate the plate thickness. Whereas this seems to work well for oceanic plates, it has given controversial results in continental collision zones. For most of these locations, additional geophysical data sets such as receiver functions and seismic tomography exist that constrain the geometry of the lithosphere and often show that it is rather complex. Yet, lithospheric geometry by itself is insufficient to understand the dynamics of the lithosphere as this also requires knowledge of the rheology of the lithosphere. Laboratory experiments suggest that rocks deform in a viscous manner if temperatures are high and stresses low, or in a plastic/brittle manner if the yield stress is exceeded. Yet, the experimental results show significant variability between various rock types and there are large uncertainties in extrapolating laboratory values to nature, which leaves room for speculation. An independent method is thus required to better understand the rheology and dynamics of the lithosphere in collision zones. The goal of this paper is to discuss such an approach. Our method relies on performing numerical thermomechanical forward models of the present-day lithosphere with an initial geometry that is constructed from geophysical data sets. We employ experimentally determined creep-laws for the various parts of the lithosphere, but assume that the parameters of these creep-laws as well as the temperature structure of the lithosphere are uncertain. This is used as a priori information to formulate a Bayesian inverse problem that employs topography, gravity, horizontal and vertical surface velocities to invert for the unknown material parameters and temperature structure. In order to test the general methodology

  5. Linear-control-based synchronization of coexisting attractor networks with time delays

    International Nuclear Information System (INIS)

    Yun-Zhong, Song

    2010-01-01

    This paper introduces the concept of linear-control-based synchronization of coexisting attractor networks with time delays. Within the new framework, closed loop control for each dynamic node is realized through linear state feedback around its own arena in a decentralized way, where the feedback matrix is determined through consideration of the coordination of the node dynamics, the inner connected matrix and the outer connected matrix. Unlike previously existing results, the feedback gain matrix here is decoupled from the inner matrix; this not only guarantees the flexible choice of the gain matrix, but also leaves much space for inner matrix configuration. Synchronization of coexisting attractor networks with time delays is made possible in virtue of local interaction, which works in a distributed way between individual neighbours, and the linear feedback control for each node. Provided that the network is connected and balanced, synchronization will come true naturally, where theoretical proof is given via a Lyapunov function. For completeness, several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme. (general)

  6. Two-Link Flexible Manipulator Control Using Sliding Mode Control Based Linear Matrix Inequality

    Science.gov (United States)

    Zulfatman; Marzuki, Mohammad; Alif Mardiyah, Nur

    2017-04-01

    Two-link flexible manipulator is a manipulator robot which at least one of its arms is made of lightweight material and not rigid. Flexible robot manipulator has some advantages over the rigid robot manipulator, such as lighter, requires less power and costs, and to result greater payload. However, suitable control algorithm to maintain the two-link flexible robot manipulator in accurate positioning is very challenging. In this study, sliding mode control (SMC) was employed as robust control algorithm due to its insensitivity on the system parameter variations and the presence of disturbances when the system states are sliding on a sliding surface. SMC algorithm was combined with linear matrix inequality (LMI), which aims to reduce the effects of chattering coming from the oscillation of the state during sliding on the sliding surface. Stability of the control algorithm is guaranteed by Lyapunov function candidate. Based on simulation works, SMC based LMI resulted in better performance improvements despite the disturbances with significant chattering reduction. This was evident from the decline of the sum of squared tracking error (SSTE) and the sum of squared of control input (SSCI) indexes respectively 25.4% and 19.4%.

  7. Time-domain induced polarization - an analysis of Cole-Cole parameter resolution and correlation using Markov Chain Monte Carlo inversion

    Science.gov (United States)

    Madsen, Line Meldgaard; Fiandaca, Gianluca; Auken, Esben; Christiansen, Anders Vest

    2017-12-01

    The application of time-domain induced polarization (TDIP) is increasing with advances in acquisition techniques, data processing and spectral inversion schemes. An inversion of TDIP data for the spectral Cole-Cole parameters is a non-linear problem, but by applying a 1-D Markov Chain Monte Carlo (MCMC) inversion algorithm, a full non-linear uncertainty analysis of the parameters and the parameter correlations can be accessed. This is essential to understand to what degree the spectral Cole-Cole parameters can be resolved from TDIP data. MCMC inversions of synthetic TDIP data, which show bell-shaped probability distributions with a single maximum, show that the Cole-Cole parameters can be resolved from TDIP data if an acquisition range above two decades in time is applied. Linear correlations between the Cole-Cole parameters are observed and by decreasing the acquisitions ranges, the correlations increase and become non-linear. It is further investigated how waveform and parameter values influence the resolution of the Cole-Cole parameters. A limiting factor is the value of the frequency exponent, C. As C decreases, the resolution of all the Cole-Cole parameters decreases and the results become increasingly non-linear. While the values of the time constant, τ, must be in the acquisition range to resolve the parameters well, the choice between a 50 per cent and a 100 per cent duty cycle for the current injection does not have an influence on the parameter resolution. The limits of resolution and linearity are also studied in a comparison between the MCMC and a linearized gradient-based inversion approach. The two methods are consistent for resolved models, but the linearized approach tends to underestimate the uncertainties for poorly resolved parameters due to the corresponding non-linear features. Finally, an MCMC inversion of 1-D field data verifies that spectral Cole-Cole parameters can also be resolved from TD field measurements.

  8. Simultaneous inversion of the background velocity and the perturbation in full-waveform inversion

    KAUST Repository

    Wu, Zedong

    2015-09-02

    The gradient of standard full-waveform inversion (FWI) attempts to map the residuals in the data to perturbations in the model. Such perturbations may include smooth background updates from the transmission components and high wavenumber updates from the reflection components. However, if we fix the reflection components using imaging, the gradient of what is referred to as reflected-waveform inversion (RWI) admits mainly transmission background-type updates. The drawback of existing RWI methods is that they lack an optimal image capable of producing reflections within the convex region of the optimization. Because the influence of velocity on the data was given mainly by its background (propagator) and perturbed (reflectivity) components, we have optimized both components simultaneously using a modified objective function. Specifically, we used an objective function that combined the data generated from a source using the background velocity, and that by the perturbed velocity through Born modeling, to fit the observed data. When the initial velocity was smooth, the data modeled from the source using the background velocity will mainly be reflection free, and most of the reflections were obtained from the image (perturbed velocity). As the background velocity becomes more accurate and can produce reflections, the role of the image will slowly diminish, and the update will be dominated by the standard FWI gradient to obtain high resolution. Because the objective function was quadratic with respect to the image, the inversion for the image was fast. To update the background velocity smoothly, we have combined different components of the gradient linearly through solving a small optimization problem. Application to the Marmousi model found that this method converged starting with a linearly increasing velocity, and with data free of frequencies below 4 Hz. Application to the 2014 Chevron Gulf of Mexico imaging challenge data set demonstrated the potential of the

  9. Inverse scattering transform for the time dependent Schroedinger equation with applications to the KPI equation

    Energy Technology Data Exchange (ETDEWEB)

    Xin, Zhou [Wisconsin Univ., Madison (USA). Dept. of Mathematics

    1990-03-01

    For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.).

  10. Inverse scattering transform for the time dependent Schroedinger equation with applications to the KPI equation

    International Nuclear Information System (INIS)

    Zhou Xin

    1990-01-01

    For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.)

  11. Application of the numerical Laplace transform inversion to neutron transport theory

    International Nuclear Information System (INIS)

    Ganapol, B.D.

    1989-01-01

    A numerical Laplace transform inversion is developed using the Hurwitz-Zweifel method of evaluating the Fourier cosine integral coupled with an Euler-Knopp transformation. The numerical inversion is then applied to problems in linear transport theory concerning slowing down, time-dependence and featuring the determination of the interior scalar flux solution to the one-group stationary transport equation in half-space geometry

  12. Elementary matrix algebra

    CERN Document Server

    Hohn, Franz E

    2012-01-01

    This complete and coherent exposition, complemented by numerous illustrative examples, offers readers a text that can teach by itself. Fully rigorous in its treatment, it offers a mathematically sound sequencing of topics. The work starts with the most basic laws of matrix algebra and progresses to the sweep-out process for obtaining the complete solution of any given system of linear equations - homogeneous or nonhomogeneous - and the role of matrix algebra in the presentation of useful geometric ideas, techniques, and terminology.Other subjects include the complete treatment of the structur

  13. Random linear codes in steganography

    Directory of Open Access Journals (Sweden)

    Kamil Kaczyński

    2016-12-01

    Full Text Available Syndrome coding using linear codes is a technique that allows improvement in the steganographic algorithms parameters. The use of random linear codes gives a great flexibility in choosing the parameters of the linear code. In parallel, it offers easy generation of parity check matrix. In this paper, the modification of LSB algorithm is presented. A random linear code [8, 2] was used as a base for algorithm modification. The implementation of the proposed algorithm, along with practical evaluation of algorithms’ parameters based on the test images was made.[b]Keywords:[/b] steganography, random linear codes, RLC, LSB

  14. Solving probabilistic inverse problems rapidly with prior samples

    NARCIS (Netherlands)

    Käufl, Paul; Valentine, Andrew P.; de Wit, Ralph W.; Trampert, Jeannot

    2016-01-01

    Owing to the increasing availability of computational resources, in recent years the probabilistic solution of non-linear, geophysical inverse problems by means of sampling methods has become increasingly feasible. Nevertheless, we still face situations in which a Monte Carlo approach is not

  15. A CMOS rail-to-rail linear VI-converter

    NARCIS (Netherlands)

    Vervoort, P.P.; Vervoort, P.P.; Wassenaar, R.F.

    1995-01-01

    A linear CMOS VI-converter operating in strong inversion with a common-mode input range from the negative to the positive supply rail is presented. The circuit consists of three linear VI-converters based on the difference of squares principle. Two of these perform the actual V to I conversion,

  16. Quasinormal-Mode Expansion of the Scattering Matrix

    Directory of Open Access Journals (Sweden)

    Filippo Alpeggiani

    2017-06-01

    Full Text Available It is well known that the quasinormal modes (or resonant states of photonic structures can be associated with the poles of the scattering matrix of the system in the complex-frequency plane. In this work, the inverse problem, i.e., the reconstruction of the scattering matrix from the knowledge of the quasinormal modes, is addressed. We develop a general and scalable quasinormal-mode expansion of the scattering matrix, requiring only the complex eigenfrequencies and the far-field properties of the eigenmodes. The theory is validated by applying it to illustrative nanophotonic systems with multiple overlapping electromagnetic modes. The examples demonstrate that our theory provides an accurate first-principles prediction of the scattering properties, without the need for postulating ad hoc nonresonant channels.

  17. A novel matrix approach for controlling the invariant densities of chaotic maps

    International Nuclear Information System (INIS)

    Rogers, Alan; Shorten, Robert; Heffernan, Daniel M.

    2008-01-01

    Recent work on positive matrices has resulted in a new matrix method for generating chaotic maps with arbitrary piecewise constant invariant densities, sometimes known as the inverse Frobenius-Perron problem (IFPP). In this paper, we give an extensive introduction to the IFPP, describing existing methods for solving it, and we describe our new matrix approach for solving the IFPP

  18. Application of the kernel method to the inverse geosounding problem.

    Science.gov (United States)

    Hidalgo, Hugo; Sosa León, Sonia; Gómez-Treviño, Enrique

    2003-01-01

    Determining the layered structure of the earth demands the solution of a variety of inverse problems; in the case of electromagnetic soundings at low induction numbers, the problem is linear, for the measurements may be represented as a linear functional of the electrical conductivity distribution. In this paper, an application of the support vector (SV) regression technique to the inversion of electromagnetic data is presented. We take advantage of the regularizing properties of the SV learning algorithm and use it as a modeling technique with synthetic and field data. The SV method presents better recovery of synthetic models than Tikhonov's regularization. As the SV formulation is solved in the space of the data, which has a small dimension in this application, a smaller problem than that considered with Tikhonov's regularization is produced. For field data, the SV formulation develops models similar to those obtained via linear programming techniques, but with the added characteristic of robustness.

  19. Neural-Based Compensation of Nonlinearities in an Airplane Longitudinal Model with Dynamic-Inversion Control

    Directory of Open Access Journals (Sweden)

    YanBin Liu

    2017-01-01

    Full Text Available The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller.

  20. Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations.

    Science.gov (United States)

    Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke

    2018-02-01

    In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

  1. Three-Dimensional Inversion of Magnetotelluric Data for the Sediment–Basement Interface

    DEFF Research Database (Denmark)

    Cai, Hongzhu; Zhdanov, Michael

    2016-01-01

    the thickness and the conductivities of the sedimentary basin. The forward modeling is based on the integral equation approach. The inverse problem is solved using a regularized conjugate gradient method. The Fréchet derivative matrix is calculated based on quasi-Born approximation. The developed method...

  2. Retrieving the correlation matrix from a truncated PCA solution : The inverse principal component problem

    NARCIS (Netherlands)

    ten Berge, Jos M.F.; Kiers, Henk A.L.

    When r Principal Components are available for k variables, the correlation matrix is approximated in the least squares sense by the loading matrix times its transpose. The approximation is generally not perfect unless r = k. In the present paper it is shown that, when r is at or above the Ledermann

  3. Speed-Sensorless DTC-SVM for Matrix Converter Drives With Simple Non-Linearity Compensation

    DEFF Research Database (Denmark)

    Lee, Kyo-Beum; Blaabjerg, Frede; Yoon, Tae-Woong

    2005-01-01

    This paper presents a new method to improve sensorless performance of matrix converter drives using a parameter estimation scheme. To improve low-speed sensorless performance, the non-Iinearities of a matrix converter drive such as commutation delays, turn-on and turn-off times of switching devic...... method is applied for high performance induction motor drives using a 3 kW matrix converter system without a speed sensor. Experimental results are shown to illustrate the feasibility of the proposed strategy....

  4. Linear and non-linear stability analysis for finite difference discretizations of high-order Boussinesq equations

    DEFF Research Database (Denmark)

    Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.

    2004-01-01

    of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water non-linearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into the numerical behaviour of this rather complicated system of non-linear PDEs....

  5. Recovery of the Dirac system from the rectangular Weyl matrix function

    International Nuclear Information System (INIS)

    Fritzsche, B; Kirstein, B; Roitberg, I Ya; Sakhnovich, A L

    2012-01-01

    Weyl theory for Dirac systems with rectangular matrix potentials is non-classical. The corresponding Weyl functions are rectangular matrix functions. Furthermore, they are non-expansive in the upper semi-plane. Inverse problems are studied for such Weyl functions, and some results are new even for the square Weyl functions. High-energy asymptotics of Weyl functions and Borg–Marchenko-type uniqueness results are derived too. (paper)

  6. A reduced-scaling density matrix-based method for the computation of the vibrational Hessian matrix at the self-consistent field level

    International Nuclear Information System (INIS)

    Kussmann, Jörg; Luenser, Arne; Beer, Matthias; Ochsenfeld, Christian

    2015-01-01

    An analytical method to calculate the molecular vibrational Hessian matrix at the self-consistent field level is presented. By analysis of the multipole expansions of the relevant derivatives of Coulomb-type two-electron integral contractions, we show that the effect of the perturbation on the electronic structure due to the displacement of nuclei decays at least as r −2 instead of r −1 . The perturbation is asymptotically local, and the computation of the Hessian matrix can, in principle, be performed with O(N) complexity. Our implementation exhibits linear scaling in all time-determining steps, with some rapid but quadratic-complexity steps remaining. Sample calculations illustrate linear or near-linear scaling in the construction of the complete nuclear Hessian matrix for sparse systems. For more demanding systems, scaling is still considerably sub-quadratic to quadratic, depending on the density of the underlying electronic structure

  7. Three-Dimensional Induced Polarization Parallel Inversion Using Nonlinear Conjugate Gradients Method

    Directory of Open Access Journals (Sweden)

    Huan Ma

    2015-01-01

    Full Text Available Four kinds of array of induced polarization (IP methods (surface, borehole-surface, surface-borehole, and borehole-borehole are widely used in resource exploration. However, due to the presence of large amounts of the sources, it will take much time to complete the inversion. In the paper, a new parallel algorithm is described which uses message passing interface (MPI and graphics processing unit (GPU to accelerate 3D inversion of these four methods. The forward finite differential equation is solved by ILU0 preconditioner and the conjugate gradient (CG solver. The inverse problem is solved by nonlinear conjugate gradients (NLCG iteration which is used to calculate one forward and two “pseudo-forward” modelings and update the direction, space, and model in turn. Because each source is independent in forward and “pseudo-forward” modelings, multiprocess modes are opened by calling MPI library. The iterative matrix solver within CULA is called in each process. Some tables and synthetic data examples illustrate that this parallel inversion algorithm is effective. Furthermore, we demonstrate that the joint inversion of surface and borehole data produces resistivity and chargeability results are superior to those obtained from inversions of individual surface data.

  8. Imaging the Flow Networks from a Harmonic Pumping in a Karstic Field with an Inversion Algorithm

    Science.gov (United States)

    Fischer, P.; Lecoq, N.; Jardani, A.; Jourde, H.; Wang, X.; Chedeville, S.; Cardiff, M. A.

    2017-12-01

    Identifying flow paths within karstic fields remains a complex task because of the high dependency of the hydraulic responses to the relative locations between the observation boreholes and the karstic conduits and interconnected fractures that control the main flows of the hydrosystem. In this context, harmonic pumping is a new investigation tool that permits to inform on the flow paths connectivity between the boreholes. We have shown that the amplitude and phase offset values in the periodic responses of a hydrosystem to a harmonic pumping test characterize three different type of flow behavior between the measurement boreholes and the pumping borehole: a direct connectivity response (conduit flow), an indirect connectivity (conduit and short matrix flows), and an absence of connectivity (matrix). When the hydraulic responses to study are numerous and complex, the interpretation of the flow paths requires an inverse modeling. Therefore, we have recently developed a Cellular Automata-based Deterministic Inversion (CADI) approach that permits to infer the spatial distribution of field hydraulic conductivities in a structurally constrained model. This method distributes hydraulic conductivities along linear structures (i.e. karst conduits) and iteratively modifies the structural geometry of this conduits network to progressively match the observed responses to the modeled ones. As a result, this method produces a conductivity model that is composed of a discrete conduit network embedded in the background matrix, capable of producing the same flow behavior as the investigated hydrologic system. We applied the CADI approach in order to reproduce, in a model, the amplitude and phase offset values of a set of periodic responses generated from harmonic pumping tests conducted in different boreholes at the Terrieu karstic field site (Southern France). This association of oscillatory responses with the CADI method provides an interpretation of the flow paths within the

  9. Gradient-type methods in inverse parabolic problems

    International Nuclear Information System (INIS)

    Kabanikhin, Sergey; Penenko, Aleksey

    2008-01-01

    This article is devoted to gradient-based methods for inverse parabolic problems. In the first part, we present a priori convergence theorems based on the conditional stability estimates for linear inverse problems. These theorems are applied to backwards parabolic problem and sideways parabolic problem. The convergence conditions obtained coincide with sourcewise representability in the self-adjoint backwards parabolic case but they differ in the sideways case. In the second part, a variational approach is formulated for a coefficient identification problem. Using adjoint equations, a formal gradient of an objective functional is constructed. A numerical test illustrates the performance of conjugate gradient algorithm with the formal gradient.

  10. Inverse opal carbons for counter electrode of dye-sensitized solar cells.

    Science.gov (United States)

    Kang, Da-Young; Lee, Youngshin; Cho, Chang-Yeol; Moon, Jun Hyuk

    2012-05-01

    We investigated the fabrication of inverse opal carbon counter electrodes using a colloidal templating method for DSSCs. Specifically, bare inverse opal carbon, mesopore-incoporated inverse opal carbon, and graphitized inverse opal carbon were synthesized and stably dispersed in ethanol solution for spray coating on a FTO substrate. The thickness of the electrode was controlled by the number of coatings, and the average relative thickness was evaluated by measuring the transmittance spectrum. The effect of the counter electrode thickness on the photovoltaic performance of the DSSCs was investigated and analyzed by interfacial charge transfer resistance (R(CT)) under EIS measurement. The effect of the surface area and conductivity of the inverse opal was also investigated by considering the increase in surface area due to the mesopore in the inverse opal carbon and conductivity by graphitization of the carbon matrix. The results showed that the FF and thereby the efficiency of DSSCs were increased as the electrode thickness increased. Consequently, the larger FF and thereby the greater efficiency of the DSSCs were achieved for mIOC and gIOC compared to IOC, which was attributed to the lower R(CT). Finally, compared to a conventional Pt counter electrode, the inverse opal-based carbon showed a comparable efficiency upon application to DSSCs.

  11. Enhanced Matrix Power Function for Cryptographic Primitive Construction

    Directory of Open Access Journals (Sweden)

    Eligijus Sakalauskas

    2018-02-01

    Full Text Available A new enhanced matrix power function (MPF is presented for the construction of cryptographic primitives. According to the definition in previously published papers, an MPF is an action of two matrices powering some base matrix on the left and right. The MPF inversion equations, corresponding to the MPF problem, are derived and have some structural similarity with classical multivariate quadratic (MQ problem equations. Unlike the MQ problem, the MPF problem seems to be more complicated, since its equations are not defined over the field, but are represented as left–right action of two matrices defined over the infinite near-semiring on the matrix defined over the certain infinite, additive, noncommuting semigroup. The main results are the following: (1 the proposition of infinite, nonsymmetric, and noncommuting algebraic structures for the construction of the enhanced MPF, satisfying associativity conditions, which are necessary for cryptographic applications; (2 the proof that MPF inversion is polynomially equivalent to the solution of a certain kind of generalized multivariate quadratic (MQ problem which can be reckoned as hard; (3 the estimation of the effectiveness of direct MPF value computation; and (4 the presentation of preliminary security analysis, the determination of the security parameter, and specification of its secure value. These results allow us to make a conjecture that enhanced MPF can be a candidate one-way function (OWF, since the effective (polynomial-time inversion algorithm for it is not yet known. An example of the application of the proposed MPF for the Key Agreement Protocol (KAP is presented. Since the direct MPF value is computed effectively, the proposed MPF is suitable for the realization of cryptographic protocols in devices with restricted computation resources.

  12. Ada Linear-Algebra Program

    Science.gov (United States)

    Klumpp, A. R.; Lawson, C. L.

    1988-01-01

    Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.

  13. Gradient for the acoustic VTI full waveform inversion based on the instantaneous traveltime sensitivity kernels

    KAUST Repository

    Djebbi, Ramzi

    2015-08-19

    The instantaneous traveltime is able to reduce the non-linearity of full waveform inversion (FWI) that originates from the wrapping of the phase. However, the adjoint state method in this case requires a total of 5 modeling calculations to compute the gradient. Also, considering the larger modeling cost for anisotropic wavefield extrapolation and the necessity to use a line-search algorithm to estimate a step length that depends on the parameters scale, we propose to calculate the gradient based on the instantaneous traveltime sensitivity kernels. We, specifically, use the sensitivity kernels computed using dynamic ray-tracing to build the gradient. The resulting update is computed using a matrix decomposition and accordingly the computational cost is reduced. We consider a simple example where an anomaly is embedded into a constant background medium and we compute the update for the VTI wave equation parameterized using vh, η and ε.

  14. Gradient for the acoustic VTI full waveform inversion based on the instantaneous traveltime sensitivity kernels

    KAUST Repository

    Djebbi, Ramzi; Alkhalifah, Tariq Ali

    2015-01-01

    The instantaneous traveltime is able to reduce the non-linearity of full waveform inversion (FWI) that originates from the wrapping of the phase. However, the adjoint state method in this case requires a total of 5 modeling calculations to compute the gradient. Also, considering the larger modeling cost for anisotropic wavefield extrapolation and the necessity to use a line-search algorithm to estimate a step length that depends on the parameters scale, we propose to calculate the gradient based on the instantaneous traveltime sensitivity kernels. We, specifically, use the sensitivity kernels computed using dynamic ray-tracing to build the gradient. The resulting update is computed using a matrix decomposition and accordingly the computational cost is reduced. We consider a simple example where an anomaly is embedded into a constant background medium and we compute the update for the VTI wave equation parameterized using vh, η and ε.

  15. ℋ-matrix techniques for approximating large covariance matrices and estimating its parameters

    KAUST Repository

    Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Keyes, David E.

    2016-01-01

    In this work the task is to use the available measurements to estimate unknown hyper-parameters (variance, smoothness parameter and covariance length) of the covariance function. We do it by maximizing the joint log-likelihood function. This is a non-convex and non-linear problem. To overcome cubic complexity in linear algebra, we approximate the discretised covariance function in the hierarchical (ℋ-) matrix format. The ℋ-matrix format has a log-linear computational cost and storage O(knlogn), where rank k is a small integer. On each iteration step of the optimization procedure the covariance matrix itself, its determinant and its Cholesky decomposition are recomputed within ℋ-matrix format. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

  16. ℋ-matrix techniques for approximating large covariance matrices and estimating its parameters

    KAUST Repository

    Litvinenko, Alexander

    2016-10-25

    In this work the task is to use the available measurements to estimate unknown hyper-parameters (variance, smoothness parameter and covariance length) of the covariance function. We do it by maximizing the joint log-likelihood function. This is a non-convex and non-linear problem. To overcome cubic complexity in linear algebra, we approximate the discretised covariance function in the hierarchical (ℋ-) matrix format. The ℋ-matrix format has a log-linear computational cost and storage O(knlogn), where rank k is a small integer. On each iteration step of the optimization procedure the covariance matrix itself, its determinant and its Cholesky decomposition are recomputed within ℋ-matrix format. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

  17. Differential analysis of matrix convex functions II

    DEFF Research Database (Denmark)

    Hansen, Frank; Tomiyama, Jun

    2009-01-01

    We continue the analysis in [F. Hansen, and J. Tomiyama, Differential analysis of matrix convex functions. Linear Algebra Appl., 420:102--116, 2007] of matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided...

  18. Fast Bayesian optimal experimental design for seismic source inversion

    KAUST Repository

    Long, Quan

    2015-07-01

    We develop a fast method for optimally designing experiments in the context of statistical seismic source inversion. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by elastodynamic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the "true" parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem. © 2015 Elsevier B.V.

  19. Fast Bayesian Optimal Experimental Design for Seismic Source Inversion

    KAUST Repository

    Long, Quan

    2016-01-06

    We develop a fast method for optimally designing experiments [1] in the context of statistical seismic source inversion [2]. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by the elastic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the true parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem.

  20. Fast Bayesian Optimal Experimental Design for Seismic Source Inversion

    KAUST Repository

    Long, Quan; Motamed, Mohammad; Tempone, Raul

    2016-01-01

    We develop a fast method for optimally designing experiments [1] in the context of statistical seismic source inversion [2]. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by the elastic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the true parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem.

  1. Extended Krylov subspaces approximations of matrix functions. Application to computational electromagnetics

    Energy Technology Data Exchange (ETDEWEB)

    Druskin, V.; Lee, Ping [Schlumberger-Doll Research, Ridgefield, CT (United States); Knizhnerman, L. [Central Geophysical Expedition, Moscow (Russian Federation)

    1996-12-31

    There is now a growing interest in the area of using Krylov subspace approximations to compute the actions of matrix functions. The main application of this approach is the solution of ODE systems, obtained after discretization of partial differential equations by method of lines. In the event that the cost of computing the matrix inverse is relatively inexpensive, it is sometimes attractive to solve the ODE using the extended Krylov subspaces, originated by actions of both positive and negative matrix powers. Examples of such problems can be found frequently in computational electromagnetics.

  2. Synchronization and Control of Linearly Coupled Singular Systems

    Directory of Open Access Journals (Sweden)

    Fang Qingxiang

    2013-01-01

    Full Text Available The synchronization and control problem of linearly coupled singular systems is investigated. The uncoupled dynamical behavior at each node is general and can be chaotic or, otherwise the coupling matrix is not assumed to be symmetrical. Some sufficient conditions for globally exponential synchronization are derived based on Lyapunov stability theory. These criteria, which are in terms of linear matrix inequality (LMI, indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold. The controllers are designed for state feedback control and pinning control, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed conditions.

  3. 3-dimensional magnetotelluric inversion including topography using deformed hexahedral edge finite elements and direct solvers parallelized on symmetric multiprocessor computers - Part II: direct data-space inverse solution

    Science.gov (United States)

    Kordy, M.; Wannamaker, P.; Maris, V.; Cherkaev, E.; Hill, G.

    2016-01-01

    Following the creation described in Part I of a deformable edge finite-element simulator for 3-D magnetotelluric (MT) responses using direct solvers, in Part II we develop an algorithm named HexMT for 3-D regularized inversion of MT data including topography. Direct solvers parallelized on large-RAM, symmetric multiprocessor (SMP) workstations are used also for the Gauss-Newton model update. By exploiting the data-space approach, the computational cost of the model update becomes much less in both time and computer memory than the cost of the forward simulation. In order to regularize using the second norm of the gradient, we factor the matrix related to the regularization term and apply its inverse to the Jacobian, which is done using the MKL PARDISO library. For dense matrix multiplication and factorization related to the model update, we use the PLASMA library which shows very good scalability across processor cores. A synthetic test inversion using a simple hill model shows that including topography can be important; in this case depression of the electric field by the hill can cause false conductors at depth or mask the presence of resistive structure. With a simple model of two buried bricks, a uniform spatial weighting for the norm of model smoothing recovered more accurate locations for the tomographic images compared to weightings which were a function of parameter Jacobians. We implement joint inversion for static distortion matrices tested using the Dublin secret model 2, for which we are able to reduce nRMS to ˜1.1 while avoiding oscillatory convergence. Finally we test the code on field data by inverting full impedance and tipper MT responses collected around Mount St Helens in the Cascade volcanic chain. Among several prominent structures, the north-south trending, eruption-controlling shear zone is clearly imaged in the inversion.

  4. Regression tools for CO2 inversions: application of a shrinkage estimator to process attribution

    International Nuclear Information System (INIS)

    Shaby, Benjamin A.; Field, Christopher B.

    2006-01-01

    In this study we perform an atmospheric inversion based on a shrinkage estimator. This method is used to estimate surface fluxes of CO 2 , first partitioned according to constituent geographic regions, and then according to constituent processes that are responsible for the total flux. Our approach differs from previous approaches in two important ways. The first is that the technique of linear Bayesian inversion is recast as a regression problem. Seen as such, standard regression tools are employed to analyse and reduce errors in the resultant estimates. A shrinkage estimator, which combines standard ridge regression with the linear 'Bayesian inversion' model, is introduced. This method introduces additional bias into the model with the aim of reducing variance such that errors are decreased overall. Compared with standard linear Bayesian inversion, the ridge technique seems to reduce both flux estimation errors and prediction errors. The second divergence from previous studies is that instead of dividing the world into geographically distinct regions and estimating the CO 2 flux in each region, the flux space is divided conceptually into processes that contribute to the total global flux. Formulating the problem in this manner adds to the interpretability of the resultant estimates and attempts to shed light on the problem of attributing sources and sinks to their underlying mechanisms

  5. Plasma diagnostics by Abel inversion in hyperbolic geometry

    International Nuclear Information System (INIS)

    Alhasi, A.S.; Elliott, J.A.

    1992-01-01

    Plasma confined in the UMIST linear quadrupole adopts a configuration with approximately hyperbolic symmetry. The normal diagnostic is a Langmuir probe, but we have developed an alternative method using optical emission tomography based upon an analytic Abel inversion. Plasma radiance is obtained as a function of a parameter identifying magnetic flux surfaces. The inversion algorithm has been tested using artificial data. Experimentally, the results show that ionizing collisions cause the confined plasma distribution to broaden as the plasma travels through the confining field. This is shown to be a consequence of the approximate incompressibility of the E x B flow. (author)

  6. Construction and Experimental Implementation of a Model-Based Inverse Filter to Attenuate Hysteresis in Ferroelectric Transducers

    National Research Council Canada - National Science Library

    Hatch, Andrew G; Smith, Ralph C; De, Tathagata; Salapaka, Murti V

    2005-01-01

    .... In this paper, we illustrate the construction of inverse filters, based on homogenized energy models, which can be used to approximately linearize the piezoceramic transducer behavior for linear...

  7. Kohn-Sham potentials from electron densities using a matrix representation within finite atomic orbital basis sets

    Science.gov (United States)

    Zhang, Xing; Carter, Emily A.

    2018-01-01

    We revisit the static response function-based Kohn-Sham (KS) inversion procedure for determining the KS effective potential that corresponds to a given target electron density within finite atomic orbital basis sets. Instead of expanding the potential in an auxiliary basis set, we directly update the potential in its matrix representation. Through numerical examples, we show that the reconstructed density rapidly converges to the target density. Preliminary results are presented to illustrate the possibility of obtaining a local potential in real space from the optimized potential in its matrix representation. We have further applied this matrix-based KS inversion approach to density functional embedding theory. A proof-of-concept study of a solvated proton transfer reaction demonstrates the method's promise.

  8. Stokes profile analysis and vector magnetic fields. I. Inversion of photospheric lines

    International Nuclear Information System (INIS)

    Skumanich, A.; Lites, B.W.

    1987-01-01

    Improvements are proposed for the Auer et al. (1977) method for the analytic inversion of Stokes profiles via nonlinear least squares. The introduction of additional physics into the Mueller absorption matrix (by including damping wings and magnetooptical birefringence, and by decoupling the intensity profile from the three-vector polarization profile in the analysis) is found to result in a more robust inversion method, providing more reliable and accurate estimates of sunspot vector magnetic fields without significant loss of economy. The method is applied to sunspot observations obtained with the High Altitude Observatory polarimeter. 29 references

  9. A gradient based algorithm to solve inverse plane bimodular problems of identification

    Science.gov (United States)

    Ran, Chunjiang; Yang, Haitian; Zhang, Guoqing

    2018-02-01

    This paper presents a gradient based algorithm to solve inverse plane bimodular problems of identifying constitutive parameters, including tensile/compressive moduli and tensile/compressive Poisson's ratios. For the forward bimodular problem, a FE tangent stiffness matrix is derived facilitating the implementation of gradient based algorithms, for the inverse bimodular problem of identification, a two-level sensitivity analysis based strategy is proposed. Numerical verification in term of accuracy and efficiency is provided, and the impacts of initial guess, number of measurement points, regional inhomogeneity, and noisy data on the identification are taken into accounts.

  10. The matrix as in-situ data structure

    NARCIS (Netherlands)

    Kaldewaij, A.; de Vries, Laurens

    1995-01-01

    It is shown how a matrix can be used to implement a class of dictionaries. Instead of the strong requirement of ascendingness of a linear array, the weaker requirement of ascendingness of a matrix is used. This results in implementations that are efficient in both computation time and storage usage.

  11. Application of optical deformation analysis system on wedge splitting test and its inverse analysis

    DEFF Research Database (Denmark)

    Skocek, Jan; Stang, Henrik

    2010-01-01

    . Results of the inverse analysis are compared with traditional inverse analysis based on clip gauge data. Then the optically measured crack profile and crack tip position are compared with predictions done by the non-linear hinge model and a finite element analysis. It is shown that the inverse analysis...... based on the optically measured data can provide material parameters of the fictitious crack model matching favorably those obtained by classical inverse analysis based on the clip gauge data. Further advantages of using of the optical deformation analysis lie in identification of such effects...

  12. Alternating minimisation for glottal inverse filtering

    International Nuclear Information System (INIS)

    Bleyer, Ismael Rodrigo; Lybeck, Lasse; Auvinen, Harri; Siltanen, Samuli; Airaksinen, Manu; Alku, Paavo

    2017-01-01

    A new method is proposed for solving the glottal inverse filtering (GIF) problem. The goal of GIF is to separate an acoustical speech signal into two parts: the glottal airflow excitation and the vocal tract filter. To recover such information one has to deal with a blind deconvolution problem. This ill-posed inverse problem is solved under a deterministic setting, considering unknowns on both sides of the underlying operator equation. A stable reconstruction is obtained using a double regularization strategy, alternating between fixing either the glottal source signal or the vocal tract filter. This enables not only splitting the nonlinear and nonconvex problem into two linear and convex problems, but also allows the use of the best parameters and constraints to recover each variable at a time. This new technique, called alternating minimization glottal inverse filtering (AM-GIF), is compared with two other approaches: Markov chain Monte Carlo glottal inverse filtering (MCMC-GIF), and iterative adaptive inverse filtering (IAIF), using synthetic speech signals. The recent MCMC-GIF has good reconstruction quality but high computational cost. The state-of-the-art IAIF method is computationally fast but its accuracy deteriorates, particularly for speech signals of high fundamental frequency ( F 0). The results show the competitive performance of the new method: With high F 0, the reconstruction quality is better than that of IAIF and close to MCMC-GIF while reducing the computational complexity by two orders of magnitude. (paper)

  13. MODELING IN MAPLE AS THE RESEARCHING MEANS OF FUNDAMENTAL CONCEPTS AND PROCEDURES IN LINEAR ALGEBRA

    Directory of Open Access Journals (Sweden)

    Vasil Kushnir

    2016-05-01

    Full Text Available The article is devoted to binary technology and "fundamental training technology." Binary training refers to the simultaneous teaching of mathematics and computer science, for example differential equations and Maple, linear algebra and Maple. Moreover the system of traditional course of Maple is not performed. The use of the opportunities of Maple-technology in teaching mathematics is based on the following fundamental concepts of computer science as an algorithm, program, a linear program, cycle, branching, relative operators, etc. That’s why only a certain system of command operators in Maple is considered. They are necessary for fundamental concepts of linear algebra and differential equations studying in Maple-environment. Relative name - "the technology of fundamental training" reflects the study of fundamental mathematical concepts and procedures that express the properties of these concepts in Maple-environment. This article deals with the study of complex fundamental concepts of linear algebra (determinant of the matrix and algorithm of its calculation, the characteristic polynomial of the matrix and the eigenvalues of matrix, canonical form of characteristic matrix, eigenvectors of matrix, elementary divisors of the characteristic matrix, etc., which are discussed in the appropriate courses briefly enough, and sometimes are not considered at all, but they are important in linear systems of differential equations, asymptotic methods for solving differential equations, systems of linear equations. Herewith complex and voluminous procedures of finding of these linear algebra concepts embedded in Maple can be performed as a result of a simple command-operator. Especially important issue is building matrix to canonical form. In fact matrix functions are effectively reduced to the functions of the diagonal matrix or matrix in Jordan canonical form. These matrices are used to rise a square matrix to a power, to extract the roots of the n

  14. Linear optical response of finite systems using multishift linear system solvers

    Energy Technology Data Exchange (ETDEWEB)

    Hübener, Hannes; Giustino, Feliciano [Department of Materials, University of Oxford, Oxford OX1 3PH (United Kingdom)

    2014-07-28

    We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.

  15. Solving Fully Fuzzy Linear System of Equations in General Form

    Directory of Open Access Journals (Sweden)

    A. Yousefzadeh

    2012-06-01

    Full Text Available In this work, we propose an approach for computing the positive solution of a fully fuzzy linear system where the coefficient matrix is a fuzzy $nimes n$ matrix. To do this, we use arithmetic operations on fuzzy numbers that introduced by Kaffman in and convert the fully fuzzy linear system into two $nimes n$ and $2nimes 2n$ crisp linear systems. If the solutions of these linear systems don't satisfy in positive fuzzy solution condition, we introduce the constrained least squares problem to obtain optimal fuzzy vector solution by applying the ranking function in given fully fuzzy linear system. Using our proposed method, the fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.

  16. Physiological type I collagen organization induces the formation of a novel class of linear invadosomes

    Science.gov (United States)

    Juin, Amélie; Billottet, Clotilde; Moreau, Violaine; Destaing, Olivier; Albiges-Rizo, Corinne; Rosenbaum, Jean; Génot, Elisabeth; Saltel, Frédéric

    2012-01-01

    Invadosomes are F-actin structures capable of degrading the matrix through the activation of matrix metalloproteases. As fibrillar type I collagen promotes pro-matrix metalloproteinase 2 activation by membrane type 1 matrix metalloproteinase, we aimed at investigating the functional relationships between collagen I organization and invadosome induction. We found that fibrillar collagen I induced linear F-actin structures, distributed along the fibrils, on endothelial cells, macrophages, fibroblasts, and tumor cells. These structures share features with conventional invadosomes, as they express cortactin and N-WASP and accumulate the scaffold protein Tks5, which proved essential for their formation. On the basis of their ability to degrade extracellular matrix elements and their original architecture, we named these structures “linear invadosomes.” Interestingly, podosomes or invadopodia were replaced by linear invadosomes upon contact of the cells with fibrillar collagen I. However, linear invadosomes clearly differ from classical invadosomes, as they do not contain paxillin, vinculin, and β1/β3 integrins. Using knockout mouse embryonic fibroblasts and RGD peptide, we demonstrate that linear invadosome formation and activity are independent of β1 and β3 integrins. Finally, linear invadosomes also formed in a three-dimensional collagen matrix. This study demonstrates that fibrillar collagen I is the physiological inducer of a novel class of invadosomes. PMID:22114353

  17. Inverse Force Determination on a Small Scale Launch Vehicle Model Using a Dynamic Balance

    Science.gov (United States)

    Ngo, Christina L.; Powell, Jessica M.; Ross, James C.

    2017-01-01

    A launch vehicle can experience large unsteady aerodynamic forces in the transonic regime that, while usually only lasting for tens of seconds during launch, could be devastating if structural components and electronic hardware are not designed to account for them. These aerodynamic loads are difficult to experimentally measure and even harder to computationally estimate. The current method for estimating buffet loads is through the use of a few hundred unsteady pressure transducers and wind tunnel test. Even with a large number of point measurements, the computed integrated load is not an accurate enough representation of the total load caused by buffeting. This paper discusses an attempt at using a dynamic balance to experimentally determine buffet loads on a generic scale hammer head launch vehicle model tested at NASA Ames Research Center's 11' x 11' transonic wind tunnel. To use a dynamic balance, the structural characteristics of the model needed to be identified so that the natural modal response could be and removed from the aerodynamic forces. A finite element model was created on a simplified version of the model to evaluate the natural modes of the balance flexures, assist in model design, and to compare to experimental data. Several modal tests were conducted on the model in two different configurations to check for non-linearity, and to estimate the dynamic characteristics of the model. The experimental results were used in an inverse force determination technique with a psuedo inverse frequency response function. Due to the non linearity, the model not being axisymmetric, and inconsistent data between the two shake tests from different mounting configuration, it was difficult to create a frequency response matrix that satisfied all input and output conditions for wind tunnel configuration to accurately predict unsteady aerodynamic loads.

  18. Efficient sparse matrix-matrix multiplication for computing periodic responses by shooting method on Intel Xeon Phi

    Science.gov (United States)

    Stoykov, S.; Atanassov, E.; Margenov, S.

    2016-10-01

    Many of the scientific applications involve sparse or dense matrix operations, such as solving linear systems, matrix-matrix products, eigensolvers, etc. In what concerns structural nonlinear dynamics, the computations of periodic responses and the determination of stability of the solution are of primary interest. Shooting method iswidely used for obtaining periodic responses of nonlinear systems. The method involves simultaneously operations with sparse and dense matrices. One of the computationally expensive operations in the method is multiplication of sparse by dense matrices. In the current work, a new algorithm for sparse matrix by dense matrix products is presented. The algorithm takes into account the structure of the sparse matrix, which is obtained by space discretization of the nonlinear Mindlin's plate equation of motion by the finite element method. The algorithm is developed to use the vector engine of Intel Xeon Phi coprocessors. It is compared with the standard sparse matrix by dense matrix algorithm and the one developed by Intel MKL and it is shown that by considering the properties of the sparse matrix better algorithms can be developed.

  19. Retrieval of the projected potential by inversion from the scattering matrix in electron-crystal scattering

    International Nuclear Information System (INIS)

    Allen, L.J.; Spargo, A.E.C.; Leeb, H.

    1998-01-01

    The retrieval of a unique crystal potential from the scattering matrix S in high energy transmission electron diffraction is discussed. It is shown that, in general, data taken at a single orientation are not sufficient to determine all the elements of S. Additional measurements with tilted incident beam are required for the determination of the whole S-matrix. An algorithm for the extraction of the crystal potential from the S-matrix measured at a single energy and thickness is presented. The limiting case of thin crystals is discussed. Several examples with simulated data are considered

  20. Optimization of radiotherapy to target volumes with concave outlines: target-dose homogenization and selective sparing of critical structures by constrained matrix inversion

    Energy Technology Data Exchange (ETDEWEB)

    Colle, C; Van den Berge, D; De Wagter, C; Fortan, L; Van Duyse, B; De Neve, W

    1995-12-01

    The design of 3D-conformal dose distributions for targets with concave outlines is a technical challenge in conformal radiotherapy. For these targets, it is impossible to find beam incidences for which the target volume can be isolated from the tissues at risk. Commonly occurring examples are most thyroid cancers and the targets located at the lower neck and upper mediastinal levels related to some head and neck. A solution to this problem was developed, using beam intensity modulation executed with a multileaf collimator by applying a static beam-segmentation technique. The method includes the definition of beam incidences and beam segments of specific shape as well as the calculation of segment weights. Tests on Sherouse`s GRATISTM planning system allowed to escalate the dose to these targets to 65-70 Gy without exceeding spinal cord tolerance. Further optimization by constrained matrix inversion was investigated to explore the possibility of further dose escalation.