A Poisson nonnegative matrix factorization method with parameter subspace clustering constraint for endmember extraction in hyperspectral imagery

Science.gov (United States)

Sun, Weiwei; Ma, Jun; Yang, Gang; Du, Bo; Zhang, Liangpei

2017-06-01

A new Bayesian method named Poisson Nonnegative Matrix Factorization with Parameter Subspace Clustering Constraint (PNMF-PSCC) has been presented to extract endmembers from Hyperspectral Imagery (HSI). First, the method integrates the liner spectral mixture model with the Bayesian framework and it formulates endmember extraction into a Bayesian inference problem. Second, the Parameter Subspace Clustering Constraint (PSCC) is incorporated into the statistical program to consider the clustering of all pixels in the parameter subspace. The PSCC could enlarge differences among ground objects and helps finding endmembers with smaller spectrum divergences. Meanwhile, the PNMF-PSCC method utilizes the Poisson distribution as the prior knowledge of spectral signals to better explain the quantum nature of light in imaging spectrometer. Third, the optimization problem of PNMF-PSCC is formulated into maximizing the joint density via the Maximum A Posterior (MAP) estimator. The program is finally solved by iteratively optimizing two sub-problems via the Alternating Direction Method of Multipliers (ADMM) framework and the FURTHESTSUM initialization scheme. Five state-of-the art methods are implemented to make comparisons with the performance of PNMF-PSCC on both the synthetic and real HSI datasets. Experimental results show that the PNMF-PSCC outperforms all the five methods in Spectral Angle Distance (SAD) and Root-Mean-Square-Error (RMSE), and especially it could identify good endmembers for ground objects with smaller spectrum divergences.

On the numerical stability analysis of pipelined Krylov subspace methods

Czech Academy of Sciences Publication Activity Database

Carson, E.T.; Rozložník, Miroslav; Strakoš, Z.; Tichý, P.; Tůma, M.

submitted 2017 (2018) R&D Projects: GA ČR GA13-06684S Grant - others:GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : Krylov subspace methods * the conjugate gradient method * numerical stability * inexact computations * delay of convergence * maximal attainable accuracy * pipelined Krylov subspace methods * exascale computations

Parallelised Krylov subspace method for reactor kinetics by IQS approach

International Nuclear Information System (INIS)

Gupta, Anurag; Modak, R.S.; Gupta, H.P.; Kumar, Vinod; Bhatt, K.

2005-01-01

Nuclear reactor kinetics involves numerical solution of space-time-dependent multi-group neutron diffusion equation. Two distinct approaches exist for this purpose: the direct (implicit time differencing) approach and the improved quasi-static (IQS) approach. Both the approaches need solution of static space-energy-dependent diffusion equations at successive time-steps; the step being relatively smaller for the direct approach. These solutions are usually obtained by Gauss-Seidel type iterative methods. For a faster solution, the Krylov sub-space methods have been tried and also parallelised by many investigators. However, these studies seem to have been done only for the direct approach. In the present paper, parallelised Krylov methods are applied to the IQS approach in addition to the direct approach. It is shown that the speed-up obtained for IQS is higher than that for the direct approach. The reasons for this are also discussed. Thus, the use of IQS approach along with parallelised Krylov solvers seems to be a promising scheme

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

KAUST Repository

Loizou, Nicolas

2017-12-27

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

KAUST Repository

Loizou, Nicolas; Richtarik, Peter

2017-01-01

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers

Energy Technology Data Exchange (ETDEWEB)

Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States)

1994-12-31

Domain decomposed preconditioners for nonsymmetric partial differential equations typically require the solution of problems on the subdomains. Most implementations employ exact solvers to obtain these solutions. Consequently work and storage requirements for the subdomain problems grow rapidly with the size of the subdomain problems. Subdomain solves constitute the single largest computational cost of a domain decomposed preconditioner, and improving the efficiency of this phase of the computation will have a significant impact on the performance of the overall method. The small local memory available on the nodes of most message-passing multicomputers motivates consideration of the use of an iterative method for solving subdomain problems. For large-scale systems of equations that are derived from three-dimensional problems, memory considerations alone may dictate the need for using iterative methods for the subdomain problems. In addition to reduced storage requirements, use of an iterative solver on the subdomains allows flexibility in specifying the accuracy of the subdomain solutions. Substantial savings in solution time is possible if the quality of the domain decomposed preconditioner is not degraded too much by relaxing the accuracy of the subdomain solutions. While some work in this direction has been conducted for symmetric problems, similar studies for nonsymmetric problems appear not to have been pursued. This work represents a first step in this direction, and explores the effectiveness of performing subdomain solves using several transpose-free Krylov subspace methods, GMRES, transpose-free QMR, CGS, and a smoothed version of CGS. Depending on the difficulty of the subdomain problem and the convergence tolerance used, a reduction in solution time is possible in addition to the reduced memory requirements. The domain decomposed preconditioner is a Schur complement method in which the interface operators are approximated using interface probing.

Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe; Farouq, S.; Neytcheva, M.

2017-01-01

Roč. 74, č. 1 (2017), s. 19-37 ISSN 1017-1398 Institutional support: RVO:68145535 Keywords : PDE-constrained optimization problems * finite elements * iterative solution methods * preconditioning Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.241, year: 2016 https://link.springer.com/article/10.1007%2Fs11075-016-0136-5

Extending the subspace hybrid method for eigenvalue problems in reactor physics calculation

International Nuclear Information System (INIS)

Zhang, Q.; Abdel-Khalik, H. S.

2013-01-01

This paper presents an innovative hybrid Monte-Carlo-Deterministic method denoted by the SUBSPACE method designed for improving the efficiency of hybrid methods for reactor analysis applications. The SUBSPACE method achieves its high computational efficiency by taking advantage of the existing correlations between desired responses. Recently, significant gains in computational efficiency have been demonstrated using this method for source driven problems. Within this work the mathematical theory behind the SUBSPACE method is introduced and extended to address core wide level k-eigenvalue problems. The method's efficiency is demonstrated based on a three-dimensional quarter-core problem, where responses are sought on the pin cell level. The SUBSPACE method is compared to the FW-CADIS method and is found to be more efficient for the utilized test problem because of the reason that the FW-CADIS method solves a forward eigenvalue problem and an adjoint fixed-source problem while the SUBSPACE method only solves an adjoint fixed-source problem. Based on the favorable results obtained here, we are confident that the applicability of Monte Carlo for large scale reactor analysis could be realized in the near future. (authors)

Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe; Farouq, S.; Neytcheva, M.

2017-01-01

Roč. 74, č. 1 (2017), s. 19-37 ISSN 1017-1398 Institutional support: RVO:68145535 Keywords : PDE-constrained optimization problems * finite elements * iterative solution method s * preconditioning Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.241, year: 2016 https://link.springer.com/article/10.1007%2Fs11075-016-0136-5

Krylov subspace methods for solving large unsymmetric linear systems

International Nuclear Information System (INIS)

Saad, Y.

1981-01-01

Some algorithms based upon a projection process onto the Krylov subspace K/sub m/ = Span(r 0 , Ar 0 ,...,A/sup m/-1r 0 ) are developed, generalizing the method of conjugate gradients to unsymmetric systems. These methods are extensions of Arnoldi's algorithm for solving eigenvalue problems. The convergence is analyzed in terms of the distance of the solution to the subspace K/sub m/ and some error bounds are established showing, in particular, a similarity with the conjugate gradient method (for symmetric matrices) when the eigenvalues are real. Several numerical experiments are described and discussed

Using CUDA Technology for Defining the Stiffness Matrix in the Subspace of Eigenvectors

Directory of Open Access Journals (Sweden)

Yu. V. Berchun

2015-01-01

Full Text Available The aim is to improve the performance of solving a problem of deformable solid mechanics through the use of GPGPU. The paper describes technologies for computing systems using both a central and a graphics processor and provides motivation for using CUDA technology as the efficient one.The paper also analyses methods to solve the problem of defining natural frequencies and design waveforms, i.e. an iteration method in the subspace. The method includes several stages. The paper considers the most resource-hungry stage, which defines the stiffness matrix in the subspace of eigenforms and gives the mathematical interpretation of this stage.The GPU choice as a computing device is justified. The paper presents an algorithm for calculating the stiffness matrix in the subspace of eigenforms taking into consideration the features of input data. The global stiffness matrix is very sparse, and its size can reach tens of millions. Therefore, it is represented as a set of the stiffness matrices of the single elements of a model. The paper analyses methods of data representation in the software and selects the best practices for GPU computing.It describes the software implementation using CUDA technology to calculate the stiffness matrix in the subspace of eigenforms. Due to the input data nature, it is impossible to use the universal libraries of matrix computations (cuSPARSE and cuBLAS for loading the GPU. For efficient use of GPU resources in the software implementation, the stiffness matrices of elements are built in the block matrices of a special form. The advantages of using shared memory in GPU calculations are described.The transfer to the GPU computations allowed a twentyfold increase in performance (as compared to the multithreaded CPU-implementation on the model of middle dimensions (degrees of freedom about 2 million. Such an acceleration of one stage speeds up defining the natural frequencies and waveforms by the iteration method in a subspace

DETECTION OF CHANGES OF THE SYSTEM TECHNICAL STATE USING STOCHASTIC SUBSPACE OBSERVATION METHOD

Directory of Open Access Journals (Sweden)

Andrzej Puchalski

2014-03-01

Full Text Available System diagnostics based on vibroacoustics signals, carried out by means of stochastic subspace methods was undertaken in the hereby paper. Subspace methods are the ones based on numerical linear algebra tools. The considered solutions belong to diagnostic methods according to data, leading to the generation of residuals allowing failure recognition of elements and assemblies in machines and devices. The algorithm of diagnostics according to the subspace observation method was applied – in the paper – for the estimation of the valve system of the spark ignition engine.

Krylov subspace method with communication avoiding technique for linear system obtained from electromagnetic analysis

International Nuclear Information System (INIS)

Ikuno, Soichiro; Chen, Gong; Yamamoto, Susumu; Itoh, Taku; Abe, Kuniyoshi; Nakamura, Hiroaki

2016-01-01

Krylov subspace method and the variable preconditioned Krylov subspace method with communication avoiding technique for a linear system obtained from electromagnetic analysis are numerically investigated. In the k−skip Krylov method, the inner product calculations are expanded by Krylov basis, and the inner product calculations are transformed to the scholar operations. k−skip CG method is applied for the inner-loop solver of Variable Preconditioned Krylov subspace methods, and the converged solution of electromagnetic problem is obtained using the method. (author)

Krylov subspace methods for the solution of large systems of ODE's

DEFF Research Database (Denmark)

Thomsen, Per Grove; Bjurstrøm, Nils Henrik

1998-01-01

In Air Pollution Modelling large systems of ODE's arise. Solving such systems may be done efficientliy by Semi Implicit Runge-Kutta methods. The internal stages may be solved using Krylov subspace methods. The efficiency of this approach is investigated and verified.......In Air Pollution Modelling large systems of ODE's arise. Solving such systems may be done efficientliy by Semi Implicit Runge-Kutta methods. The internal stages may be solved using Krylov subspace methods. The efficiency of this approach is investigated and verified....

Central subspace dimensionality reduction using covariance operators.

Science.gov (United States)

Kim, Minyoung; Pavlovic, Vladimir

2011-04-01

We consider the task of dimensionality reduction informed by real-valued multivariate labels. The problem is often treated as Dimensionality Reduction for Regression (DRR), whose goal is to find a low-dimensional representation, the central subspace, of the input data that preserves the statistical correlation with the targets. A class of DRR methods exploits the notion of inverse regression (IR) to discover central subspaces. Whereas most existing IR techniques rely on explicit output space slicing, we propose a novel method called the Covariance Operator Inverse Regression (COIR) that generalizes IR to nonlinear input/output spaces without explicit target slicing. COIR's unique properties make DRR applicable to problem domains with high-dimensional output data corrupted by potentially significant amounts of noise. Unlike recent kernel dimensionality reduction methods that employ iterative nonconvex optimization, COIR yields a closed-form solution. We also establish the link between COIR, other DRR techniques, and popular supervised dimensionality reduction methods, including canonical correlation analysis and linear discriminant analysis. We then extend COIR to semi-supervised settings where many of the input points lack their labels. We demonstrate the benefits of COIR on several important regression problems in both fully supervised and semi-supervised settings.

Generalized subspace correction methods

Energy Technology Data Exchange (ETDEWEB)

Kolm, P. [Royal Institute of Technology, Stockholm (Sweden); Arbenz, P.; Gander, W. [Eidgenoessiche Technische Hochschule, Zuerich (Switzerland)

1996-12-31

A fundamental problem in scientific computing is the solution of large sparse systems of linear equations. Often these systems arise from the discretization of differential equations by finite difference, finite volume or finite element methods. Iterative methods exploiting these sparse structures have proven to be very effective on conventional computers for a wide area of applications. Due to the rapid development and increasing demand for the large computing powers of parallel computers, it has become important to design iterative methods specialized for these new architectures.

Integrated Phoneme Subspace Method for Speech Feature Extraction

Directory of Open Access Journals (Sweden)

Park Hyunsin

2009-01-01

Full Text Available Speech feature extraction has been a key focus in robust speech recognition research. In this work, we discuss data-driven linear feature transformations applied to feature vectors in the logarithmic mel-frequency filter bank domain. Transformations are based on principal component analysis (PCA, independent component analysis (ICA, and linear discriminant analysis (LDA. Furthermore, this paper introduces a new feature extraction technique that collects the correlation information among phoneme subspaces and reconstructs feature space for representing phonemic information efficiently. The proposed speech feature vector is generated by projecting an observed vector onto an integrated phoneme subspace (IPS based on PCA or ICA. The performance of the new feature was evaluated for isolated word speech recognition. The proposed method provided higher recognition accuracy than conventional methods in clean and reverberant environments.

Scalable Density-Based Subspace Clustering

DEFF Research Database (Denmark)

Müller, Emmanuel; Assent, Ira; Günnemann, Stephan

2011-01-01

For knowledge discovery in high dimensional databases, subspace clustering detects clusters in arbitrary subspace projections. Scalability is a crucial issue, as the number of possible projections is exponential in the number of dimensions. We propose a scalable density-based subspace clustering...... method that steers mining to few selected subspace clusters. Our novel steering technique reduces subspace processing by identifying and clustering promising subspaces and their combinations directly. Thereby, it narrows down the search space while maintaining accuracy. Thorough experiments on real...... and synthetic databases show that steering is efficient and scalable, with high quality results. For future work, our steering paradigm for density-based subspace clustering opens research potential for speeding up other subspace clustering approaches as well....

Parallel algorithms for unconstrained optimization by multisplitting with inexact subspace search - the abstract

Energy Technology Data Exchange (ETDEWEB)

Renaut, R.; He, Q. [Arizona State Univ., Tempe, AZ (United States)

1994-12-31

In a new parallel iterative algorithm for unconstrained optimization by multisplitting is proposed. In this algorithm the original problem is split into a set of small optimization subproblems which are solved using well known sequential algorithms. These algorithms are iterative in nature, e.g. DFP variable metric method. Here the authors use sequential algorithms based on an inexact subspace search, which is an extension to the usual idea of an inexact fine search. Essentially the idea of the inexact line search for nonlinear minimization is that at each iteration the authors only find an approximate minimum in the line search direction. Hence by inexact subspace search, they mean that, instead of finding the minimum of the subproblem at each interation, they do an incomplete down hill search to give an approximate minimum. Some convergence and numerical results for this algorithm will be presented. Further, the original theory will be generalized to the situation with a singular Hessian. Applications for nonlinear least squares problems will be presented. Experimental results will be presented for implementations on an Intel iPSC/860 Hypercube with 64 nodes as well as on the Intel Paragon.

Subspace K-means clustering.

Science.gov (United States)

Timmerman, Marieke E; Ceulemans, Eva; De Roover, Kim; Van Leeuwen, Karla

2013-12-01

To achieve an insightful clustering of multivariate data, we propose subspace K-means. Its central idea is to model the centroids and cluster residuals in reduced spaces, which allows for dealing with a wide range of cluster types and yields rich interpretations of the clusters. We review the existing related clustering methods, including deterministic, stochastic, and unsupervised learning approaches. To evaluate subspace K-means, we performed a comparative simulation study, in which we manipulated the overlap of subspaces, the between-cluster variance, and the error variance. The study shows that the subspace K-means algorithm is sensitive to local minima but that the problem can be reasonably dealt with by using partitions of various cluster procedures as a starting point for the algorithm. Subspace K-means performs very well in recovering the true clustering across all conditions considered and appears to be superior to its competitor methods: K-means, reduced K-means, factorial K-means, mixtures of factor analyzers (MFA), and MCLUST. The best competitor method, MFA, showed a performance similar to that of subspace K-means in easy conditions but deteriorated in more difficult ones. Using data from a study on parental behavior, we show that subspace K-means analysis provides a rich insight into the cluster characteristics, in terms of both the relative positions of the clusters (via the centroids) and the shape of the clusters (via the within-cluster residuals).

Visual tracking based on the sparse representation of the PCA subspace

Science.gov (United States)

Chen, Dian-bing; Zhu, Ming; Wang, Hui-li

2017-09-01

We construct a collaborative model of the sparse representation and the subspace representation. First, we represent the tracking target in the principle component analysis (PCA) subspace, and then we employ an L 1 regularization to restrict the sparsity of the residual term, an L 2 regularization term to restrict the sparsity of the representation coefficients, and an L 2 norm to restrict the distance between the reconstruction and the target. Then we implement the algorithm in the particle filter framework. Furthermore, an iterative method is presented to get the global minimum of the residual and the coefficients. Finally, an alternative template update scheme is adopted to avoid the tracking drift which is caused by the inaccurate update. In the experiment, we test the algorithm on 9 sequences, and compare the results with 5 state-of-art methods. According to the results, we can conclude that our algorithm is more robust than the other methods.

Diomres (k,m): An efficient method based on Krylov subspaces to solve big, dispersed, unsymmetrical linear systems

Energy Technology Data Exchange (ETDEWEB)

de la Torre Vega, E. [Instituto de Investigaciones Electricas, Cuernavaca (Mexico); Cesar Suarez Arriaga, M. [Universidad Michoacana SNH, Michoacan (Mexico)

1995-03-01

In geothermal simulation processes, MULKOM uses Integrated Finite Differences to solve the corresponding partial differential equations. This method requires to resolve efficiently big linear dispersed systems of non-symmetrical nature on each temporal iteration. The order of the system is usually greater than one thousand its solution could represent around 80% of CPU total calculation time. If the elapsed time solving this class of linear systems is reduced, the duration of numerical simulation decreases notably. When the matrix is big (N{ge}500) and with holes, it is inefficient to handle all the system`s elements, because it is perfectly figured out by its elements distinct of zero, quantity greatly minor than N{sup 2}. In this area, iteration methods introduce advantages with respect to gaussian elimination methods, because these last replenish matrices not having any special distribution of their non-zero elements and because they do not make use of the available solution estimations. The iterating methods of the Conjugated Gradient family, based on the subspaces of Krylov, possess the advantage of improving the convergence speed by means of preconditioning techniques. The creation of DIOMRES(k,m) method guarantees the continuous descent of the residual norm, without incurring in division by zero. This technique converges at most in N iterations if the system`s matrix is symmetrical, it does not employ too much memory to converge and updates immediately the approximation by using incomplete orthogonalization and adequate restarting. A preconditioned version of DIOMRES was applied to problems related to unsymmetrical systems with 1000 unknowns and less than five terms per equation. We found that this technique could reduce notably the time needful to find the solution without requiring memory increment. The coupling of this method to geothermal versions of MULKOM is in process.

The Detection of Subsynchronous Oscillation in HVDC Based on the Stochastic Subspace Identification Method

Directory of Open Access Journals (Sweden)

Chen Shi

2014-01-01

Full Text Available Subsynchronous oscillation (SSO usually caused by series compensation, power system stabilizer (PSS, high voltage direct current transmission (HVDC and other power electronic equipment, which will affect the safe operation of generator shafting even the system. It is very important to identify the modal parameters of SSO to take effective control strategies as well. Since the identification accuracy of traditional methods are not high enough, the stochastic subspace identification (SSI method is proposed to improve the identification accuracy of subsynchronous oscillation modal. The stochastic subspace identification method was compared with the other two methods on subsynchronous oscillation IEEE benchmark model and Xiang-Shang HVDC system model, the simulation results show that the stochastic subspace identification method has the advantages of high identification precision, high operation efficiency and strong ability of anti-noise.

Active Subspace Methods for Data-Intensive Inverse Problems

Energy Technology Data Exchange (ETDEWEB)

Wang, Qiqi [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

2017-04-27

The project has developed theory and computational tools to exploit active subspaces to reduce the dimension in statistical calibration problems. This dimension reduction enables MCMC methods to calibrate otherwise intractable models. The same theoretical and computational tools can also reduce the measurement dimension for calibration problems that use large stores of data.

LogDet Rank Minimization with Application to Subspace Clustering

Directory of Open Access Journals (Sweden)

Zhao Kang

2015-01-01

Full Text Available Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. In this paper, we propose using a log-determinant (LogDet function as a smooth and closer, though nonconvex, approximation to rank for obtaining a low-rank representation in subspace clustering. Augmented Lagrange multipliers strategy is applied to iteratively optimize the LogDet-based nonconvex objective function on potentially large-scale data. By making use of the angular information of principal directions of the resultant low-rank representation, an affinity graph matrix is constructed for spectral clustering. Experimental results on motion segmentation and face clustering data demonstrate that the proposed method often outperforms state-of-the-art subspace clustering algorithms.

Comparison Study of Subspace Identification Methods Applied to Flexible Structures

Science.gov (United States)

Abdelghani, M.; Verhaegen, M.; Van Overschee, P.; De Moor, B.

1998-09-01

In the past few years, various time domain methods for identifying dynamic models of mechanical structures from modal experimental data have appeared. Much attention has been given recently to so-called subspace methods for identifying state space models. This paper presents a detailed comparison study of these subspace identification methods: the eigensystem realisation algorithm with observer/Kalman filter Markov parameters computed from input/output data (ERA/OM), the robust version of the numerical algorithm for subspace system identification (N4SID), and a refined version of the past outputs scheme of the multiple-output error state space (MOESP) family of algorithms. The comparison is performed by simulating experimental data using the five mode reduced model of the NASA Mini-Mast structure. The general conclusion is that for the case of white noise excitations as well as coloured noise excitations, the N4SID/MOESP algorithms perform equally well but give better results (improved transfer function estimates, improved estimates of the output) compared to the ERA/OM algorithm. The key computational step in the three algorithms is the approximation of the extended observability matrix of the system to be identified, for N4SID/MOESP, or of the observer for the system to be identified, for the ERA/OM. Furthermore, the three algorithms only require the specification of one dimensioning parameter.

An additive subspace preconditioning method for the iterative solution of some problems with extreme contrasts in coefficients

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe

2014-01-01

Roč. 22, č. 4 (2014), s. 289-310 ISSN 1570-2820 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : preconditioning * additive subspace * small eigenvalues Subject RIV: BA - General Mathematics Impact factor: 2.310, year: 2014 http://www.degruyter.com/view/j/jnma.2014.22.issue-4/jnma-2014-0013/jnma-2014-0013. xml

OpenSubspace

DEFF Research Database (Denmark)

Müller, Emmanuel; Assent, Ira; Günnemann, Stephan

2009-01-01

Subspace clustering and projected clustering are recent research areas for clustering in high dimensional spaces. As the field is rather young, there is a lack of comparative studies on the advantages and disadvantages of the different algorithms. Part of the underlying problem is the lack...... of available open source implementations that could be used by researchers to understand, compare, and extend subspace and projected clustering algorithms. In this paper, we discuss the requirements for open source evaluation software. We propose OpenSubspace, an open source framework that meets...... these requirements. OpenSubspace integrates state-of-the-art performance measures and visualization techniques to foster research in subspace and projected clustering....

Subspace Based Blind Sparse Channel Estimation

DEFF Research Database (Denmark)

Hayashi, Kazunori; Matsushima, Hiroki; Sakai, Hideaki

2012-01-01

The paper proposes a subspace based blind sparse channel estimation method using 1–2 optimization by replacing the 2–norm minimization in the conventional subspace based method by the 1–norm minimization problem. Numerical results confirm that the proposed method can significantly improve...

Invariant subspaces

CERN Document Server

Radjavi, Heydar

2003-01-01

This broad survey spans a wealth of studies on invariant subspaces, focusing on operators on separable Hilbert space. Largely self-contained, it requires only a working knowledge of measure theory, complex analysis, and elementary functional analysis. Subjects include normal operators, analytic functions of operators, shift operators, examples of invariant subspace lattices, compact operators, and the existence of invariant and hyperinvariant subspaces. Additional chapters cover certain results on von Neumann algebras, transitive operator algebras, algebras associated with invariant subspaces,

Greedy subspace clustering.

Science.gov (United States)

2016-09-01

We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses the sets ...

Relevant Subspace Clustering

DEFF Research Database (Denmark)

Müller, Emmanuel; Assent, Ira; Günnemann, Stephan

2009-01-01

Subspace clustering aims at detecting clusters in any subspace projection of a high dimensional space. As the number of possible subspace projections is exponential in the number of dimensions, the result is often tremendously large. Recent approaches fail to reduce results to relevant subspace...... clusters. Their results are typically highly redundant, i.e. many clusters are detected multiple times in several projections. In this work, we propose a novel model for relevant subspace clustering (RESCU). We present a global optimization which detects the most interesting non-redundant subspace clusters...... achieves top clustering quality while competing approaches show greatly varying performance....

NITSOL: A Newton iterative solver for nonlinear systems

Energy Technology Data Exchange (ETDEWEB)

Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States)

1996-12-31

Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.

Krylov subspace method for evaluating the self-energy matrices in electron transport calculations

DEFF Research Database (Denmark)

Sørensen, Hans Henrik Brandenborg; Hansen, Per Christian; Petersen, D. E.

2008-01-01

We present a Krylov subspace method for evaluating the self-energy matrices used in the Green's function formulation of electron transport in nanoscale devices. A procedure based on the Arnoldi method is employed to obtain solutions of the quadratic eigenvalue problem associated with the infinite...... calculations. Numerical tests within a density functional theory framework are provided to validate the accuracy and robustness of the proposed method, which in most cases is an order of magnitude faster than conventional methods.......We present a Krylov subspace method for evaluating the self-energy matrices used in the Green's function formulation of electron transport in nanoscale devices. A procedure based on the Arnoldi method is employed to obtain solutions of the quadratic eigenvalue problem associated with the infinite...

Sinusoidal Order Estimation Using Angles between Subspaces

Directory of Open Access Journals (Sweden)

Søren Holdt Jensen

2009-01-01

Full Text Available We consider the problem of determining the order of a parametric model from a noisy signal based on the geometry of the space. More specifically, we do this using the nontrivial angles between the candidate signal subspace model and the noise subspace. The proposed principle is closely related to the subspace orthogonality property known from the MUSIC algorithm, and we study its properties and compare it to other related measures. For the problem of estimating the number of complex sinusoids in white noise, a computationally efficient implementation exists, and this problem is therefore considered in detail. In computer simulations, we compare the proposed method to various well-known methods for order estimation. These show that the proposed method outperforms the other previously published subspace methods and that it is more robust to the noise being colored than the previously published methods.

Cumulant-Based Coherent Signal Subspace Method for Bearing and Range Estimation

Directory of Open Access Journals (Sweden)

Bourennane Salah

2007-01-01

Full Text Available A new method for simultaneous range and bearing estimation for buried objects in the presence of an unknown Gaussian noise is proposed. This method uses the MUSIC algorithm with noise subspace estimated by using the slice fourth-order cumulant matrix of the received data. The higher-order statistics aim at the removal of the additive unknown Gaussian noise. The bilinear focusing operator is used to decorrelate the received signals and to estimate the coherent signal subspace. A new source steering vector is proposed including the acoustic scattering model at each sensor. Range and bearing of the objects at each sensor are expressed as a function of those at the first sensor. This leads to the improvement of object localization anywhere, in the near-field or in the far-field zone of the sensor array. Finally, the performances of the proposed method are validated on data recorded during experiments in a water tank.

Iterative solution of linear equations in ODE codes. [Krylov subspaces

Energy Technology Data Exchange (ETDEWEB)

Gear, C. W.; Saad, Y.

1981-01-01

Each integration step of a stiff equation involves the solution of a nonlinear equation, usually by a quasi-Newton method that leads to a set of linear problems. Iterative methods for these linear equations are studied. Of particular interest are methods that do not require an explicit Jacobian, but can work directly with differences of function values using J congruent to f(x + delta) - f(x). Some numerical experiments using a modification of LSODE are reported. 1 figure, 2 tables.

Numerical solution of stiff burnup equation with short half lived nuclides by the Krylov subspace method

International Nuclear Information System (INIS)

Yamamoto, Akio; Tatsumi, Masahiro; Sugimura, Naoki

2007-01-01

The Krylov subspace method is applied to solve nuclide burnup equations used for lattice physics calculations. The Krylov method is an efficient approach for solving ordinary differential equations with stiff nature such as the nuclide burnup with short lived nuclides. Some mathematical fundamentals of the Krylov subspace method and its application to burnup equations are discussed. Verification calculations are carried out in a PWR pin-cell geometry with UO 2 fuel. A detailed burnup chain that includes 193 fission products and 28 heavy nuclides is used in the verification calculations. Shortest half life found in the present burnup chain is approximately 30 s ( 106 Rh). Therefore, conventional methods (e.g., the Taylor series expansion with scaling and squaring) tend to require longer computation time due to numerical stiffness. Comparison with other numerical methods (e.g., the 4-th order Runge-Kutta-Gill) reveals that the Krylov subspace method can provide accurate solution for a detailed burnup chain used in the present study with short computation time. (author)

External Evaluation Measures for Subspace Clustering

DEFF Research Database (Denmark)

Günnemann, Stephan; Färber, Ines; Müller, Emmanuel

2011-01-01

research area of subspace clustering. We formalize general quality criteria for subspace clustering measures not yet addressed in the literature. We compare the existing external evaluation methods based on these criteria and pinpoint limitations. We propose a novel external evaluation measure which meets...

Unsupervised spike sorting based on discriminative subspace learning.

Science.gov (United States)

Keshtkaran, Mohammad Reza; Yang, Zhi

2014-01-01

Spike sorting is a fundamental preprocessing step for many neuroscience studies which rely on the analysis of spike trains. In this paper, we present two unsupervised spike sorting algorithms based on discriminative subspace learning. The first algorithm simultaneously learns the discriminative feature subspace and performs clustering. It uses histogram of features in the most discriminative projection to detect the number of neurons. The second algorithm performs hierarchical divisive clustering that learns a discriminative 1-dimensional subspace for clustering in each level of the hierarchy until achieving almost unimodal distribution in the subspace. The algorithms are tested on synthetic and in-vivo data, and are compared against two widely used spike sorting methods. The comparative results demonstrate that our spike sorting methods can achieve substantially higher accuracy in lower dimensional feature space, and they are highly robust to noise. Moreover, they provide significantly better cluster separability in the learned subspace than in the subspace obtained by principal component analysis or wavelet transform.

Independence and totalness of subspaces in phase space methods

Science.gov (United States)

Vourdas, A.

2018-04-01

The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the non-distributivity of the lattice of subspaces, there are various levels of independence, from pairwise independence up to (full) independence. Pairwise totalness, totalness and other intermediate concepts are also introduced, which roughly express that the subspaces overlap strongly among themselves, and they cover the full Hilbert space. A duality between independence and totalness, that involves orthocomplementation (logical NOT operation), is discussed. Another approach to independence is also studied, using Rota's formalism on independent partitions of the Hilbert space. This is used to define informational independence, which is proved to be equivalent to independence. As an application, the pentagram (used in discussions on contextuality) is analysed using these concepts.

Projected Gauss-Seidel subspace minimization method for interactive rigid body dynamics

DEFF Research Database (Denmark)

Silcowitz-Hansen, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny

2010-01-01

artifacts such as viscous or damped contact response. In this paper, we present a new approach to contact force determination. We formulate the contact force problem as a nonlinear complementarity problem, and discretize the problem to derive the Projected Gauss–Seidel method. We combine the Projected Gauss......–Seidel method with a subspace minimization method. Our new method shows improved qualities and superior convergence properties for specific configurations....

Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems - Poisson and convection-diffusion control

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe; Farouq, S.; Neytcheva, M.

2016-01-01

Roč. 73, č. 3 (2016), s. 631-633 ISSN 1017-1398 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : PDE-constrained optimization problems * finite elements * iterative solution methods Subject RIV: BA - General Mathematics Impact factor: 1.241, year: 2016 http://link.springer.com/article/10.1007%2Fs11075-016-0111-1

Subspace-based analysis of the ERT inverse problem

Science.gov (United States)

Ben Hadj Miled, Mohamed Khames; Miller, Eric L.

2004-05-01

In a previous work, we proposed a source-type formulation to the electrical resistance tomography (ERT) problem. Specifically, we showed that inhomogeneities in the medium can be viewed as secondary sources embedded in the homogeneous background medium and located at positions associated with variation in electrical conductivity. Assuming a piecewise constant conductivity distribution, the support of equivalent sources is equal to the boundary of the inhomogeneity. The estimation of the anomaly shape takes the form of an inverse source-type problem. In this paper, we explore the use of subspace methods to localize the secondary equivalent sources associated with discontinuities in the conductivity distribution. Our first alternative is the multiple signal classification (MUSIC) algorithm which is commonly used in the localization of multiple sources. The idea is to project a finite collection of plausible pole (or dipole) sources onto an estimated signal subspace and select those with largest correlations. In ERT, secondary sources are excited simultaneously but in different ways, i.e. with distinct amplitude patterns, depending on the locations and amplitudes of primary sources. If the number of receivers is "large enough", different source configurations can lead to a set of observation vectors that span the data subspace. However, since sources that are spatially close to each other have highly correlated signatures, seperation of such signals becomes very difficult in the presence of noise. To overcome this problem we consider iterative MUSIC algorithms like R-MUSIC and RAP-MUSIC. These recursive algorithms pose a computational burden as they require multiple large combinatorial searches. Results obtained with these algorithms using simulated data of different conductivity patterns are presented.

Geometric mean for subspace selection.

Science.gov (United States)

Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J

2009-02-01

Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions.

A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

Science.gov (United States)

Heinkenschloss, Matthias

2005-01-01

We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

Seismic noise attenuation using an online subspace tracking algorithm

Science.gov (United States)

Zhou, Yatong; Li, Shuhua; Zhang, Dong; Chen, Yangkang

2018-02-01

We propose a new low-rank based noise attenuation method using an efficient algorithm for tracking subspaces from highly corrupted seismic observations. The subspace tracking algorithm requires only basic linear algebraic manipulations. The algorithm is derived by analysing incremental gradient descent on the Grassmannian manifold of subspaces. When the multidimensional seismic data are mapped to a low-rank space, the subspace tracking algorithm can be directly applied to the input low-rank matrix to estimate the useful signals. Since the subspace tracking algorithm is an online algorithm, it is more robust to random noise than traditional truncated singular value decomposition (TSVD) based subspace tracking algorithm. Compared with the state-of-the-art algorithms, the proposed denoising method can obtain better performance. More specifically, the proposed method outperforms the TSVD-based singular spectrum analysis method in causing less residual noise and also in saving half of the computational cost. Several synthetic and field data examples with different levels of complexities demonstrate the effectiveness and robustness of the presented algorithm in rejecting different types of noise including random noise, spiky noise, blending noise, and coherent noise.

Modal–Physical Hybrid System Identification of High-rise Building via Subspace and Inverse-Mode Methods

Directory of Open Access Journals (Sweden)

Kohei Fujita

2017-08-01

Full Text Available A system identification (SI problem of high-rise buildings is investigated under restricted data environments. The shear and bending stiffnesses of a shear-bending model (SB model representing the high-rise buildings are identified via the smart combination of the subspace and inverse-mode methods. Since the shear and bending stiffnesses of the SB model can be identified in the inverse-mode method by using the lowest mode of horizontal displacements and floor rotation angles, the lowest mode of the objective building is identified first by using the subspace method. Identification of the lowest mode is performed by using the amplitude of transfer functions derived in the subspace method. Considering the resolution in measuring the floor rotation angles in lower stories, floor rotation angles in most stories are predicted from the floor rotation angle at the top floor. An empirical equation of floor rotation angles is proposed by investigating those for various building models. From the viewpoint of application of the present SI method to practical situations, a non-simultaneous measurement system is also proposed. In order to investigate the reliability and accuracy of the proposed SI method, a 10-story building frame subjected to micro-tremor is examined.

Data-driven modeling and predictive control for boiler-turbine unit using fuzzy clustering and subspace methods.

Science.gov (United States)

Wu, Xiao; Shen, Jiong; Li, Yiguo; Lee, Kwang Y

2014-05-01

This paper develops a novel data-driven fuzzy modeling strategy and predictive controller for boiler-turbine unit using fuzzy clustering and subspace identification (SID) methods. To deal with the nonlinear behavior of boiler-turbine unit, fuzzy clustering is used to provide an appropriate division of the operation region and develop the structure of the fuzzy model. Then by combining the input data with the corresponding fuzzy membership functions, the SID method is extended to extract the local state-space model parameters. Owing to the advantages of the both methods, the resulting fuzzy model can represent the boiler-turbine unit very closely, and a fuzzy model predictive controller is designed based on this model. As an alternative approach, a direct data-driven fuzzy predictive control is also developed following the same clustering and subspace methods, where intermediate subspace matrices developed during the identification procedure are utilized directly as the predictor. Simulation results show the advantages and effectiveness of the proposed approach. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Gene selection for microarray data classification via subspace learning and manifold regularization.

Science.gov (United States)

Tang, Chang; Cao, Lijuan; Zheng, Xiao; Wang, Minhui

2017-12-19

With the rapid development of DNA microarray technology, large amount of genomic data has been generated. Classification of these microarray data is a challenge task since gene expression data are often with thousands of genes but a small number of samples. In this paper, an effective gene selection method is proposed to select the best subset of genes for microarray data with the irrelevant and redundant genes removed. Compared with original data, the selected gene subset can benefit the classification task. We formulate the gene selection task as a manifold regularized subspace learning problem. In detail, a projection matrix is used to project the original high dimensional microarray data into a lower dimensional subspace, with the constraint that the original genes can be well represented by the selected genes. Meanwhile, the local manifold structure of original data is preserved by a Laplacian graph regularization term on the low-dimensional data space. The projection matrix can serve as an importance indicator of different genes. An iterative update algorithm is developed for solving the problem. Experimental results on six publicly available microarray datasets and one clinical dataset demonstrate that the proposed method performs better when compared with other state-of-the-art methods in terms of microarray data classification. Graphical Abstract The graphical abstract of this work.

KRYSI, Ordinary Differential Equations Solver with Sdirk Krylov Method

International Nuclear Information System (INIS)

Hindmarsh, A.C.; Norsett, S.P.

2001-01-01

1 - Description of program or function: KRYSI is a set of FORTRAN subroutines for solving ordinary differential equations initial value problems. It is suitable for both stiff and non-stiff systems. When solving the implicit stage equations in the stiff case, KRYSI uses a Krylov subspace iteration method called the SPIGMR (Scaled Preconditioned Incomplete Generalized Minimum Residual) method. No explicit Jacobian storage is required, except where used in pre- conditioning. A demonstration problem is included with a description of two pre-conditioners that are natural for its solution by KRYSI. 2 - Method of solution: KRYSI uses a three-stage, third-order singly diagonally implicit Runge-Kutta (SDIRK) method. In the stiff case, a preconditioned Krylov subspace iteration within a (so-called) inexact Newton iteration is used to solve the system of nonlinear algebraic equations

LSODKR, Stiff Ordinary Differential Equations (ODE) System Solver with Krylov Iteration and Root-finding

International Nuclear Information System (INIS)

Hindmarsh, A.D.; Brown, P.N.

1996-01-01

1 - Description of program or function: LSODKR is a new initial value ODE solver for stiff and non-stiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fix point) iteration and modified Newton iteration, c) LSODKR includes the ability to find roots of given functions of the solution during the integration. 2 - Method of solution: Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by Newton or fix point iteration, determined dynamically. Linear system solution is by a preconditioned Krylov iteration, selected by user from Incomplete Orthogonalization Method, Generalized Minimum Residual Method, and two variants of Preconditioned Conjugate Gradient Method. Preconditioning is to be supplied by the user. 3 - Restrictions on the complexity of the problem: None

Introduction: a brief overview of iterative algorithms in X-ray computed tomography.

Science.gov (United States)

Soleimani, M; Pengpen, T

2015-06-13

This paper presents a brief overview of some basic iterative algorithms, and more sophisticated methods are presented in the research papers in this issue. A range of algebraic iterative algorithms are covered here including ART, SART and OS-SART. A major limitation of the traditional iterative methods is their computational time. The Krylov subspace based methods such as the conjugate gradients (CG) algorithm and its variants can be used to solve linear systems of equations arising from large-scale CT with possible implementation using modern high-performance computing tools. The overall aim of this theme issue is to stimulate international efforts to develop the next generation of X-ray computed tomography (CT) image reconstruction software. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Subspace-based optimization method for inverse scattering problems with an inhomogeneous background medium

International Nuclear Information System (INIS)

Chen, Xudong

2010-01-01

This paper proposes a version of the subspace-based optimization method to solve the inverse scattering problem with an inhomogeneous background medium where the known inhomogeneities are bounded in a finite domain. Although the background Green's function at each discrete point in the computational domain is not directly available in an inhomogeneous background scenario, the paper uses the finite element method to simultaneously obtain the Green's function at all discrete points. The essence of the subspace-based optimization method is that part of the contrast source is determined from the spectrum analysis without using any optimization, whereas the orthogonally complementary part is determined by solving a lower dimension optimization problem. This feature significantly speeds up the convergence of the algorithm and at the same time makes it robust against noise. Numerical simulations illustrate the efficacy of the proposed algorithm. The algorithm presented in this paper finds wide applications in nondestructive evaluation, such as through-wall imaging

Hankel Matrix Correlation Function-Based Subspace Identification Method for UAV Servo System

Directory of Open Access Journals (Sweden)

Minghong She

2018-01-01

Full Text Available For the identification problem of closed-loop subspace model, we propose a zero space projection method based on the estimation of correlation function to fill the block Hankel matrix of identification model by combining the linear algebra with geometry. By using the same projection of related data in time offset set and LQ decomposition, the multiplication operation of projection is achieved and dynamics estimation of the unknown equipment system model is obtained. Consequently, we have solved the problem of biased estimation caused when the open-loop subspace identification algorithm is applied to the closed-loop identification. A simulation example is given to show the effectiveness of the proposed approach. In final, the practicability of the identification algorithm is verified by hardware test of UAV servo system in real environment.

Random matrix improved subspace clustering

KAUST Repository

Couillet, Romain; Kammoun, Abla

2017-01-01

This article introduces a spectral method for statistical subspace clustering. The method is built upon standard kernel spectral clustering techniques, however carefully tuned by theoretical understanding arising from random matrix findings. We show

Subspace Barzilai-Borwein Gradient Method for Large-Scale Bound Constrained Optimization

International Nuclear Information System (INIS)

Xiao Yunhai; Hu Qingjie

2008-01-01

An active set subspace Barzilai-Borwein gradient algorithm for large-scale bound constrained optimization is proposed. The active sets are estimated by an identification technique. The search direction consists of two parts: some of the components are simply defined; the other components are determined by the Barzilai-Borwein gradient method. In this work, a nonmonotone line search strategy that guarantees global convergence is used. Preliminary numerical results show that the proposed method is promising, and competitive with the well-known method SPG on a subset of bound constrained problems from CUTEr collection

Subspace-Based Holistic Registration for Low-Resolution Facial Images

Directory of Open Access Journals (Sweden)

Boom BJ

2010-01-01

Full Text Available Subspace-based holistic registration is introduced as an alternative to landmark-based face registration, which has a poor performance on low-resolution images, as obtained in camera surveillance applications. The proposed registration method finds the alignment by maximizing the similarity score between a probe and a gallery image. We use a novel probabilistic framework for both user-independent as well as user-specific face registration. The similarity is calculated using the probability that the face image is correctly aligned in a face subspace, but additionally we take the probability into account that the face is misaligned based on the residual error in the dimensions perpendicular to the face subspace. We perform extensive experiments on the FRGCv2 database to evaluate the impact that the face registration methods have on face recognition. Subspace-based holistic registration on low-resolution images can improve face recognition in comparison with landmark-based registration on high-resolution images. The performance of the tested face recognition methods after subspace-based holistic registration on a low-resolution version of the FRGC database is similar to that after manual registration.

A block Krylov subspace time-exact solution method for linear ordinary differential equation systems

NARCIS (Netherlands)

Bochev, Mikhail A.

2013-01-01

We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of

Iterative schemes for obtaining dominant alpha-modes of the neutron diffusion equation

International Nuclear Information System (INIS)

Singh, K.P.; Modak, R.S.; Degweker, S.B.; Singh, Kanchhi

2009-01-01

Two new methods of obtaining dominant prompt alpha-modes (sometimes referred to as time-eigenfunctions) of the multigroup neutron diffusion equation are discussed. In the first of these, we initially compute the dominant K-eigenfunctions and K-eigenvalues (denoted by λ 1 , λ 2 , λ 3 ...λ 1 being equal to the K eff ) for the given nuclear reactor model, by existing method based on sub-space iteration (SSI) which is an improved version of power iteration method. Subsequently, a uniformly distributed (positive or negative) 1/v absorber of sufficient concentration is added so as to make a particular eigenvalue λ i equal to unity. This gives ith alpha-mode. This procedure is repeated to find all the required alpha-modes. In the second method, we solve the alpha-eigenvalue problem directly by SSI method. This is clearly possible for a sub-critical reactor for which the inverse of the dominant alpha-eigenvalues are also the largest in magnitude as required by the SSI method. Here, the procedure is made applicable even to a super-critical reactor by making the reactor model sub-critical by the addition of a 1/v absorber. Results of these calculations for a 3-D two group PHWR test-case are given. These results are validated against the results as obtained by a completely different approach based on Orthomin(1) algorithm published earlier. The direct method based on the sub-space iteration strategy is found to be a simple and reliable method for obtaining any number of alpha-modes. Also comments have been made on the relationship between fundamental α and k values.

CLAss-Specific Subspace Kernel Representations and Adaptive Margin Slack Minimization for Large Scale Classification.

Science.gov (United States)

Yu, Yinan; Diamantaras, Konstantinos I; McKelvey, Tomas; Kung, Sun-Yuan

2018-02-01

In kernel-based classification models, given limited computational power and storage capacity, operations over the full kernel matrix becomes prohibitive. In this paper, we propose a new supervised learning framework using kernel models for sequential data processing. The framework is based on two components that both aim at enhancing the classification capability with a subset selection scheme. The first part is a subspace projection technique in the reproducing kernel Hilbert space using a CLAss-specific Subspace Kernel representation for kernel approximation. In the second part, we propose a novel structural risk minimization algorithm called the adaptive margin slack minimization to iteratively improve the classification accuracy by an adaptive data selection. We motivate each part separately, and then integrate them into learning frameworks for large scale data. We propose two such frameworks: the memory efficient sequential processing for sequential data processing and the parallelized sequential processing for distributed computing with sequential data acquisition. We test our methods on several benchmark data sets and compared with the state-of-the-art techniques to verify the validity of the proposed techniques.

Domain decomposition methods and deflated Krylov subspace iterations

NARCIS (Netherlands)

Nabben, R.; Vuik, C.

2006-01-01

The balancing Neumann-Neumann (BNN) and the additive coarse grid correction (BPS) preconditioner are fast and successful preconditioners within domain decomposition methods for solving partial differential equations. For certain elliptic problems these preconditioners lead to condition numbers which

Seismic noise attenuation using an online subspace tracking algorithm

NARCIS (Netherlands)

Zhou, Yatong; Li, Shuhua; Zhang, D.; Chen, Yangkang

2018-01-01

We propose a new low-rank based noise attenuation method using an efficient algorithm for tracking subspaces from highly corrupted seismic observations. The subspace tracking algorithm requires only basic linear algebraic manipulations. The algorithm is derived by analysing incremental gradient

Advances in iterative methods

International Nuclear Information System (INIS)

Beauwens, B.; Arkuszewski, J.; Boryszewicz, M.

1981-01-01

Results obtained in the field of linear iterative methods within the Coordinated Research Program on Transport Theory and Advanced Reactor Calculations are summarized. The general convergence theory of linear iterative methods is essentially based on the properties of nonnegative operators on ordered normed spaces. The following aspects of this theory have been improved: new comparison theorems for regular splittings, generalization of the notions of M- and H-matrices, new interpretations of classical convergence theorems for positive-definite operators. The estimation of asymptotic convergence rates was developed with two purposes: the analysis of model problems and the optimization of relaxation parameters. In the framework of factorization iterative methods, model problem analysis is needed to investigate whether the increased computational complexity of higher-order methods does not offset their increased asymptotic convergence rates, as well as to appreciate the effect of standard relaxation techniques (polynomial relaxation). On the other hand, the optimal use of factorization iterative methods requires the development of adequate relaxation techniques and their optimization. The relative performances of a few possibilities have been explored for model problems. Presently, the best results have been obtained with optimal diagonal-Chebyshev relaxation

Projection methods for line radiative transfer in spherical media.

Science.gov (United States)

Anusha, L. S.; Nagendra, K. N.

An efficient numerical method called the Preconditioned Bi-Conjugate Gradient (Pre-BiCG) method is presented for the solution of radiative transfer equation in spherical geometry. A variant of this method called Stabilized Preconditioned Bi-Conjugate Gradient (Pre-BiCG-STAB) is also presented. These methods are based on projections on the subspaces of the n dimensional Euclidean space mathbb {R}n called Krylov subspaces. The methods are shown to be faster in terms of convergence rate compared to the contemporary iterative methods such as Jacobi, Gauss-Seidel and Successive Over Relaxation (SOR).

On the Kalman Filter error covariance collapse into the unstable subspace

Directory of Open Access Journals (Sweden)

A. Trevisan

2011-03-01

Full Text Available When the Extended Kalman Filter is applied to a chaotic system, the rank of the error covariance matrices, after a sufficiently large number of iterations, reduces to N⁺ + N⁰ where N⁺ and N⁰ are the number of positive and null Lyapunov exponents. This is due to the collapse into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter. Therefore the solution is the same as the solution obtained by confining the assimilation to the space spanned by the Lyapunov vectors with non-negative Lyapunov exponents. Theoretical arguments and numerical verification are provided to show that the asymptotic state and covariance estimates of the full EKF and of its reduced form, with assimilation in the unstable and neutral subspace (EKF-AUS are the same. The consequences of these findings on applications of Kalman type Filters to chaotic models are discussed.

Subspace System Identification of the Kalman Filter

Directory of Open Access Journals (Sweden)

David Di Ruscio

2003-07-01

Full Text Available Some proofs concerning a subspace identification algorithm are presented. It is proved that the Kalman filter gain and the noise innovations process can be identified directly from known input and output data without explicitly solving the Riccati equation. Furthermore, it is in general and for colored inputs, proved that the subspace identification of the states only is possible if the deterministic part of the system is known or identified beforehand. However, if the inputs are white, then, it is proved that the states can be identified directly. Some alternative projection matrices which can be used to compute the extended observability matrix directly from the data are presented. Furthermore, an efficient method for computing the deterministic part of the system is presented. The closed loop subspace identification problem is also addressed and it is shown that this problem is solved and unbiased estimates are obtained by simply including a filter in the feedback. Furthermore, an algorithm for consistent closed loop subspace estimation is presented. This algorithm is using the controller parameters in order to overcome the bias problem.

Noise-robust unsupervised spike sorting based on discriminative subspace learning with outlier handling.

Science.gov (United States)

Keshtkaran, Mohammad Reza; Yang, Zhi

2017-06-01

Spike sorting is a fundamental preprocessing step for many neuroscience studies which rely on the analysis of spike trains. Most of the feature extraction and dimensionality reduction techniques that have been used for spike sorting give a projection subspace which is not necessarily the most discriminative one. Therefore, the clusters which appear inherently separable in some discriminative subspace may overlap if projected using conventional feature extraction approaches leading to a poor sorting accuracy especially when the noise level is high. In this paper, we propose a noise-robust and unsupervised spike sorting algorithm based on learning discriminative spike features for clustering. The proposed algorithm uses discriminative subspace learning to extract low dimensional and most discriminative features from the spike waveforms and perform clustering with automatic detection of the number of the clusters. The core part of the algorithm involves iterative subspace selection using linear discriminant analysis and clustering using Gaussian mixture model with outlier detection. A statistical test in the discriminative subspace is proposed to automatically detect the number of the clusters. Comparative results on publicly available simulated and real in vivo datasets demonstrate that our algorithm achieves substantially improved cluster distinction leading to higher sorting accuracy and more reliable detection of clusters which are highly overlapping and not detectable using conventional feature extraction techniques such as principal component analysis or wavelets. By providing more accurate information about the activity of more number of individual neurons with high robustness to neural noise and outliers, the proposed unsupervised spike sorting algorithm facilitates more detailed and accurate analysis of single- and multi-unit activities in neuroscience and brain machine interface studies.

Noise-robust unsupervised spike sorting based on discriminative subspace learning with outlier handling

Science.gov (United States)

Keshtkaran, Mohammad Reza; Yang, Zhi

2017-06-01

Objective. Spike sorting is a fundamental preprocessing step for many neuroscience studies which rely on the analysis of spike trains. Most of the feature extraction and dimensionality reduction techniques that have been used for spike sorting give a projection subspace which is not necessarily the most discriminative one. Therefore, the clusters which appear inherently separable in some discriminative subspace may overlap if projected using conventional feature extraction approaches leading to a poor sorting accuracy especially when the noise level is high. In this paper, we propose a noise-robust and unsupervised spike sorting algorithm based on learning discriminative spike features for clustering. Approach. The proposed algorithm uses discriminative subspace learning to extract low dimensional and most discriminative features from the spike waveforms and perform clustering with automatic detection of the number of the clusters. The core part of the algorithm involves iterative subspace selection using linear discriminant analysis and clustering using Gaussian mixture model with outlier detection. A statistical test in the discriminative subspace is proposed to automatically detect the number of the clusters. Main results. Comparative results on publicly available simulated and real in vivo datasets demonstrate that our algorithm achieves substantially improved cluster distinction leading to higher sorting accuracy and more reliable detection of clusters which are highly overlapping and not detectable using conventional feature extraction techniques such as principal component analysis or wavelets. Significance. By providing more accurate information about the activity of more number of individual neurons with high robustness to neural noise and outliers, the proposed unsupervised spike sorting algorithm facilitates more detailed and accurate analysis of single- and multi-unit activities in neuroscience and brain machine interface studies.

Colorado Conference on iterative methods. Volume 1

Energy Technology Data Exchange (ETDEWEB)

NONE

1994-12-31

The conference provided a forum on many aspects of iterative methods. Volume I topics were:Session: domain decomposition, nonlinear problems, integral equations and inverse problems, eigenvalue problems, iterative software kernels. Volume II presents nonsymmetric solvers, parallel computation, theory of iterative methods, software and programming environment, ODE solvers, multigrid and multilevel methods, applications, robust iterative methods, preconditioners, Toeplitz and circulation solvers, and saddle point problems. Individual papers are indexed separately on the EDB.

Experimental Comparison of Signal Subspace Based Noise Reduction Methods

DEFF Research Database (Denmark)

Hansen, Peter Søren Kirk; Hansen, Per Christian; Hansen, Steffen Duus

1999-01-01

The signal subspace approach for non-parametric speech enhancement is considered. Several algorithms have been proposed in the literature but only partly analyzed. Here, the different algorithms are compared, and the emphasis is put onto the limiting factors and practical behavior of the estimators...

High resolution through-the-wall radar image based on beamspace eigenstructure subspace methods

Science.gov (United States)

Yoon, Yeo-Sun; Amin, Moeness G.

2008-04-01

Through-the-wall imaging (TWI) is a challenging problem, even if the wall parameters and characteristics are known to the system operator. Proper target classification and correct imaging interpretation require the application of high resolution techniques using limited array size. In inverse synthetic aperture radar (ISAR), signal subspace methods such as Multiple Signal Classification (MUSIC) are used to obtain high resolution imaging. In this paper, we adopt signal subspace methods and apply them to the 2-D spectrum obtained from the delay-andsum beamforming image. This is in contrast to ISAR, where raw data, in frequency and angle, is directly used to form the estimate of the covariance matrix and array response vector. Using beams rather than raw data has two main advantages, namely, it improves the signal-to-noise ratio (SNR) and can correctly image typical indoor extended targets, such as tables and cabinets, as well as point targets. The paper presents both simulated and experimental results using synthesized and real data. It compares the performance of beam-space MUSIC and Capon beamformer. The experimental data is collected at the test facility in the Radar Imaging Laboratory, Villanova University.

An acceleration technique for 2D MOC based on Krylov subspace and domain decomposition methods

International Nuclear Information System (INIS)

Zhang Hongbo; Wu Hongchun; Cao Liangzhi

2011-01-01

Highlights: → We convert MOC into linear system solved by GMRES as an acceleration method. → We use domain decomposition method to overcome the inefficiency on large matrices. → Parallel technology is applied and a matched ray tracing system is developed. → Results show good efficiency even in large-scale and strong scattering problems. → The emphasis is that the technique is geometry-flexible. - Abstract: The method of characteristics (MOC) has great geometrical flexibility but poor computational efficiency in neutron transport calculations. The generalized minimal residual (GMRES) method, a type of Krylov subspace method, is utilized to accelerate a 2D generalized geometry characteristics solver AutoMOC. In this technique, a form of linear algebraic equation system for angular flux moments and boundary fluxes is derived to replace the conventional characteristics sweep (i.e. inner iteration) scheme, and then the GMRES method is implemented as an efficient linear system solver. This acceleration method is proved to be reliable in theory and simple for implementation. Furthermore, as introducing no restriction in geometry treatment, it is suitable for acceleration of an arbitrary geometry MOC solver. However, it is observed that the speedup decreases when the matrix becomes larger. The spatial domain decomposition method and multiprocessing parallel technology are then employed to overcome the problem. The calculation domain is partitioned into several sub-domains. For each of them, a smaller matrix is established and solved by GMRES; and the adjacent sub-domains are coupled by 'inner-edges', where the trajectory mismatches are considered adequately. Moreover, a matched ray tracing system is developed on the basis of AutoCAD, which allows a user to define the sub-domains on demand conveniently. Numerical results demonstrate that the acceleration techniques are efficient without loss of accuracy, even in the case of large-scale and strong scattering

Mitigating Wind Induced Noise in Outdoor Microphone Signals Using a Singular Spectral Subspace Method

Directory of Open Access Journals (Sweden)

Omar Eldwaik

2018-01-01

Full Text Available Wind induced noise is one of the major concerns of outdoor acoustic signal acquisition. It affects many field measurement and audio recording scenarios. Filtering such noise is known to be difficult due to its broadband and time varying nature. In this paper, a new method to mitigate wind induced noise in microphone signals is developed. Instead of applying filtering techniques, wind induced noise is statistically separated from wanted signals in a singular spectral subspace. The paper is presented in the context of handling microphone signals acquired outdoor for acoustic sensing and environmental noise monitoring or soundscapes sampling. The method includes two complementary stages, namely decomposition and reconstruction. The first stage decomposes mixed signals in eigen-subspaces, selects and groups the principal components according to their contributions to wind noise and wanted signals in the singular spectrum domain. The second stage reconstructs the signals in the time domain, resulting in the separation of wind noise and wanted signals. Results show that microphone wind noise is separable in the singular spectrum domain evidenced by the weighted correlation. The new method might be generalized to other outdoor sound acquisition applications.

A new subspace based approach to iterative learning control

NARCIS (Netherlands)

Nijsse, G.; Verhaegen, M.; Doelman, N.J.

2001-01-01

This paper1 presents an iterative learning control (ILC) procedure based on an inverse model of the plant under control. Our first contribution is that we formulate the inversion procedure as a Kalman smoothing problem: based on a compact state space model of a possibly non-minimum phase system,

Iterative Splitting Methods for Differential Equations

CERN Document Server

Geiser, Juergen

2011-01-01

Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential

Subspace Correction Methods for Total Variation and $\\ell_1$-Minimization

KAUST Repository

Fornasier, Massimo; Schö nlieb, Carola-Bibiane

2009-01-01

This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a seminorm for a subspace. The optimization is realized by alternating minimizations of the functional on a

Adiabatic evolution of decoherence-free subspaces and its shortcuts

Science.gov (United States)

Wu, S. L.; Huang, X. L.; Li, H.; Yi, X. X.

2017-10-01

The adiabatic theorem and shortcuts to adiabaticity for time-dependent open quantum systems are explored in this paper. Starting from the definition of dynamical stable decoherence-free subspace, we show that, under a compact adiabatic condition, the quantum state remains in the time-dependent decoherence-free subspace with an extremely high purity, even though the dynamics of the open quantum system may not be adiabatic. The adiabatic condition mentioned here in the adiabatic theorem for open systems is very similar to that for closed quantum systems, except that the operators required to change slowly are the Lindblad operators. We also show that the adiabatic evolution of decoherence-free subspaces depends on the existence of instantaneous decoherence-free subspaces, which requires that the Hamiltonian of open quantum systems be engineered according to the incoherent control protocol. In addition, shortcuts to adiabaticity for adiabatic decoherence-free subspaces are also presented based on the transitionless quantum driving method. Finally, we provide an example that consists of a two-level system coupled to a broadband squeezed vacuum field to show our theory. Our approach employs Markovian master equations and the theory can apply to finite-dimensional quantum open systems.

Random matrix improved subspace clustering

KAUST Repository

Couillet, Romain

2017-03-06

This article introduces a spectral method for statistical subspace clustering. The method is built upon standard kernel spectral clustering techniques, however carefully tuned by theoretical understanding arising from random matrix findings. We show in particular that our method provides high clustering performance while standard kernel choices provably fail. An application to user grouping based on vector channel observations in the context of massive MIMO wireless communication networks is provided.

A Comfort-Aware Energy Efficient HVAC System Based on the Subspace Identification Method

Directory of Open Access Journals (Sweden)

O. Tsakiridis

2016-01-01

Full Text Available A proactive heating method is presented aiming at reducing the energy consumption in a HVAC system while maintaining the thermal comfort of the occupants. The proposed technique fuses time predictions for the zones’ temperatures, based on a deterministic subspace identification method, and zones’ occupancy predictions, based on a mobility model, in a decision scheme that is capable of regulating the balance between the total energy consumed and the total discomfort cost. Simulation results for various occupation-mobility models demonstrate the efficiency of the proposed technique.

Projection preconditioning for Lanczos-type methods

Energy Technology Data Exchange (ETDEWEB)

Bielawski, S.S.; Mulyarchik, S.G.; Popov, A.V. [Belarusian State Univ., Minsk (Belarus)

1996-12-31

We show how auxiliary subspaces and related projectors may be used for preconditioning nonsymmetric system of linear equations. It is shown that preconditioned in such a way (or projected) system is better conditioned than original system (at least if the coefficient matrix of the system to be solved is symmetrizable). Two approaches for solving projected system are outlined. The first one implies straightforward computation of the projected matrix and consequent using some direct or iterative method. The second approach is the projection preconditioning of conjugate gradient-type solver. The latter approach is developed here in context with biconjugate gradient iteration and some related Lanczos-type algorithms. Some possible particular choices of auxiliary subspaces are discussed. It is shown that one of them is equivalent to using colorings. Some results of numerical experiments are reported.

Consistency analysis of subspace identification methods based on a linear regression approach

DEFF Research Database (Denmark)

Knudsen, Torben

2001-01-01

In the literature results can be found which claim consistency for the subspace method under certain quite weak assumptions. Unfortunately, a new result gives a counter example showing inconsistency under these assumptions and then gives new more strict sufficient assumptions which however does n...... not include important model structures as e.g. Box-Jenkins. Based on a simple least squares approach this paper shows the possible inconsistency under the weak assumptions and develops only slightly stricter assumptions sufficient for consistency and which includes any model structure...

LSODKR, Stiff Ordinary Differential Equations (ODE) System Solver with Krylov Iteration with Root-finding

International Nuclear Information System (INIS)

Hindmarsh, A.C.; Petzold, L.R.

2005-01-01

1 - Description of program or function: LSODKR is a new initial value ODE solver for stiff and non-stiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fix point) iteration and modified Newton iteration, The nonlinear iteration method-switching differs from the method-switching in LSODA and LSODAR, but provides similar savings by using the cheaper method in the non-stiff regions of the problem. c) LSODKR includes the ability to find roots of given functions of the solution during the integration. d) LSODKR also improves on the Krylov methods in LSODPK by offering the option to save and reuse the approximate Jacobian data underlying the pre-conditioner. The LSODKR source is commented extensively to facilitate modification. Both a single-precision version and a double-precision version are available. 2 - Methods: It is assumed that the ODEs are given explicitly, so that the system can be written in the form dy/dt = f(t,y), where y is the vector of dependent variables, and t is the independent variable. Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by Newton or fix point iteration, determined dynamically. Linear system solution is by a preconditioned Krylov iteration, selected by user from Incomplete Orthogonalization Method, Generalized Minimum Residual Method, and two variants of Preconditioned Conjugate Gradient Method. Preconditioning is to be supplied by the user

INDOOR SUBSPACING TO IMPLEMENT INDOORGML FOR INDOOR NAVIGATION

Directory of Open Access Journals (Sweden)

H. Jung

2015-10-01

Full Text Available According to an increasing demand for indoor navigation, there are great attempts to develop applicable indoor network. Representation for a room as a node is not sufficient to apply complex and large buildings. As OGC established IndoorGML, subspacing to partition the space for constructing logical network is introduced. Concerning subspacing for indoor network, transition space like halls or corridors also have to be considered. This study presents the subspacing process for creating an indoor network in shopping mall. Furthermore, categorization of transition space is performed and subspacing of this space is considered. Hall and squares in mall is especially defined for subspacing. Finally, implementation of subspacing process for indoor network is presented.

Indoor Subspacing to Implement Indoorgml for Indoor Navigation

Science.gov (United States)

Jung, H.; Lee, J.

2015-10-01

According to an increasing demand for indoor navigation, there are great attempts to develop applicable indoor network. Representation for a room as a node is not sufficient to apply complex and large buildings. As OGC established IndoorGML, subspacing to partition the space for constructing logical network is introduced. Concerning subspacing for indoor network, transition space like halls or corridors also have to be considered. This study presents the subspacing process for creating an indoor network in shopping mall. Furthermore, categorization of transition space is performed and subspacing of this space is considered. Hall and squares in mall is especially defined for subspacing. Finally, implementation of subspacing process for indoor network is presented.

Bio-inspired varying subspace based computational framework for a class of nonlinear constrained optimal trajectory planning problems.

Science.gov (United States)

Xu, Y; Li, N

2014-09-01

Biological species have produced many simple but efficient rules in their complex and critical survival activities such as hunting and mating. A common feature observed in several biological motion strategies is that the predator only moves along paths in a carefully selected or iteratively refined subspace (or manifold), which might be able to explain why these motion strategies are effective. In this paper, a unified linear algebraic formulation representing such a predator-prey relationship is developed to simplify the construction and refinement process of the subspace (or manifold). Specifically, the following three motion strategies are studied and modified: motion camouflage, constant absolute target direction and local pursuit. The framework constructed based on this varying subspace concept could significantly reduce the computational cost in solving a class of nonlinear constrained optimal trajectory planning problems, particularly for the case with severe constraints. Two non-trivial examples, a ground robot and a hypersonic aircraft trajectory optimization problem, are used to show the capabilities of the algorithms in this new computational framework.

Bio-inspired varying subspace based computational framework for a class of nonlinear constrained optimal trajectory planning problems

International Nuclear Information System (INIS)

Xu, Y; Li, N

2014-01-01

Biological species have produced many simple but efficient rules in their complex and critical survival activities such as hunting and mating. A common feature observed in several biological motion strategies is that the predator only moves along paths in a carefully selected or iteratively refined subspace (or manifold), which might be able to explain why these motion strategies are effective. In this paper, a unified linear algebraic formulation representing such a predator–prey relationship is developed to simplify the construction and refinement process of the subspace (or manifold). Specifically, the following three motion strategies are studied and modified: motion camouflage, constant absolute target direction and local pursuit. The framework constructed based on this varying subspace concept could significantly reduce the computational cost in solving a class of nonlinear constrained optimal trajectory planning problems, particularly for the case with severe constraints. Two non-trivial examples, a ground robot and a hypersonic aircraft trajectory optimization problem, are used to show the capabilities of the algorithms in this new computational framework. (paper)

Controllable Subspaces of Open Quantum Dynamical Systems

International Nuclear Information System (INIS)

Zhang Ming; Gong Erling; Xie Hongwei; Hu Dewen; Dai Hongyi

2008-01-01

This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable. This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable. To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.

Convergence estimates for iterative methods via the Kriess Matrix Theorem on a general complex domain

Energy Technology Data Exchange (ETDEWEB)

Toh, K.C.; Trefethen, L.N. [Cornell Univ., Ithaca, NY (United States)

1994-12-31

What properties of a nonsymmetric matrix A determine the convergence rate of iterations such as GMRES, QMR, and Arnoldi? If A is far from normal, should one replace the usual Ritz values {r_arrow} eigenvalues notion of convergence of Arnoldi by alternative notions such as Arnoldi lemniscates {r_arrow} pseudospectra? Since Krylov subspace iterations can be interpreted as minimization processes involving polynomials of matrices, the answers to questions such as these depend upon mathematical problems of the following kind. Given a polynomial p(z), how can one bound the norm of p(A) in terms of (1) the size of p(z) on various sets in the complex plane, and (2) the locations of the spectrum and pseudospectra of A? This talk reports some progress towards solving these problems. In particular, the authors present theorems that generalize the Kreiss matrix theorem from the unit disk (for the monomial A{sup n}) to a class of general complex domains (for polynomials p(A)).

A Comparison of Sequential and GPU Implementations of Iterative Methods to Compute Reachability Probabilities

Directory of Open Access Journals (Sweden)

Elise Cormie-Bowins

2012-10-01

Full Text Available We consider the problem of computing reachability probabilities: given a Markov chain, an initial state of the Markov chain, and a set of goal states of the Markov chain, what is the probability of reaching any of the goal states from the initial state? This problem can be reduced to solving a linear equation Ax = b for x, where A is a matrix and b is a vector. We consider two iterative methods to solve the linear equation: the Jacobi method and the biconjugate gradient stabilized (BiCGStab method. For both methods, a sequential and a parallel version have been implemented. The parallel versions have been implemented on the compute unified device architecture (CUDA so that they can be run on a NVIDIA graphics processing unit (GPU. From our experiments we conclude that as the size of the matrix increases, the CUDA implementations outperform the sequential implementations. Furthermore, the BiCGStab method performs better than the Jacobi method for dense matrices, whereas the Jacobi method does better for sparse ones. Since the reachability probabilities problem plays a key role in probabilistic model checking, we also compared the implementations for matrices obtained from a probabilistic model checker. Our experiments support the conjecture by Bosnacki et al. that the Jacobi method is superior to Krylov subspace methods, a class to which the BiCGStab method belongs, for probabilistic model checking.

Roller Bearing Monitoring by New Subspace-Based Damage Indicator

Directory of Open Access Journals (Sweden)

G. Gautier

2015-01-01

Full Text Available A frequency-band subspace-based damage identification method for fault diagnosis in roller bearings is presented. Subspace-based damage indicators are obtained by filtering the vibration data in the frequency range where damage is likely to occur, that is, around the bearing characteristic frequencies. The proposed method is validated by considering simulated data of a damaged bearing. Also, an experimental case is considered which focuses on collecting the vibration data issued from a run-to-failure test. It is shown that the proposed method can detect bearing defects and, as such, it appears to be an efficient tool for diagnosis purpose.

Consistency Analysis of Nearest Subspace Classifier

OpenAIRE

Wang, Yi

2015-01-01

The Nearest subspace classifier (NSS) finds an estimation of the underlying subspace within each class and assigns data points to the class that corresponds to its nearest subspace. This paper mainly studies how well NSS can be generalized to new samples. It is proved that NSS is strongly consistent under certain assumptions. For completeness, NSS is evaluated through experiments on various simulated and real data sets, in comparison with some other linear model based classifiers. It is also ...

Milestones in the Development of Iterative Solution Methods

Directory of Open Access Journals (Sweden)

Owe Axelsson

2010-01-01

Full Text Available Iterative solution methods to solve linear systems of equations were originally formulated as basic iteration methods of defect-correction type, commonly referred to as Richardson's iteration method. These methods developed further into various versions of splitting methods, including the successive overrelaxation (SOR method. Later, immensely important developments included convergence acceleration methods, such as the Chebyshev and conjugate gradient iteration methods and preconditioning methods of various forms. A major strive has been to find methods with a total computational complexity of optimal order, that is, proportional to the degrees of freedom involved in the equation. Methods that have turned out to have been particularly important for the further developments of linear equation solvers are surveyed. Some of them are presented in greater detail.

The implicit restarted Arnoldi method, an efficient alternative to solve the neutron diffusion equation

Energy Technology Data Exchange (ETDEWEB)

Verdu, G.; Miro, R. [Departamento de Ingenieria Quimica y Nuclear, Universidad Politecnica de Valencia, Valencia (Spain); Ginestar, D. [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Valencia (Spain); Vidal, V. [Departamento de Sistemas Informaticos y Computacion, Universidad Politecnica de Valencia, Valencia (Spain)

1999-05-01

To calculate the neutronic steady state of a nuclear power reactor core and its subcritical modes, it is necessary to solve a partial eigenvalue problem. In this paper, an implicit restarted Arnoldi method is presented as an advantageous alternative to classical methods as the Power Iteration method and the Subspace Iteration method. The efficiency of these methods, has been compared calculating the dominant Lambda modes of several configurations of the Three Mile Island reactor core.

Time stepping free numerical solution of linear differential equations: Krylov subspace versus waveform relaxation

NARCIS (Netherlands)

Bochev, Mikhail A.; Oseledets, I.V.; Tyrtyshnikov, E.E.

2013-01-01

The aim of this paper is two-fold. First, we propose an efficient implementation of the continuous time waveform relaxation method based on block Krylov subspaces. Second, we compare this new implementation against Krylov subspace methods combined with the shift and invert technique.

Iterative Brinkman penalization for remeshed vortex methods

DEFF Research Database (Denmark)

Hejlesen, Mads Mølholm; Koumoutsakos, Petros; Leonard, Anthony

2015-01-01

We introduce an iterative Brinkman penalization method for the enforcement of the no-slip boundary condition in remeshed vortex methods. In the proposed method, the Brinkman penalization is applied iteratively only in the neighborhood of the body. This allows for using significantly larger time...

Acoustic Source Localization via Subspace Based Method Using Small Aperture MEMS Arrays

Directory of Open Access Journals (Sweden)

Xin Zhang

2014-01-01

Full Text Available Small aperture microphone arrays provide many advantages for portable devices and hearing aid equipment. In this paper, a subspace based localization method is proposed for acoustic source using small aperture arrays. The effects of array aperture on localization are analyzed by using array response (array manifold. Besides array aperture, the frequency of acoustic source and the variance of signal power are simulated to demonstrate how to optimize localization performance, which is carried out by introducing frequency error with the proposed method. The proposed method for 5 mm array aperture is validated by simulations and experiments with MEMS microphone arrays. Different types of acoustic sources can be localized with the highest precision of 6 degrees even in the presence of wind noise and other noises. Furthermore, the proposed method reduces the computational complexity compared with other methods.

A linear iterative unfolding method

International Nuclear Information System (INIS)

László, András

2012-01-01

A frequently faced task in experimental physics is to measure the probability distribution of some quantity. Often this quantity to be measured is smeared by a non-ideal detector response or by some physical process. The procedure of removing this smearing effect from the measured distribution is called unfolding, and is a delicate problem in signal processing, due to the well-known numerical ill behavior of this task. Various methods were invented which, given some assumptions on the initial probability distribution, try to regularize the unfolding problem. Most of these methods definitely introduce bias into the estimate of the initial probability distribution. We propose a linear iterative method (motivated by the Neumann series / Landweber iteration known in functional analysis), which has the advantage that no assumptions on the initial probability distribution is needed, and the only regularization parameter is the stopping order of the iteration, which can be used to choose the best compromise between the introduced bias and the propagated statistical and systematic errors. The method is consistent: 'binwise' convergence to the initial probability distribution is proved in absence of measurement errors under a quite general condition on the response function. This condition holds for practical applications such as convolutions, calorimeter response functions, momentum reconstruction response functions based on tracking in magnetic field etc. In presence of measurement errors, explicit formulae for the propagation of the three important error terms is provided: bias error (distance from the unknown to-be-reconstructed initial distribution at a finite iteration order), statistical error, and systematic error. A trade-off between these three error terms can be used to define an optimal iteration stopping criterion, and the errors can be estimated there. We provide a numerical C library for the implementation of the method, which incorporates automatic

Subspace preservation, subspace locality, and gluing of completely positive maps

International Nuclear Information System (INIS)

Aaberg, Johan

2004-01-01

Three concepts concerning completely positive maps (CPMs) and trace preserving CPMs (channels) are introduced and investigated. These are named subspace preserving (SP) CPMs, subspace local (SL) channels, and gluing of CPMs. SP CPMs has, in the case of trace preserving CPMs, a simple interpretation as those which preserve probability weights on a given orthogonal sum decomposition of the Hilbert space of a quantum system. The proposed definition of subspace locality of quantum channels is an attempt to answer the question of what kind of restriction should be put on a channel, if it is to act 'locally' with respect to two 'locations', when these naturally correspond to a separation of the total Hilbert space in an orthogonal sum of subspaces, rather than a tensor product decomposition. As a description of the concept of gluings of quantum channels, consider a pair of 'evolution machines', each with the ability to evolve the internal state of a 'particle' inserted into its input. Each of these machines is characterized by a channel describing the operation the internal state has experienced when the particle is returned at the output. Suppose a particle is put in a superposition between the input of the first and the second machine. Here it is shown that the total evolution caused by a pair of such devices is not uniquely determined by the channels of the two machines. Such 'global' channels describing the machine pair are examples of gluings of the two single machine channels. Various expressions to generate the set of SP and SL channels, as well as expressions to generate the set of gluings of given channels, are deduced. We discuss conceptual aspects of the nature of these channels and the nature of the non-uniqueness of gluings

Active Subspaces of Airfoil Shape Parameterizations

Science.gov (United States)

Grey, Zachary J.; Constantine, Paul G.

2018-05-01

Design and optimization benefit from understanding the dependence of a quantity of interest (e.g., a design objective or constraint function) on the design variables. A low-dimensional active subspace, when present, identifies important directions in the space of design variables; perturbing a design along the active subspace associated with a particular quantity of interest changes that quantity more, on average, than perturbing the design orthogonally to the active subspace. This low-dimensional structure provides insights that characterize the dependence of quantities of interest on design variables. Airfoil design in a transonic flow field with a parameterized geometry is a popular test problem for design methodologies. We examine two particular airfoil shape parameterizations, PARSEC and CST, and study the active subspaces present in two common design quantities of interest, transonic lift and drag coefficients, under each shape parameterization. We mathematically relate the two parameterizations with a common polynomial series. The active subspaces enable low-dimensional approximations of lift and drag that relate to physical airfoil properties. In particular, we obtain and interpret a two-dimensional approximation of both transonic lift and drag, and we show how these approximation inform a multi-objective design problem.

A General Algorithm for Reusing Krylov Subspace Information. I. Unsteady Navier-Stokes

Science.gov (United States)

Carpenter, Mark H.; Vuik, C.; Lucas, Peter; vanGijzen, Martin; Bijl, Hester

2010-01-01

A general algorithm is developed that reuses available information to accelerate the iterative convergence of linear systems with multiple right-hand sides A x = b (sup i), which are commonly encountered in steady or unsteady simulations of nonlinear equations. The algorithm is based on the classical GMRES algorithm with eigenvector enrichment but also includes a Galerkin projection preprocessing step and several novel Krylov subspace reuse strategies. The new approach is applied to a set of test problems, including an unsteady turbulent airfoil, and is shown in some cases to provide significant improvement in computational efficiency relative to baseline approaches.

Preconditioned Krylov subspace methods for eigenvalue problems

Energy Technology Data Exchange (ETDEWEB)

Wu, Kesheng; Saad, Y.; Stathopoulos, A. [Univ. of Minnesota, Minneapolis, MN (United States)

1996-12-31

Lanczos algorithm is a commonly used method for finding a few extreme eigenvalues of symmetric matrices. It is effective if the wanted eigenvalues have large relative separations. If separations are small, several alternatives are often used, including the shift-invert Lanczos method, the preconditioned Lanczos method, and Davidson method. The shift-invert Lanczos method requires direct factorization of the matrix, which is often impractical if the matrix is large. In these cases preconditioned schemes are preferred. Many applications require solution of hundreds or thousands of eigenvalues of large sparse matrices, which pose serious challenges for both iterative eigenvalue solver and preconditioner. In this paper we will explore several preconditioned eigenvalue solvers and identify the ones suited for finding large number of eigenvalues. Methods discussed in this paper make up the core of a preconditioned eigenvalue toolkit under construction.

Curve Evolution in Subspaces and Exploring the Metameric Class of Histogram of Gradient Orientation based Features using Nonlinear Projection Methods

DEFF Research Database (Denmark)

Tatu, Aditya Jayant

This thesis deals with two unrelated issues, restricting curve evolution to subspaces and computing image patches in the equivalence class of Histogram of Gradient orientation based features using nonlinear projection methods. Curve evolution is a well known method used in various applications like...... tracking interfaces, active contour based segmentation methods and others. It can also be used to study shape spaces, as deforming a shape can be thought of as evolving its boundary curve. During curve evolution a curve traces out a path in the infinite dimensional space of curves. Due to application...... specific requirements like shape priors or a given data model, and due to limitations of the computer, the computed curve evolution forms a path in some finite dimensional subspace of the space of curves. We give methods to restrict the curve evolution to a finite dimensional linear or implicitly defined...

Subspace based adaptive denoising of surface EMG from neurological injury patients

Science.gov (United States)

Liu, Jie; Ying, Dongwen; Zev Rymer, William; Zhou, Ping

2014-10-01

Objective: After neurological injuries such as spinal cord injury, voluntary surface electromyogram (EMG) signals recorded from affected muscles are often corrupted by interferences, such as spurious involuntary spikes and background noises produced by physiological and extrinsic/accidental origins, imposing difficulties for signal processing. Conventional methods did not well address the problem caused by interferences. It is difficult to mitigate such interferences using conventional methods. The aim of this study was to develop a subspace-based denoising method to suppress involuntary background spikes contaminating voluntary surface EMG recordings. Approach: The Karhunen-Loeve transform was utilized to decompose a noisy signal into a signal subspace and a noise subspace. An optimal estimate of EMG signal is derived from the signal subspace and the noise power. Specifically, this estimator is capable of making a tradeoff between interference reduction and signal distortion. Since the estimator partially relies on the estimate of noise power, an adaptive method was presented to sequentially track the variation of interference power. The proposed method was evaluated using both semi-synthetic and real surface EMG signals. Main results: The experiments confirmed that the proposed method can effectively suppress interferences while keep the distortion of voluntary EMG signal in a low level. The proposed method can greatly facilitate further signal processing, such as onset detection of voluntary muscle activity. Significance: The proposed method can provide a powerful tool for suppressing background spikes and noise contaminating voluntary surface EMG signals of paretic muscles after neurological injuries, which is of great importance for their multi-purpose applications.

Sparse subspace clustering for data with missing entries and high-rank matrix completion.

Science.gov (United States)

Fan, Jicong; Chow, Tommy W S

2017-09-01

Many methods have recently been proposed for subspace clustering, but they are often unable to handle incomplete data because of missing entries. Using matrix completion methods to recover missing entries is a common way to solve the problem. Conventional matrix completion methods require that the matrix should be of low-rank intrinsically, but most matrices are of high-rank or even full-rank in practice, especially when the number of subspaces is large. In this paper, a new method called Sparse Representation with Missing Entries and Matrix Completion is proposed to solve the problems of incomplete-data subspace clustering and high-rank matrix completion. The proposed algorithm alternately computes the matrix of sparse representation coefficients and recovers the missing entries of a data matrix. The proposed algorithm recovers missing entries through minimizing the representation coefficients, representation errors, and matrix rank. Thorough experimental study and comparative analysis based on synthetic data and natural images were conducted. The presented results demonstrate that the proposed algorithm is more effective in subspace clustering and matrix completion compared with other existing methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Introduction to the spectral distribution method. Application example to the subspaces with a large number of quasi particles

International Nuclear Information System (INIS)

Arvieu, R.

The assumptions and principles of the spectral distribution method are reviewed. The object of the method is to deduce information on the nuclear spectra by constructing a frequency function which has the same first few moments, as the exact frequency function, these moments being then exactly calculated. The method is applied to subspaces containing a large number of quasi particles [fr

New concurrent iterative methods with monotonic convergence

Energy Technology Data Exchange (ETDEWEB)

Yao, Qingchuan [Michigan State Univ., East Lansing, MI (United States)

1996-12-31

This paper proposes the new concurrent iterative methods without using any derivatives for finding all zeros of polynomials simultaneously. The new methods are of monotonic convergence for both simple and multiple real-zeros of polynomials and are quadratically convergent. The corresponding accelerated concurrent iterative methods are obtained too. The new methods are good candidates for the application in solving symmetric eigenproblems.

Subspace learning from image gradient orientations

NARCIS (Netherlands)

Tzimiropoulos, Georgios; Zafeiriou, Stefanos; Pantic, Maja

2012-01-01

We introduce the notion of subspace learning from image gradient orientations for appearance-based object recognition. As image data is typically noisy and noise is substantially different from Gaussian, traditional subspace learning from pixel intensities fails very often to estimate reliably the

Multicore Performance of Block Algebraic Iterative Reconstruction Methods

DEFF Research Database (Denmark)

Sørensen, Hans Henrik B.; Hansen, Per Christian

2014-01-01

Algebraic iterative methods are routinely used for solving the ill-posed sparse linear systems arising in tomographic image reconstruction. Here we consider the algebraic reconstruction technique (ART) and the simultaneous iterative reconstruction techniques (SIRT), both of which rely on semiconv......Algebraic iterative methods are routinely used for solving the ill-posed sparse linear systems arising in tomographic image reconstruction. Here we consider the algebraic reconstruction technique (ART) and the simultaneous iterative reconstruction techniques (SIRT), both of which rely...... on semiconvergence. Block versions of these methods, based on a partitioning of the linear system, are able to combine the fast semiconvergence of ART with the better multicore properties of SIRT. These block methods separate into two classes: those that, in each iteration, access the blocks in a sequential manner...... a fixed relaxation parameter in each method, namely, the one that leads to the fastest semiconvergence. Computational results show that for multicore computers, the sequential approach is preferable....

Development of a Burnup Module DECBURN Based on the Krylov Subspace Method

Energy Technology Data Exchange (ETDEWEB)

Cho, J. Y.; Kim, K. S.; Shim, H. J.; Song, J. S

2008-05-15

This report is to develop a burnup module DECBURN that is essential for the reactor analysis and the assembly homogenization codes to trace the fuel composition change during the core burnup. The developed burnup module solves the burnup equation by the matrix exponential method based on the Krylov Subspace method. The final solution of the matrix exponential is obtained by the matrix scaling and squaring method. To develop DECBURN module, this report includes the followings as: (1) Krylov Subspace Method for Burnup Equation, (2) Manufacturing of the DECBURN module, (3) Library Structure Setup and Library Manufacturing, (4) Examination of the DECBURN module, (5) Implementation to the DeCART code and Verification. DECBURN library includes the decay constants, one-group cross section and the fission yields. Examination of the DECBURN module is performed by manufacturing a driver program, and the results of the DECBURN module is compared with those of the ORIGEN program. Also, the implemented DECBURN module to the DeCART code is applied to the LWR depletion benchmark and a OPR-1000 pin cell problem, and the solutions are compared with the HELIOS code to verify the computational soundness and accuracy. In this process, the criticality calculation method and the predictor-corrector scheme are introduced to the DeCART code for a function of the homogenization code. The examination by a driver program shows that the DECBURN module produces exactly the same solution with the ORIGEN program. DeCART code that equips the DECBURN module produces a compatible solution to the other codes for the LWR depletion benchmark. Also the multiplication factors of the DeCART code for the OPR-1000 pin cell problem agree to the HELIOS code within 100 pcm over the whole burnup steps. The multiplication factors with the criticality calculation are also compatible with the HELIOS code. These results mean that the developed DECBURN module works soundly and produces an accurate solution

Random Subspace Aggregation for Cancer Prediction with Gene Expression Profiles

Directory of Open Access Journals (Sweden)

Liying Yang

2016-01-01

Full Text Available Background. Precisely predicting cancer is crucial for cancer treatment. Gene expression profiles make it possible to analyze patterns between genes and cancers on the genome-wide scale. Gene expression data analysis, however, is confronted with enormous challenges for its characteristics, such as high dimensionality, small sample size, and low Signal-to-Noise Ratio. Results. This paper proposes a method, termed RS_SVM, to predict gene expression profiles via aggregating SVM trained on random subspaces. After choosing gene features through statistical analysis, RS_SVM randomly selects feature subsets to yield random subspaces and training SVM classifiers accordingly and then aggregates SVM classifiers to capture the advantage of ensemble learning. Experiments on eight real gene expression datasets are performed to validate the RS_SVM method. Experimental results show that RS_SVM achieved better classification accuracy and generalization performance in contrast with single SVM, K-nearest neighbor, decision tree, Bagging, AdaBoost, and the state-of-the-art methods. Experiments also explored the effect of subspace size on prediction performance. Conclusions. The proposed RS_SVM method yielded superior performance in analyzing gene expression profiles, which demonstrates that RS_SVM provides a good channel for such biological data.

Various Newton-type iterative methods for solving nonlinear equations

Directory of Open Access Journals (Sweden)

Manoj Kumar

2013-10-01

Full Text Available The aim of the present paper is to introduce and investigate new ninth and seventh order convergent Newton-type iterative methods for solving nonlinear equations. The ninth order convergent Newton-type iterative method is made derivative free to obtain seventh-order convergent Newton-type iterative method. These new with and without derivative methods have efficiency indices 1.5518 and 1.6266, respectively. The error equations are used to establish the order of convergence of these proposed iterative methods. Finally, various numerical comparisons are implemented by MATLAB to demonstrate the performance of the developed methods.

Closed and Open Loop Subspace System Identification of the Kalman Filter

Directory of Open Access Journals (Sweden)

David Di Ruscio

2009-04-01

Full Text Available Some methods for consistent closed loop subspace system identification presented in the literature are analyzed and compared to a recently published subspace algorithm for both open as well as for closed loop data, the DSR_e algorithm. Some new variants of this algorithm are presented and discussed. Simulation experiments are included in order to illustrate if the algorithms are variance efficient or not.

Subspace exclusion zones for damage localization

DEFF Research Database (Denmark)

Bernal, Dionisio; Ulriksen, Martin Dalgaard

2018-01-01

, this is exploited in the context of structural damage localization to cast the Subspace Exclusion Zone (SEZ) scheme, which locates damage by reconstructing the captured field quantity shifts from analytical subspaces indexed by postulated boundaries, the so-called exclusion zones (EZs), in a model of the structure...

The influence of different PAST-based subspace trackers on DaPT parameter estimation

Science.gov (United States)

Lechtenberg, M.; Götze, J.

2012-09-01

In the context of parameter estimation, subspace-based methods like ESPRIT have become common. They require a subspace separation e.g. based on eigenvalue/-vector decomposition. In time-varying environments, this can be done by subspace trackers. One class of these is based on the PAST algorithm. Our non-linear parameter estimation algorithm DaPT builds on-top of the ESPRIT algorithm. Evaluation of the different variants of the PAST algorithm shows which variant of the PAST algorithm is worthwhile in the context of frequency estimation.

On Covering Approximation Subspaces

Directory of Open Access Journals (Sweden)

Xun Ge

2009-06-01

Full Text Available Let (U';C' be a subspace of a covering approximation space (U;C and X⊂U'. In this paper, we show that and B'(X⊂B(X∩U'. Also, iff (U;C has Property Multiplication. Furthermore, some connections between outer (resp. inner definable subsets in (U;C and outer (resp. inner definable subsets in (U';C' are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.

Active Subspaces for Wind Plant Surrogate Modeling

Energy Technology Data Exchange (ETDEWEB)

King, Ryan N [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Quick, Julian [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Dykes, Katherine L [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Adcock, Christiane [Massachusetts Institute of Technology

2018-01-12

Understanding the uncertainty in wind plant performance is crucial to their cost-effective design and operation. However, conventional approaches to uncertainty quantification (UQ), such as Monte Carlo techniques or surrogate modeling, are often computationally intractable for utility-scale wind plants because of poor congergence rates or the curse of dimensionality. In this paper we demonstrate that wind plant power uncertainty can be well represented with a low-dimensional active subspace, thereby achieving a significant reduction in the dimension of the surrogate modeling problem. We apply the active sub-spaces technique to UQ of plant power output with respect to uncertainty in turbine axial induction factors, and find a single active subspace direction dominates the sensitivity in power output. When this single active subspace direction is used to construct a quadratic surrogate model, the number of model unknowns can be reduced by up to 3 orders of magnitude without compromising performance on unseen test data. We conclude that the dimension reduction achieved with active subspaces makes surrogate-based UQ approaches tractable for utility-scale wind plants.

On the dimension of subspaces with bounded Schmidt rank

International Nuclear Information System (INIS)

Cubitt, Toby; Montanaro, Ashley; Winter, Andreas

2008-01-01

We consider the question of how large a subspace of a given bipartite quantum system can be when the subspace contains only highly entangled states. This is motivated in part by results of Hayden et al. [e-print arXiv:quant-ph/0407049; Commun. Math. Phys., 265, 95 (2006)], which show that in large dxd-dimensional systems there exist random subspaces of dimension almost d 2 , all of whose states have entropy of entanglement at least log d-O(1). It is also a generalization of results on the dimension of completely entangled subspaces, which have connections with the construction of unextendible product bases. Here we take as entanglement measure the Schmidt rank, and determine, for every pair of local dimensions d A and d B , and every r, the largest dimension of a subspace consisting only of entangled states of Schmidt rank r or larger. This exact answer is a significant improvement on the best bounds that can be obtained using the random subspace techniques in Hayden et al. We also determine the converse: the largest dimension of a subspace with an upper bound on the Schmidt rank. Finally, we discuss the question of subspaces containing only states with Schmidt equal to r

Boundary regularity of Nevanlinna domains and univalent functions in model subspaces

International Nuclear Information System (INIS)

Baranov, Anton D; Fedorovskiy, Konstantin Yu

2011-01-01

In the paper we study boundary regularity of Nevanlinna domains, which have appeared in problems of uniform approximation by polyanalytic polynomials. A new method for constructing Nevanlinna domains with essentially irregular nonanalytic boundaries is suggested; this method is based on finding appropriate univalent functions in model subspaces, that is, in subspaces of the form K Θ =H 2 ominus ΘH 2 , where Θ is an inner function. To describe the irregularity of the boundaries of the domains obtained, recent results by Dolzhenko about boundary regularity of conformal mappings are used. Bibliography: 18 titles.

Iterative Refinement Methods for Time-Domain Equalizer Design

Directory of Open Access Journals (Sweden)

Evans Brian L

2006-01-01

Full Text Available Commonly used time domain equalizer (TEQ design methods have been recently unified as an optimization problem involving an objective function in the form of a Rayleigh quotient. The direct generalized eigenvalue solution relies on matrix decompositions. To reduce implementation complexity, we propose an iterative refinement approach in which the TEQ length starts at two taps and increases by one tap at each iteration. Each iteration involves matrix-vector multiplications and vector additions with matrices and two-element vectors. At each iteration, the optimization of the objective function either improves or the approach terminates. The iterative refinement approach provides a range of communication performance versus implementation complexity tradeoffs for any TEQ method that fits the Rayleigh quotient framework. We apply the proposed approach to three such TEQ design methods: maximum shortening signal-to-noise ratio, minimum intersymbol interference, and minimum delay spread.

Conformable variational iteration method

Directory of Open Access Journals (Sweden)

Omer Acan

2017-02-01

Full Text Available In this study, we introduce the conformable variational iteration method based on new defined fractional derivative called conformable fractional derivative. This new method is applied two fractional order ordinary differential equations. To see how the solutions of this method, linear homogeneous and non-linear non-homogeneous fractional ordinary differential equations are selected. Obtained results are compared the exact solutions and their graphics are plotted to demonstrate efficiency and accuracy of the method.

A subspace approach to high-resolution spectroscopic imaging.

Science.gov (United States)

Lam, Fan; Liang, Zhi-Pei

2014-04-01

To accelerate spectroscopic imaging using sparse sampling of (k,t)-space and subspace (or low-rank) modeling to enable high-resolution metabolic imaging with good signal-to-noise ratio. The proposed method, called SPectroscopic Imaging by exploiting spatiospectral CorrElation, exploits a unique property known as partial separability of spectroscopic signals. This property indicates that high-dimensional spectroscopic signals reside in a very low-dimensional subspace and enables special data acquisition and image reconstruction strategies to be used to obtain high-resolution spatiospectral distributions with good signal-to-noise ratio. More specifically, a hybrid chemical shift imaging/echo-planar spectroscopic imaging pulse sequence is proposed for sparse sampling of (k,t)-space, and a low-rank model-based algorithm is proposed for subspace estimation and image reconstruction from sparse data with the capability to incorporate prior information and field inhomogeneity correction. The performance of the proposed method has been evaluated using both computer simulations and phantom studies, which produced very encouraging results. For two-dimensional spectroscopic imaging experiments on a metabolite phantom, a factor of 10 acceleration was achieved with a minimal loss in signal-to-noise ratio compared to the long chemical shift imaging experiments and with a significant gain in signal-to-noise ratio compared to the accelerated echo-planar spectroscopic imaging experiments. The proposed method, SPectroscopic Imaging by exploiting spatiospectral CorrElation, is able to significantly accelerate spectroscopic imaging experiments, making high-resolution metabolic imaging possible. Copyright © 2014 Wiley Periodicals, Inc.

Estimation of POL-iteration methods in fast running DNBR code

Energy Technology Data Exchange (ETDEWEB)

Kwon, Hyuk; Kim, S. J.; Seo, K. W.; Hwang, D. H. [KAERI, Daejeon (Korea, Republic of)

2016-05-15

In this study, various root finding methods are applied to the POL-iteration module in SCOMS and POLiteration efficiency is compared with reference method. On the base of these results, optimum algorithm of POL iteration is selected. The POL requires the iteration until present local power reach limit power. The process to search the limiting power is equivalent with a root finding of nonlinear equation. POL iteration process involved in online monitoring system used a variant bisection method that is the most robust algorithm to find the root of nonlinear equation. The method including the interval accelerating factor and escaping routine out of ill-posed condition assured the robustness of SCOMS system. POL iteration module in SCOMS shall satisfy the requirement which is a minimum calculation time. For this requirement of calculation time, non-iterative algorithm, few channel model, simple steam table are implemented into SCOMS to improve the calculation time. MDNBR evaluation at a given operating condition requires the DNBR calculation at all axial locations. An increasing of POL-iteration number increased a calculation load of SCOMS significantly. Therefore, calculation efficiency of SCOMS is strongly dependent on the POL iteration number. In case study, the iterations of the methods have a superlinear convergence for finding limiting power but Brent method shows a quardratic convergence speed. These methods are effective and better than the reference bisection algorithm.

A non-iterative sampling approach using noise subspace projection for EIT

International Nuclear Information System (INIS)

Bellis, Cédric; Constantinescu, Andrei; Coquet, Thomas; Jaravel, Thomas; Lechleiter, Armin

2012-01-01

This study concerns the problem of the reconstruction of inclusions embedded in a conductive medium in the context of electrical impedance tomography (EIT), which is investigated within the framework of a non-iterative sampling approach. This type of identification strategy relies on the construction of a special indicator function that takes, roughly speaking, small values outside the inclusion and large values inside. Such a function is constructed in this paper from the projection of a fundamental singular solution onto the space spanned by the singular vectors associated with some of the smallest singular values of the data-to-measurement operator. The behavior of the novel indicator function is analyzed. For a subsequent implementation in a discrete setting, the quality of classical finite-dimensional approximations of the measurement operator is discussed. The robustness of this approach is also analyzed when only noisy spectral information is available. Finally, this identification method is implemented numerically and experimentally, and its efficiency is discussed on a set of, partly experimental, examples. (paper)

Robust subspace estimation using low-rank optimization theory and applications

CERN Document Server

Oreifej, Omar

2014-01-01

Various fundamental applications in computer vision and machine learning require finding the basis of a certain subspace. Examples of such applications include face detection, motion estimation, and activity recognition. An increasing interest has been recently placed on this area as a result of significant advances in the mathematics of matrix rank optimization. Interestingly, robust subspace estimation can be posed as a low-rank optimization problem, which can be solved efficiently using techniques such as the method of Augmented Lagrange Multiplier. In this book,?the authors?discuss fundame

Advances in iterative methods for nonlinear equations

CERN Document Server

Busquier, Sonia

2016-01-01

This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations...

Iterative methods for weighted least-squares

Energy Technology Data Exchange (ETDEWEB)

Bobrovnikova, E.Y.; Vavasis, S.A. [Cornell Univ., Ithaca, NY (United States)

1996-12-31

A weighted least-squares problem with a very ill-conditioned weight matrix arises in many applications. Because of round-off errors, the standard conjugate gradient method for solving this system does not give the correct answer even after n iterations. In this paper we propose an iterative algorithm based on a new type of reorthogonalization that converges to the solution.

Modified conjugate gradient method for diagonalizing large matrices.

Science.gov (United States)

Jie, Quanlin; Liu, Dunhuan

2003-11-01

We present an iterative method to diagonalize large matrices. The basic idea is the same as the conjugate gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroducing errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trial vectors, play a similar role as the conjugate gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitable for first principle calculations.

Kernel based subspace projection of hyperspectral images

DEFF Research Database (Denmark)

Larsen, Rasmus; Nielsen, Allan Aasbjerg; Arngren, Morten

In hyperspectral image analysis an exploratory approach to analyse the image data is to conduct subspace projections. As linear projections often fail to capture the underlying structure of the data, we present kernel based subspace projections of PCA and Maximum Autocorrelation Factors (MAF...

An alternative subspace approach to EEG dipole source localization

Science.gov (United States)

Xu, Xiao-Liang; Xu, Bobby; He, Bin

2004-01-01

In the present study, we investigate a new approach to electroencephalography (EEG) three-dimensional (3D) dipole source localization by using a non-recursive subspace algorithm called FINES. In estimating source dipole locations, the present approach employs projections onto a subspace spanned by a small set of particular vectors (FINES vector set) in the estimated noise-only subspace instead of the entire estimated noise-only subspace in the case of classic MUSIC. The subspace spanned by this vector set is, in the sense of principal angle, closest to the subspace spanned by the array manifold associated with a particular brain region. By incorporating knowledge of the array manifold in identifying FINES vector sets in the estimated noise-only subspace for different brain regions, the present approach is able to estimate sources with enhanced accuracy and spatial resolution, thus enhancing the capability of resolving closely spaced sources and reducing estimation errors. The present computer simulations show, in EEG 3D dipole source localization, that compared to classic MUSIC, FINES has (1) better resolvability of two closely spaced dipolar sources and (2) better estimation accuracy of source locations. In comparison with RAP-MUSIC, FINES' performance is also better for the cases studied when the noise level is high and/or correlations among dipole sources exist.

An alternative subspace approach to EEG dipole source localization

International Nuclear Information System (INIS)

Xu Xiaoliang; Xu, Bobby; He Bin

2004-01-01

In the present study, we investigate a new approach to electroencephalography (EEG) three-dimensional (3D) dipole source localization by using a non-recursive subspace algorithm called FINES. In estimating source dipole locations, the present approach employs projections onto a subspace spanned by a small set of particular vectors (FINES vector set) in the estimated noise-only subspace instead of the entire estimated noise-only subspace in the case of classic MUSIC. The subspace spanned by this vector set is, in the sense of principal angle, closest to the subspace spanned by the array manifold associated with a particular brain region. By incorporating knowledge of the array manifold in identifying FINES vector sets in the estimated noise-only subspace for different brain regions, the present approach is able to estimate sources with enhanced accuracy and spatial resolution, thus enhancing the capability of resolving closely spaced sources and reducing estimation errors. The present computer simulations show, in EEG 3D dipole source localization, that compared to classic MUSIC, FINES has (1) better resolvability of two closely spaced dipolar sources and (2) better estimation accuracy of source locations. In comparison with RAP-MUSIC, FINES' performance is also better for the cases studied when the noise level is high and/or correlations among dipole sources exist

A new approach to passivity preserving model reduction : the dominant spectral zero method

NARCIS (Netherlands)

Ionutiu, R.; Rommes, J.; Antoulas, A.C.; Roos, J.; Costa, L.R.J.

2010-01-01

A new model reduction method for circuit simulation is presented, which preserves passivity by interpolating dominant spectral zeros. These are computed as poles of an associated Hamiltonian system, using an iterative solver: the subspace accelerated dominant pole algorithm (SADPA). Based on a

A Jacobi-Davidson type method for the generalized singular value problem

NARCIS (Netherlands)

Hochstenbach, M.E.

2009-01-01

We discuss a new method for the iterative computation of some of the generalized singular values and vectors of a large sparse matrix. Our starting point is the augmented matrix formulation of the GSVD. The subspace expansion is performed by (approximately) solving a Jacobi–Davidson type correction

Leapfrog variants of iterative methods for linear algebra equations

Science.gov (United States)

Saylor, Paul E.

1988-01-01

Two iterative methods are considered, Richardson's method and a general second order method. For both methods, a variant of the method is derived for which only even numbered iterates are computed. The variant is called a leapfrog method. Comparisons between the conventional form of the methods and the leapfrog form are made under the assumption that the number of unknowns is large. In the case of Richardson's method, it is possible to express the final iterate in terms of only the initial approximation, a variant of the iteration called the grand-leap method. In the case of the grand-leap variant, a set of parameters is required. An algorithm is presented to compute these parameters that is related to algorithms to compute the weights and abscissas for Gaussian quadrature. General algorithms to implement the leapfrog and grand-leap methods are presented. Algorithms for the important special case of the Chebyshev method are also given.

Shape analysis with subspace symmetries

KAUST Repository

Berner, Alexander

2011-04-01

We address the problem of partial symmetry detection, i.e., the identification of building blocks a complex shape is composed of. Previous techniques identify parts that relate to each other by simple rigid mappings, similarity transforms, or, more recently, intrinsic isometries. Our approach generalizes the notion of partial symmetries to more general deformations. We introduce subspace symmetries whereby we characterize similarity by requiring the set of symmetric parts to form a low dimensional shape space. We present an algorithm to discover subspace symmetries based on detecting linearly correlated correspondences among graphs of invariant features. We evaluate our technique on various data sets. We show that for models with pronounced surface features, subspace symmetries can be found fully automatically. For complicated cases, a small amount of user input is used to resolve ambiguities. Our technique computes dense correspondences that can subsequently be used in various applications, such as model repair and denoising. © 2010 The Author(s).

Quantum Computing in Decoherence-Free Subspace Constructed by Triangulation

OpenAIRE

Bi, Qiao; Guo, Liu; Ruda, H. E.

2010-01-01

A formalism for quantum computing in decoherence-free subspaces is presented. The constructed subspaces are partial triangulated to an index related to environment. The quantum states in the subspaces are just projected states which are ruled by a subdynamic kinetic equation. These projected states can be used to perform ideal quantum logical operations without decoherence.

Subspace identification of distributed clusters of homogeneous systems

NARCIS (Netherlands)

Yu, C.; Verhaegen, M.H.G.

2017-01-01

This note studies the identification of a network comprised of interconnected clusters of LTI systems. Each cluster consists of homogeneous dynamical systems, and its interconnections with the rest of the network are unmeasurable. A subspace identification method is proposed for identifying a single

Quantum Computing in Decoherence-Free Subspace Constructed by Triangulation

Directory of Open Access Journals (Sweden)

Qiao Bi

2010-01-01

Full Text Available A formalism for quantum computing in decoherence-free subspaces is presented. The constructed subspaces are partial triangulated to an index related to environment. The quantum states in the subspaces are just projected states which are ruled by a subdynamic kinetic equation. These projected states can be used to perform ideal quantum logical operations without decoherence.

LBAS: Lanczos Bidiagonalization with Subspace Augmentation for Discrete Inverse Problems

DEFF Research Database (Denmark)

Hansen, Per Christian; Abe, Kyniyoshi

The regularizing properties of Lanczos bidiagonalization are powerful when the underlying Krylov subspace captures the dominating components of the solution. In some applications the regularized solution can be further improved by augmenting the Krylov subspace with a low-dimensional subspace tha...

Iteration of ultrasound aberration correction methods

Science.gov (United States)

Maasoey, Svein-Erik; Angelsen, Bjoern; Varslot, Trond

2004-05-01

Aberration in ultrasound medical imaging is usually modeled by time-delay and amplitude variations concentrated on the transmitting/receiving array. This filter process is here denoted a TDA filter. The TDA filter is an approximation to the physical aberration process, which occurs over an extended part of the human body wall. Estimation of the TDA filter, and performing correction on transmit and receive, has proven difficult. It has yet to be shown that this method works adequately for severe aberration. Estimation of the TDA filter can be iterated by retransmitting a corrected signal and re-estimate until a convergence criterion is fulfilled (adaptive imaging). Two methods for estimating time-delay and amplitude variations in receive signals from random scatterers have been developed. One method correlates each element signal with a reference signal. The other method use eigenvalue decomposition of the receive cross-spectrum matrix, based upon a receive energy-maximizing criterion. Simulations of iterating aberration correction with a TDA filter have been investigated to study its convergence properties. A weak and strong human-body wall model generated aberration. Both emulated the human abdominal wall. Results after iteration improve aberration correction substantially, and both estimation methods converge, even for the case of strong aberration.

Variational iteration method for one dimensional nonlinear thermoelasticity

International Nuclear Information System (INIS)

Sweilam, N.H.; Khader, M.M.

2007-01-01

This paper applies the variational iteration method to solve the Cauchy problem arising in one dimensional nonlinear thermoelasticity. The advantage of this method is to overcome the difficulty of calculation of Adomian's polynomials in the Adomian's decomposition method. The numerical results of this method are compared with the exact solution of an artificial model to show the efficiency of the method. The approximate solutions show that the variational iteration method is a powerful mathematical tool for solving nonlinear problems

An Iterative Brinkman penalization for particle vortex methods

DEFF Research Database (Denmark)

Walther, Jens Honore; Hejlesen, Mads Mølholm; Leonard, A.

2013-01-01

We present an iterative Brinkman penalization method for the enforcement of the no-slip boundary condition in vortex particle methods. This is achieved by implementing a penalization of the velocity field using iteration of the penalized vorticity. We show that using the conventional Brinkman...... condition. These are: the impulsively started flow past a cylinder, the impulsively started flow normal to a flat plate, and the uniformly accelerated flow normal to a flat plate. The iterative penalization algorithm is shown to give significantly improved results compared to the conventional penalization...

New methods of testing nonlinear hypothesis using iterative NLLS estimator

Science.gov (United States)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper discusses the method of testing nonlinear hypothesis using iterative Nonlinear Least Squares (NLLS) estimator. Takeshi Amemiya [1] explained this method. However in the present research paper, a modified Wald test statistic due to Engle, Robert [6] is proposed to test the nonlinear hypothesis using iterative NLLS estimator. An alternative method for testing nonlinear hypothesis using iterative NLLS estimator based on nonlinear hypothesis using iterative NLLS estimator based on nonlinear studentized residuals has been proposed. In this research article an innovative method of testing nonlinear hypothesis using iterative restricted NLLS estimator is derived. Pesaran and Deaton [10] explained the methods of testing nonlinear hypothesis. This paper uses asymptotic properties of nonlinear least squares estimator proposed by Jenrich [8]. The main purpose of this paper is to provide very innovative methods of testing nonlinear hypothesis using iterative NLLS estimator, iterative NLLS estimator based on nonlinear studentized residuals and iterative restricted NLLS estimator. Eakambaram et al. [12] discussed least absolute deviation estimations versus nonlinear regression model with heteroscedastic errors and also they studied the problem of heteroscedasticity with reference to nonlinear regression models with suitable illustration. William Grene [13] examined the interaction effect in nonlinear models disused by Ai and Norton [14] and suggested ways to examine the effects that do not involve statistical testing. Peter [15] provided guidelines for identifying composite hypothesis and addressing the probability of false rejection for multiple hypotheses.

AIR Tools - A MATLAB package of algebraic iterative reconstruction methods

DEFF Research Database (Denmark)

Hansen, Per Christian; Saxild-Hansen, Maria

2012-01-01

We present a MATLAB package with implementations of several algebraic iterative reconstruction methods for discretizations of inverse problems. These so-called row action methods rely on semi-convergence for achieving the necessary regularization of the problem. Two classes of methods are impleme......We present a MATLAB package with implementations of several algebraic iterative reconstruction methods for discretizations of inverse problems. These so-called row action methods rely on semi-convergence for achieving the necessary regularization of the problem. Two classes of methods...... are implemented: Algebraic Reconstruction Techniques (ART) and Simultaneous Iterative Reconstruction Techniques (SIRT). In addition we provide a few simplified test problems from medical and seismic tomography. For each iterative method, a number of strategies are available for choosing the relaxation parameter...

A new non-iterative method for fitting Lorentzian to Moessbauer spectra

International Nuclear Information System (INIS)

Mukoyama, T.; Vegh, J.

1980-01-01

A new method for fitting a Lorentzian function without an iterative procedure is presented. The method is quicker and simpler than the previously proposed method of non-iterative fitting. Comparison with the previous method and with the conventional iterative method has been made. It is shown that the present method gives satisfactory results. (orig.)

A comparison theorem for the SOR iterative method

Science.gov (United States)

Sun, Li-Ying

2005-09-01

In 1997, Kohno et al. have reported numerically that the improving modified Gauss-Seidel method, which was referred to as the IMGS method, is superior to the SOR iterative method. In this paper, we prove that the spectral radius of the IMGS method is smaller than that of the SOR method and Gauss-Seidel method, if the relaxation parameter [omega][set membership, variant](0,1]. As a result, we prove theoretically that this method is succeeded in improving the convergence of some classical iterative methods. Some recent results are improved.

Enhancing Low-Rank Subspace Clustering by Manifold Regularization.

Science.gov (United States)

Liu, Junmin; Chen, Yijun; Zhang, JiangShe; Xu, Zongben

2014-07-25

Recently, low-rank representation (LRR) method has achieved great success in subspace clustering (SC), which aims to cluster the data points that lie in a union of low-dimensional subspace. Given a set of data points, LRR seeks the lowest rank representation among the many possible linear combinations of the bases in a given dictionary or in terms of the data itself. However, LRR only considers the global Euclidean structure, while the local manifold structure, which is often important for many real applications, is ignored. In this paper, to exploit the local manifold structure of the data, a manifold regularization characterized by a Laplacian graph has been incorporated into LRR, leading to our proposed Laplacian regularized LRR (LapLRR). An efficient optimization procedure, which is based on alternating direction method of multipliers (ADMM), is developed for LapLRR. Experimental results on synthetic and real data sets are presented to demonstrate that the performance of LRR has been enhanced by using the manifold regularization.

Similarity measurement method of high-dimensional data based on normalized net lattice subspace

Institute of Scientific and Technical Information of China (English)

Li Wenfa; Wang Gongming; Li Ke; Huang Su

2017-01-01

The performance of conventional similarity measurement methods is affected seriously by the curse of dimensionality of high-dimensional data.The reason is that data difference between sparse and noisy dimensionalities occupies a large proportion of the similarity, leading to the dissimilarities between any results.A similarity measurement method of high-dimensional data based on normalized net lattice subspace is proposed.The data range of each dimension is divided into several intervals, and the components in different dimensions are mapped onto the corresponding interval.Only the component in the same or adjacent interval is used to calculate the similarity.To validate this meth-od, three data types are used, and seven common similarity measurement methods are compared. The experimental result indicates that the relative difference of the method is increasing with the di-mensionality and is approximately two or three orders of magnitude higher than the conventional method.In addition, the similarity range of this method in different dimensions is [0, 1], which is fit for similarity analysis after dimensionality reduction.

Subspace confinement: how good is your qubit?

International Nuclear Information System (INIS)

Devitt, Simon J; Schirmer, Sonia G; Oi, Daniel K L; Cole, Jared H; Hollenberg, Lloyd C L

2007-01-01

The basic operating element of standard quantum computation is the qubit, an isolated two-level system that can be accurately controlled, initialized and measured. However, the majority of proposed physical architectures for quantum computation are built from systems that contain much more complicated Hilbert space structures. Hence, defining a qubit requires the identification of an appropriate controllable two-dimensional sub-system. This prompts the obvious question of how well a qubit, thus defined, is confined to this subspace, and whether we can experimentally quantify the potential leakage into states outside the qubit subspace. We demonstrate how subspace leakage can be characterized using minimal theoretical assumptions by examining the Fourier spectrum of the oscillation experiment

The danger of iteration methods

International Nuclear Information System (INIS)

Villain, J.; Semeria, B.

1983-01-01

When a Hamiltonian H depends on variables phisub(i), the values of these variables which minimize H satisfy the equations deltaH/deltaphisub(i) = O. If this set of equations is solved by iteration, there is no guarantee that the solution is the one which minimizes H. In the case of a harmonic system with a random potential periodic with respect to the phisub(i)'s, the fluctuations have been calculated by Efetov and Larkin by means of the iteration method. The result is wrong in the case of a strong disorder. Even in the weak disorder case, it is wrong for a one-dimensional system and for a finite system of 2 particles. It is argued that the results obtained by iteration are always wrong, and that between 2 and 4 dimensions, spin-pair correlation functions decay like powers of the distance, as found by Aharony and Pytte for another model

AIR Tools II: algebraic iterative reconstruction methods, improved implementation

DEFF Research Database (Denmark)

Hansen, Per Christian; Jørgensen, Jakob Sauer

2017-01-01

with algebraic iterative methods and their convergence properties. The present software is a much expanded and improved version of the package AIR Tools from 2012, based on a new modular design. In addition to improved performance and memory use, we provide more flexible iterative methods, a column-action method...

Iterative Runge–Kutta-type methods for nonlinear ill-posed problems

International Nuclear Information System (INIS)

Böckmann, C; Pornsawad, P

2008-01-01

We present a regularization method for solving nonlinear ill-posed problems by applying the family of Runge–Kutta methods to an initial value problem, in particular, to the asymptotical regularization method. We prove that the developed iterative regularization method converges to a solution under certain conditions and with a general stopping rule. Some particular iterative regularization methods are numerically implemented. Numerical results of the examples show that the developed Runge–Kutta-type regularization methods yield stable solutions and that particular implicit methods are very efficient in saving iteration steps

A transport synthetic acceleration method for transport iterations

International Nuclear Information System (INIS)

Ramone, G.L.; Adams, M.L.

1997-01-01

A family of transport synthetic acceleration (TSA) methods for iteratively solving within group scattering problems is presented. A single iteration in these schemes consists of a transport sweep followed by a low-order calculation, which itself is a simplified transport problem. The method for isotropic-scattering problems in X-Y geometry is described. The Fourier analysis of a model problem for equations with no spatial discretization shows that a previously proposed TSA method is unstable in two dimensions but that the modifications make it stable and rapidly convergent. The same procedure for discretized transport equations, using the step characteristic and two bilinear discontinuous methods, shows that discretization enhances TSA performance. A conjugate gradient algorithm for the low-order problem is described, a crude quadrature set for the low-order problem is proposed, and the number of low-order iterations per high-order sweep is limited to a relatively small value. These features lead to simple and efficient improvements to the method. TSA is tested on a series of problems, and a set of parameters is proposed for which the method behaves especially well. TSA achieves a substantial reduction in computational cost over source iteration, regardless of discretization parameters or material properties, and this reduction increases with the difficulty of the problem

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.

Iterative method for Amado's model

International Nuclear Information System (INIS)

Tomio, L.

1980-01-01

A recently proposed iterative method for solving scattering integral equations is applied to the spin doublet and spin quartet neutron-deuteron scattering in the Amado model. The method is tested numerically in the calculation of scattering lengths and phase-shifts and results are found better than those obtained by using the conventional Pade technique. (Author) [pt

Prewhitening for Rank-Deficient Noise in Subspace Methods for Noise Reduction

DEFF Research Database (Denmark)

Hansen, Per Christian; Jensen, Søren Holdt

2005-01-01

A fundamental issue in connection with subspace methods for noise reduction is that the covariance matrix for the noise is required to have full rank, in order for the prewhitening step to be defined. However, there are important cases where this requirement is not fulfilled, e.g., when the noise...... has narrow-band characteristics, or in the case of tonal noise. We extend the concept of prewhitening to include the case when the noise covariance matrix is rank deficient, using a weighted pseudoinverse and the quotient SVD, and we show how to formulate a general rank-reduction algorithm that works...... also for rank deficient noise. We also demonstrate how to formulate this algorithm by means of a quotient ULV decomposition, which allows for faster computation and updating. Finally we apply our algorithm to a problem involving a speech signal contaminated by narrow-band noise....

R3GMRES: including prior information in GMRES-type methods for discrete inverse problems

DEFF Research Database (Denmark)

Dong, Yiqiu; Garde, Henrik; Hansen, Per Christian

2014-01-01

Lothar Reichel and his collaborators proposed several iterative algorithms that augment the underlying Krylov subspace with an additional low-dimensional subspace in order to produce improved regularized solutions. We take a closer look at this approach and investigate a particular Regularized Ra...

Overview of hybrid subspace methods for uncertainty quantification, sensitivity analysis

International Nuclear Information System (INIS)

Abdel-Khalik, Hany S.; Bang, Youngsuk; Wang, Congjian

2013-01-01

Highlights: ► We overview the state-of-the-art in uncertainty quantification and sensitivity analysis. ► We overview new developments in above areas using hybrid methods. ► We give a tutorial introduction to above areas and the new developments. ► Hybrid methods address the explosion in dimensionality in nonlinear models. ► Representative numerical experiments are given. -- Abstract: The role of modeling and simulation has been heavily promoted in recent years to improve understanding of complex engineering systems. To realize the benefits of modeling and simulation, concerted efforts in the areas of uncertainty quantification and sensitivity analysis are required. The manuscript intends to serve as a pedagogical presentation of the material to young researchers and practitioners with little background on the subjects. We believe this is important as the role of these subjects is expected to be integral to the design, safety, and operation of existing as well as next generation reactors. In addition to covering the basics, an overview of the current state-of-the-art will be given with particular emphasis on the challenges pertaining to nuclear reactor modeling. The second objective will focus on presenting our own development of hybrid subspace methods intended to address the explosion in the computational overhead required when handling real-world complex engineering systems.

Two-qubit quantum computing in a projected subspace

International Nuclear Information System (INIS)

Bi Qiao; Ruda, H.E.; Zhan, M.S.

2002-01-01

A formulation for performing quantum computing in a projected subspace is presented, based on the subdynamical kinetic equation (SKE) for an open quantum system. The eigenvectors of the kinetic equation are shown to remain invariant before and after interaction with the environment. However, the eigenvalues in the projected subspace exhibit a type of phase shift to the evolutionary states. This phase shift does not destroy the decoherence-free (DF) property of the subspace because the associated fidelity is 1. This permits a universal formalism to be presented--the eigenprojectors of the free part of the Hamiltonian for the system and bath may be used to construct a DF projected subspace based on the SKE. To eliminate possible phase or unitary errors induced by the change in the eigenvalues, a cancellation technique is proposed, using the adjustment of the coupling time, and applied to a two-qubit computing system. A general criteria for constructing a DF-projected subspace from the SKE is discussed. Finally, a proposal for using triangulation to realize a decoherence-free subsystem based on SKE is presented. The concrete formulation for a two-qubit model is given exactly. Our approach is general and appears to be applicable to any type of decoherence

Investigation of the stochastic subspace identification method for on-line wind turbine tower monitoring

Science.gov (United States)

Dai, Kaoshan; Wang, Ying; Lu, Wensheng; Ren, Xiaosong; Huang, Zhenhua

2017-04-01

Structural health monitoring (SHM) of wind turbines has been applied in the wind energy industry to obtain their real-time vibration parameters and to ensure their optimum performance. For SHM, the accuracy of its results and the efficiency of its measurement methodology and data processing algorithm are the two major concerns. Selection of proper measurement parameters could improve such accuracy and efficiency. The Stochastic Subspace Identification (SSI) is a widely used data processing algorithm for SHM. This research discussed the accuracy and efficiency of SHM using SSI method to identify vibration parameters of on-line wind turbine towers. Proper measurement parameters, such as optimum measurement duration, are recommended.

Robust Adaptive Beamforming with Sensor Position Errors Using Weighted Subspace Fitting-Based Covariance Matrix Reconstruction.

Science.gov (United States)

Chen, Peng; Yang, Yixin; Wang, Yong; Ma, Yuanliang

2018-05-08

When sensor position errors exist, the performance of recently proposed interference-plus-noise covariance matrix (INCM)-based adaptive beamformers may be severely degraded. In this paper, we propose a weighted subspace fitting-based INCM reconstruction algorithm to overcome sensor displacement for linear arrays. By estimating the rough signal directions, we construct a novel possible mismatched steering vector (SV) set. We analyze the proximity of the signal subspace from the sample covariance matrix (SCM) and the space spanned by the possible mismatched SV set. After solving an iterative optimization problem, we reconstruct the INCM using the estimated sensor position errors. Then we estimate the SV of the desired signal by solving an optimization problem with the reconstructed INCM. The main advantage of the proposed algorithm is its robustness against SV mismatches dominated by unknown sensor position errors. Numerical examples show that even if the position errors are up to half of the assumed sensor spacing, the output signal-to-interference-plus-noise ratio is only reduced by 4 dB. Beam patterns plotted using experiment data show that the interference suppression capability of the proposed beamformer outperforms other tested beamformers.

A Rank-Constrained Matrix Representation for Hypergraph-Based Subspace Clustering

Directory of Open Access Journals (Sweden)

Yubao Sun

2015-01-01

Full Text Available This paper presents a novel, rank-constrained matrix representation combined with hypergraph spectral analysis to enable the recovery of the original subspace structures of corrupted data. Real-world data are frequently corrupted with both sparse error and noise. Our matrix decomposition model separates the low-rank, sparse error, and noise components from the data in order to enhance robustness to the corruption. In order to obtain the desired rank representation of the data within a dictionary, our model directly utilizes rank constraints by restricting the upper bound of the rank range. An alternative projection algorithm is proposed to estimate the low-rank representation and separate the sparse error from the data matrix. To further capture the complex relationship between data distributed in multiple subspaces, we use hypergraph to represent the data by encapsulating multiple related samples into one hyperedge. The final clustering result is obtained by spectral decomposition of the hypergraph Laplacian matrix. Validation experiments on the Extended Yale Face Database B, AR, and Hopkins 155 datasets show that the proposed method is a promising tool for subspace clustering.

The Semianalytical Solutions for Stiff Systems of Ordinary Differential Equations by Using Variational Iteration Method and Modified Variational Iteration Method with Comparison to Exact Solutions

Directory of Open Access Journals (Sweden)

Mehmet Tarik Atay

2013-01-01

Full Text Available The Variational Iteration Method (VIM and Modified Variational Iteration Method (MVIM are used to find solutions of systems of stiff ordinary differential equations for both linear and nonlinear problems. Some examples are given to illustrate the accuracy and effectiveness of these methods. We compare our results with exact results. In some studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method. Comparisons with exact solutions reveal that the Variational Iteration Method (VIM and the Modified Variational Iteration Method (MVIM are easier to implement. In fact, these methods are promising methods for various systems of linear and nonlinear stiff ordinary differential equations. Furthermore, VIM, or in some cases MVIM, is giving exact solutions in linear cases and very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.

Stopping test of iterative methods for solving PDE

International Nuclear Information System (INIS)

Wang Bangrong

1991-01-01

In order to assure the accuracy of the numerical solution of the iterative method for solving PDE (partial differential equation), the stopping test is very important. If the coefficient matrix of the system of linear algebraic equations is strictly diagonal dominant or irreducible weakly diagonal dominant, the stopping test formulas of the iterative method for solving PDE is proposed. Several numerical examples are given to illustrate the applications of the stopping test formulas

Monomial codes seen as invariant subspaces

Directory of Open Access Journals (Sweden)

García-Planas María Isabel

2017-08-01

Full Text Available It is well known that cyclic codes are very useful because of their applications, since they are not computationally expensive and encoding can be easily implemented. The relationship between cyclic codes and invariant subspaces is also well known. In this paper a generalization of this relationship is presented between monomial codes over a finite field and hyperinvariant subspaces of n under an appropriate linear transformation. Using techniques of Linear Algebra it is possible to deduce certain properties for this particular type of codes, generalizing known results on cyclic codes.

On the maximal dimension of a completely entangled subspace for ...

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

dim S = d1d2 ...dk − (d1 +···+ dk) + k − 1, where E is the collection of all completely entangled subspaces. When H1 = H2 and k = 2 an explicit orthonormal basis of a maximal completely entangled subspace of H1 ⊗ H2 is given. We also introduce a more delicate notion of a perfectly entangled subspace for a multipartite ...

Experimental fault-tolerant quantum cryptography in a decoherence-free subspace

International Nuclear Information System (INIS)

Zhang Qiang; Pan Jianwei; Yin Juan; Chen Tengyun; Lu Shan; Zhang Jun; Li Xiaoqiang; Yang Tao; Wang Xiangbin

2006-01-01

We experimentally implement a fault-tolerant quantum key distribution protocol with two photons in a decoherence-free subspace [Phys. Rev. A 72, 050304(R) (2005)]. It is demonstrated that our protocol can yield a good key rate even with a large bit-flip error rate caused by collective rotation, while the usual realization of the Bennett-Brassard 1984 protocol cannot produce any secure final key given the same channel. Since the experiment is performed in polarization space and does not need the calibration of a reference frame, important applications in free-space quantum communication are expected. Moreover, our method can also be used to robustly transmit an arbitrary two-level quantum state in a type of decoherence-free subspace

Iterative algorithm for the volume integral method for magnetostatics problems

International Nuclear Information System (INIS)

Pasciak, J.E.

1980-11-01

Volume integral methods for solving nonlinear magnetostatics problems are considered in this paper. The integral method is discretized by a Galerkin technique. Estimates are given which show that the linearized problems are well conditioned and hence easily solved using iterative techniques. Comparisons of iterative algorithms with the elimination method of GFUN3D shows that the iterative method gives an order of magnitude improvement in computational time as well as memory requirements for large problems. Computational experiments for a test problem as well as a double layer dipole magnet are given. Error estimates for the linearized problem are also derived

Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems

Czech Academy of Sciences Publication Activity Database

Morikuni, Keiichi; Hayami, K.

2015-01-01

Roč. 36, č. 1 (2015), s. 225-250 ISSN 0895-4798 Institutional support: RVO:67985807 Keywords : least squares problem * iterative methods * preconditioner * inner-outer iteration * GMRES method * stationary iterative method * rank-deficient problem Subject RIV: BA - General Mathematics Impact factor: 1.883, year: 2015

Iterative approach as alternative to S-matrix in modal methods

Science.gov (United States)

Semenikhin, Igor; Zanuccoli, Mauro

2014-12-01

The continuously increasing complexity of opto-electronic devices and the rising demands of simulation accuracy lead to the need of solving very large systems of linear equations making iterative methods promising and attractive from the computational point of view with respect to direct methods. In particular, iterative approach potentially enables the reduction of required computational time to solve Maxwell's equations by Eigenmode Expansion algorithms. Regardless of the particular eigenmodes finding method used, the expansion coefficients are computed as a rule by scattering matrix (S-matrix) approach or similar techniques requiring order of M3 operations. In this work we consider alternatives to the S-matrix technique which are based on pure iterative or mixed direct-iterative approaches. The possibility to diminish the impact of M3 -order calculations to overall time and in some cases even to reduce the number of arithmetic operations to M2 by applying iterative techniques are discussed. Numerical results are illustrated to discuss validity and potentiality of the proposed approaches.

Improved Stochastic Subspace System Identification for Structural Health Monitoring

Science.gov (United States)

Chang, Chia-Ming; Loh, Chin-Hsiung

2015-07-01

Structural health monitoring acquires structural information through numerous sensor measurements. Vibrational measurement data render the dynamic characteristics of structures to be extracted, in particular of the modal properties such as natural frequencies, damping, and mode shapes. The stochastic subspace system identification has been recognized as a power tool which can present a structure in the modal coordinates. To obtain qualitative identified data, this tool needs to spend computational expense on a large set of measurements. In study, a stochastic system identification framework is proposed to improve the efficiency and quality of the conventional stochastic subspace system identification. This framework includes 1) measured signal processing, 2) efficient space projection, 3) system order selection, and 4) modal property derivation. The measured signal processing employs the singular spectrum analysis algorithm to lower the noise components as well as to present a data set in a reduced dimension. The subspace is subsequently derived from the data set presented in a delayed coordinate. With the proposed order selection criteria, the number of structural modes is determined, resulting in the modal properties. This system identification framework is applied to a real-world bridge for exploring the feasibility in real-time applications. The results show that this improved system identification method significantly decreases computational time, while qualitative modal parameters are still attained.

Properties of a class of block-iterative methods

International Nuclear Information System (INIS)

Elfving, Tommy; Nikazad, Touraj

2009-01-01

We study a class of block-iterative (BI) methods proposed in image reconstruction for solving linear systems. A subclass, symmetric block-iteration (SBI), is derived such that for this subclass both semi-convergence analysis and stopping-rules developed for fully simultaneous iteration apply. Also results on asymptotic convergence are given, e.g., BI exhibit cyclic convergence irrespective of the consistency of the linear system. Further it is shown that the limit points of SBI satisfy a weighted least-squares problem. We also present numerical results obtained using a trained stopping rule on SBI

Semitransitive subspaces of operators

Czech Academy of Sciences Publication Activity Database

Bernik, J.; Drnovšek, R.; Hadwin, D.; Jafarian, A.; Bukovšek, D.K.; Košir, T.; Fijavž, M.K.; Laffey, T.; Livshits, L.; Mastnak, M.; Meshulam, R.; Müller, Vladimír; Nordgren, E.; Okniński, J.; Omladič, M.; Radjavi, H.; Sourour, A.; Timoney, R.

2006-01-01

Roč. 15, č. 1 (2006), s. 225-238 E-ISSN 1081-3810 Institutional research plan: CEZ:AV0Z10190503 Keywords : semitransitive subspaces Subject RIV: BA - General Mathematics Impact factor: 0.322, year: 2006 http://www.math.technion.ac.il/iic/ ela

Recursive Subspace Identification of AUV Dynamic Model under General Noise Assumption

Directory of Open Access Journals (Sweden)

Zheping Yan

2014-01-01

Full Text Available A recursive subspace identification algorithm for autonomous underwater vehicles (AUVs is proposed in this paper. Due to the advantages at handling nonlinearities and couplings, the AUV model investigated here is for the first time constructed as a Hammerstein model with nonlinear feedback in the linear part. To better take the environment and sensor noises into consideration, the identification problem is concerned as an errors-in-variables (EIV one which means that the identification procedure is under general noise assumption. In order to make the algorithm recursively, propagator method (PM based subspace approach is extended into EIV framework to form the recursive identification method called PM-EIV algorithm. With several identification experiments carried out by the AUV simulation platform, the proposed algorithm demonstrates its effectiveness and feasibility.

Intelligent Control of a Sensor-Actuator System via Kernelized Least-Squares Policy Iteration

Directory of Open Access Journals (Sweden)

Bo Liu

2012-02-01

Full Text Available In this paper a new framework, called Compressive Kernelized Reinforcement Learning (CKRL, for computing near-optimal policies in sequential decision making with uncertainty is proposed via incorporating the non-adaptive data-independent Random Projections and nonparametric Kernelized Least-squares Policy Iteration (KLSPI. Random Projections are a fast, non-adaptive dimensionality reduction framework in which high-dimensionality data is projected onto a random lower-dimension subspace via spherically random rotation and coordination sampling. KLSPI introduce kernel trick into the LSPI framework for Reinforcement Learning, often achieving faster convergence and providing automatic feature selection via various kernel sparsification approaches. In this approach, policies are computed in a low-dimensional subspace generated by projecting the high-dimensional features onto a set of random basis. We first show how Random Projections constitute an efficient sparsification technique and how our method often converges faster than regular LSPI, while at lower computational costs. Theoretical foundation underlying this approach is a fast approximation of Singular Value Decomposition (SVD. Finally, simulation results are exhibited on benchmark MDP domains, which confirm gains both in computation time and in performance in large feature spaces.

Copper Mountain conference on iterative methods: Proceedings: Volume 2

Energy Technology Data Exchange (ETDEWEB)

NONE

1996-10-01

This volume (the second of two) contains information presented during the last two days of the Copper Mountain Conference on Iterative Methods held April 9-13, 1996 at Copper Mountain, Colorado. Topics of the sessions held these two days include domain decomposition, Krylov methods, computational fluid dynamics, Markov chains, sparse and parallel basic linear algebra subprograms, multigrid methods, applications of iterative methods, equation systems with multiple right-hand sides, projection methods, and the Helmholtz equation. Selected papers indexed separately for the Energy Science and Technology Database.

Fast regularizing sequential subspace optimization in Banach spaces

International Nuclear Information System (INIS)

Schöpfer, F; Schuster, T

2009-01-01

We are concerned with fast computations of regularized solutions of linear operator equations in Banach spaces in case only noisy data are available. To this end we modify recently developed sequential subspace optimization methods in such a way that the therein employed Bregman projections onto hyperplanes are replaced by Bregman projections onto stripes whose width is in the order of the noise level

A Framework for Generalising the Newton Method and Other Iterative Methods from Euclidean Space to Manifolds

OpenAIRE

Manton, Jonathan H.

2012-01-01

The Newton iteration is a popular method for minimising a cost function on Euclidean space. Various generalisations to cost functions defined on manifolds appear in the literature. In each case, the convergence rate of the generalised Newton iteration needed establishing from first principles. The present paper presents a framework for generalising iterative methods from Euclidean space to manifolds that ensures local convergence rates are preserved. It applies to any (memoryless) iterative m...

Intrinsic Grassmann Averages for Online Linear and Robust Subspace Learning

DEFF Research Database (Denmark)

Chakraborty, Rudrasis; Hauberg, Søren; Vemuri, Baba C.

2017-01-01

Principal Component Analysis (PCA) is a fundamental method for estimating a linear subspace approximation to high-dimensional data. Many algorithms exist in literature to achieve a statistically robust version of PCA called RPCA. In this paper, we present a geometric framework for computing the p...

Conformal mapping and convergence of Krylov iterations

Energy Technology Data Exchange (ETDEWEB)

Driscoll, T.A.; Trefethen, L.N. [Cornell Univ., Ithaca, NY (United States)

1994-12-31

Connections between conformal mapping and matrix iterations have been known for many years. The idea underlying these connections is as follows. Suppose the spectrum of a matrix or operator A is contained in a Jordan region E in the complex plane with 0 not an element of E. Let {phi}(z) denote a conformal map of the exterior of E onto the exterior of the unit disk, with {phi}{infinity} = {infinity}. Then 1/{vert_bar}{phi}(0){vert_bar} is an upper bound for the optimal asymptotic convergence factor of any Krylov subspace iteration. This idea can be made precise in various ways, depending on the matrix iterations, on whether A is finite or infinite dimensional, and on what bounds are assumed on the non-normality of A. This paper explores these connections for a variety of matrix examples, making use of a new MATLAB Schwarz-Christoffel Mapping Toolbox developed by the first author. Unlike the earlier Fortran Schwarz-Christoffel package SCPACK, the new toolbox computes exterior as well as interior Schwarz-Christoffel maps, making it easy to experiment with spectra that are not necessarily symmetric about an axis.

Overlapping domain decomposition preconditioners for the generalized Davidson method for the eigenvalue problem

Energy Technology Data Exchange (ETDEWEB)

Stathopoulos, A.; Fischer, C.F. [Vanderbilt Univ., Nashville, TN (United States); Saad, Y.

1994-12-31

The solution of the large, sparse, symmetric eigenvalue problem, Ax = {lambda}x, is central to many scientific applications. Among many iterative methods that attempt to solve this problem, the Lanczos and the Generalized Davidson (GD) are the most widely used methods. The Lanczos method builds an orthogonal basis for the Krylov subspace, from which the required eigenvectors are approximated through a Rayleigh-Ritz procedure. Each Lanczos iteration is economical to compute but the number of iterations may grow significantly for difficult problems. The GD method can be considered a preconditioned version of Lanczos. In each step the Rayleigh-Ritz procedure is solved and explicit orthogonalization of the preconditioned residual ((M {minus} {lambda}I){sup {minus}1}(A {minus} {lambda}I)x) is performed. Therefore, the GD method attempts to improve convergence and robustness at the expense of a more complicated step.

Simultaneous multislice magnetic resonance fingerprinting with low-rank and subspace modeling.

Science.gov (United States)

Bo Zhao; Bilgic, Berkin; Adalsteinsson, Elfar; Griswold, Mark A; Wald, Lawrence L; Setsompop, Kawin

2017-07-01

Magnetic resonance fingerprinting (MRF) is a new quantitative imaging paradigm that enables simultaneous acquisition of multiple magnetic resonance tissue parameters (e.g., T 1 , T 2 , and spin density). Recently, MRF has been integrated with simultaneous multislice (SMS) acquisitions to enable volumetric imaging with faster scan time. In this paper, we present a new image reconstruction method based on low-rank and subspace modeling for improved SMS-MRF. Here the low-rank model exploits strong spatiotemporal correlation among contrast-weighted images, while the subspace model captures the temporal evolution of magnetization dynamics. With the proposed model, the image reconstruction problem is formulated as a convex optimization problem, for which we develop an algorithm based on variable splitting and the alternating direction method of multipliers. The performance of the proposed method has been evaluated by numerical experiments, and the results demonstrate that the proposed method leads to improved accuracy over the conventional approach. Practically, the proposed method has a potential to allow for a 3× speedup with minimal reconstruction error, resulting in less than 5 sec imaging time per slice.

Subspace K-means clustering

NARCIS (Netherlands)

Timmerman, Marieke E.; Ceulemans, Eva; De Roover, Kim; Van Leeuwen, Karla

2013-01-01

To achieve an insightful clustering of multivariate data, we propose subspace K-means. Its central idea is to model the centroids and cluster residuals in reduced spaces, which allows for dealing with a wide range of cluster types and yields rich interpretations of the clusters. We review the

A frequency domain subspace algorithm for mixed causal, anti-causal LTI systems

NARCIS (Netherlands)

Fraanje, Rufus; Verhaegen, Michel; Verdult, Vincent; Pintelon, Rik

2003-01-01

The paper extends the subspacc identification method to estimate state-space models from frequency response function (FRF) samples, proposed by McKelvey et al. (1996) for mixed causal/anti-causal systems, and shows that other frequency domain subspace algorithms can be extended similarly. The method

An iterative method for near-field Fresnel region polychromatic phase contrast imaging

Science.gov (United States)

Carroll, Aidan J.; van Riessen, Grant A.; Balaur, Eugeniu; Dolbnya, Igor P.; Tran, Giang N.; Peele, Andrew G.

2017-07-01

We present an iterative method for polychromatic phase contrast imaging that is suitable for broadband illumination and which allows for the quantitative determination of the thickness of an object given the refractive index of the sample material. Experimental and simulation results suggest the iterative method provides comparable image quality and quantitative object thickness determination when compared to the analytical polychromatic transport of intensity and contrast transfer function methods. The ability of the iterative method to work over a wider range of experimental conditions means the iterative method is a suitable candidate for use with polychromatic illumination and may deliver more utility for laboratory-based x-ray sources, which typically have a broad spectrum.

Constructing Frozen Jacobian Iterative Methods for Solving Systems of Nonlinear Equations, Associated with ODEs and PDEs Using the Homotopy Method

Directory of Open Access Journals (Sweden)

Uswah Qasim

2016-03-01

Full Text Available A homotopy method is presented for the construction of frozen Jacobian iterative methods. The frozen Jacobian iterative methods are attractive because the inversion of the Jacobian is performed in terms of LUfactorization only once, for a single instance of the iterative method. We embedded parameters in the iterative methods with the help of the homotopy method: the values of the parameters are determined in such a way that a better convergence rate is achieved. The proposed homotopy technique is general and has the ability to construct different families of iterative methods, for solving weakly nonlinear systems of equations. Further iterative methods are also proposed for solving general systems of nonlinear equations.

Conjunctive patches subspace learning with side information for collaborative image retrieval.

Science.gov (United States)

Zhang, Lining; Wang, Lipo; Lin, Weisi

2012-08-01

Content-Based Image Retrieval (CBIR) has attracted substantial attention during the past few years for its potential practical applications to image management. A variety of Relevance Feedback (RF) schemes have been designed to bridge the semantic gap between the low-level visual features and the high-level semantic concepts for an image retrieval task. Various Collaborative Image Retrieval (CIR) schemes aim to utilize the user historical feedback log data with similar and dissimilar pairwise constraints to improve the performance of a CBIR system. However, existing subspace learning approaches with explicit label information cannot be applied for a CIR task, although the subspace learning techniques play a key role in various computer vision tasks, e.g., face recognition and image classification. In this paper, we propose a novel subspace learning framework, i.e., Conjunctive Patches Subspace Learning (CPSL) with side information, for learning an effective semantic subspace by exploiting the user historical feedback log data for a CIR task. The CPSL can effectively integrate the discriminative information of labeled log images, the geometrical information of labeled log images and the weakly similar information of unlabeled images together to learn a reliable subspace. We formally formulate this problem into a constrained optimization problem and then present a new subspace learning technique to exploit the user historical feedback log data. Extensive experiments on both synthetic data sets and a real-world image database demonstrate the effectiveness of the proposed scheme in improving the performance of a CBIR system by exploiting the user historical feedback log data.

A novel variable selection approach that iteratively optimizes variable space using weighted binary matrix sampling.

Science.gov (United States)

Deng, Bai-chuan; Yun, Yong-huan; Liang, Yi-zeng; Yi, Lun-zhao

2014-10-07

In this study, a new optimization algorithm called the Variable Iterative Space Shrinkage Approach (VISSA) that is based on the idea of model population analysis (MPA) is proposed for variable selection. Unlike most of the existing optimization methods for variable selection, VISSA statistically evaluates the performance of variable space in each step of optimization. Weighted binary matrix sampling (WBMS) is proposed to generate sub-models that span the variable subspace. Two rules are highlighted during the optimization procedure. First, the variable space shrinks in each step. Second, the new variable space outperforms the previous one. The second rule, which is rarely satisfied in most of the existing methods, is the core of the VISSA strategy. Compared with some promising variable selection methods such as competitive adaptive reweighted sampling (CARS), Monte Carlo uninformative variable elimination (MCUVE) and iteratively retaining informative variables (IRIV), VISSA showed better prediction ability for the calibration of NIR data. In addition, VISSA is user-friendly; only a few insensitive parameters are needed, and the program terminates automatically without any additional conditions. The Matlab codes for implementing VISSA are freely available on the website: https://sourceforge.net/projects/multivariateanalysis/files/VISSA/.

A block-iterative nodal integral method for forced convection problems

International Nuclear Information System (INIS)

Decker, W.J.; Dorning, J.J.

1992-01-01

A new efficient iterative nodal integral method for the time-dependent two- and three-dimensional incompressible Navier-Stokes equations has been developed. Using the approach introduced by Azmy and Droning to develop nodal mehtods with high accuracy on coarse spatial grids for two-dimensional steady-state problems and extended to coarse two-dimensional space-time grids by Wilson et al. for thermal convection problems, we have developed a new iterative nodal integral method for the time-dependent Navier-Stokes equations for mechanically forced convection. A new, extremely efficient block iterative scheme is employed to invert the Jacobian within each of the Newton-Raphson iterations used to solve the final nonlinear discrete-variable equations. By taking advantage of the special structure of the Jacobian, this scheme greatly reduces memory requirements. The accuracy of the overall method is illustrated by appliying it to the time-dependent version of the classic two-dimensional driven cavity problem of computational fluid dynamics

COMPARISON OF HOLOGRAPHIC AND ITERATIVE METHODS FOR AMPLITUDE OBJECT RECONSTRUCTION

Directory of Open Access Journals (Sweden)

I. A. Shevkunov

2015-01-01

Full Text Available Experimental comparison of four methods for the wavefront reconstruction is presented. We considered two iterative and two holographic methods with different mathematical models and algorithms for recovery. The first two of these methods do not use a reference wave recording scheme that reduces requirements for stability of the installation. A major role in phase information reconstruction by such methods is played by a set of spatial intensity distributions, which are recorded as the recording matrix is being moved along the optical axis. The obtained data are used consistently for wavefront reconstruction using an iterative procedure. In the course of this procedure numerical distribution of the wavefront between the planes is performed. Thus, phase information of the wavefront is stored in every plane and calculated amplitude distributions are replaced for the measured ones in these planes. In the first of the compared methods, a two-dimensional Fresnel transform and iterative calculation in the object plane are used as a mathematical model. In the second approach, an angular spectrum method is used for numerical wavefront propagation, and the iterative calculation is carried out only between closely located planes of data registration. Two digital holography methods, based on the usage of the reference wave in the recording scheme and differing from each other by numerical reconstruction algorithm of digital holograms, are compared with the first two methods. The comparison proved that the iterative method based on 2D Fresnel transform gives results comparable with the result of common holographic method with the Fourier-filtering. It is shown that holographic method for reconstructing of the object complex amplitude in the process of the object amplitude reduction is the best among considered ones.

A hyperpower iterative method for computing the generalized Drazin ...

Indian Academy of Sciences (India)

A quadratically convergent Newton-type iterative scheme is proposed for approximating the generalized Drazin inverse bd of the Banach algebra element b. Further, its extension into the form of the hyperpower iterative method of arbitrary order p ≤ 2 is presented. Convergence criteria along with the estimation of error ...

Gamow state vectors as functionals over subspaces of the nuclear space

International Nuclear Information System (INIS)

Bohm, A.

1979-12-01

Exponentially decaying Gamow state vectors are obtained from S-matrix poles in the lower half of the second sheet, and are defined as functionals over a subspace of the nuclear space, PHI. Exponentially growing Gamow state vectors are obtained from S-matrix poles in the upper half of the second sheet, and are defined as functionals over another subspace of PHI. On functionals over these two subspaces the dynamical group of time development splits into two semigroups

Estimation of direction of arrival of a moving target using subspace based approaches

Science.gov (United States)

Ghosh, Ripul; Das, Utpal; Akula, Aparna; Kumar, Satish; Sardana, H. K.

2016-05-01

In this work, array processing techniques based on subspace decomposition of signal have been evaluated for estimation of direction of arrival of moving targets using acoustic signatures. Three subspace based approaches - Incoherent Wideband Multiple Signal Classification (IWM), Least Square-Estimation of Signal Parameters via Rotation Invariance Techniques (LS-ESPRIT) and Total Least Square- ESPIRIT (TLS-ESPRIT) are considered. Their performance is compared with conventional time delay estimation (TDE) approaches such as Generalized Cross Correlation (GCC) and Average Square Difference Function (ASDF). Performance evaluation has been conducted on experimentally generated data consisting of acoustic signatures of four different types of civilian vehicles moving in defined geometrical trajectories. Mean absolute error and standard deviation of the DOA estimates w.r.t. ground truth are used as performance evaluation metrics. Lower statistical values of mean error confirm the superiority of subspace based approaches over TDE based techniques. Amongst the compared methods, LS-ESPRIT indicated better performance.

Structured Kernel Subspace Learning for Autonomous Robot Navigation.

Science.gov (United States)

Kim, Eunwoo; Choi, Sungjoon; Oh, Songhwai

2018-02-14

This paper considers two important problems for autonomous robot navigation in a dynamic environment, where the goal is to predict pedestrian motion and control a robot with the prediction for safe navigation. While there are several methods for predicting the motion of a pedestrian and controlling a robot to avoid incoming pedestrians, it is still difficult to safely navigate in a dynamic environment due to challenges, such as the varying quality and complexity of training data with unwanted noises. This paper addresses these challenges simultaneously by proposing a robust kernel subspace learning algorithm based on the recent advances in nuclear-norm and l 1 -norm minimization. We model the motion of a pedestrian and the robot controller using Gaussian processes. The proposed method efficiently approximates a kernel matrix used in Gaussian process regression by learning low-rank structured matrix (with symmetric positive semi-definiteness) to find an orthogonal basis, which eliminates the effects of erroneous and inconsistent data. Based on structured kernel subspace learning, we propose a robust motion model and motion controller for safe navigation in dynamic environments. We evaluate the proposed robust kernel learning in various tasks, including regression, motion prediction, and motion control problems, and demonstrate that the proposed learning-based systems are robust against outliers and outperform existing regression and navigation methods.

Geometric subspace updates with applications to online adaptive nonlinear model reduction

DEFF Research Database (Denmark)

Zimmermann, Ralf; Peherstorfer, Benjamin; Willcox, Karen

2018-01-01

In many scientific applications, including model reduction and image processing, subspaces are used as ansatz spaces for the low-dimensional approximation and reconstruction of the state vectors of interest. We introduce a procedure for adapting an existing subspace based on information from...... Estimation (GROUSE). We establish for GROUSE a closed-form expression for the residual function along the geodesic descent direction. Specific applications of subspace adaptation are discussed in the context of image processing and model reduction of nonlinear partial differential equation systems....

Independent Subspace Analysis of the Sea Surface Temperature Variability: Non-Gaussian Sources and Sensitivity to Sampling and Dimensionality

Directory of Open Access Journals (Sweden)

Carlos A. L. Pires

2017-01-01

Full Text Available We propose an expansion of multivariate time-series data into maximally independent source subspaces. The search is made among rotations of prewhitened data which maximize non-Gaussianity of candidate sources. We use a tensorial invariant approximation of the multivariate negentropy in terms of a linear combination of squared coskewness and cokurtosis. By solving a high-order singular value decomposition problem, we extract the axes associated with most non-Gaussianity. Moreover, an estimate of the Gaussian subspace is provided by the trailing singular vectors. The independent subspaces are obtained through the search of “quasi-independent” components within the estimated non-Gaussian subspace, followed by the identification of groups with significant joint negentropies. Sources result essentially from the coherency of extremes of the data components. The method is then applied to the global sea surface temperature anomalies, equatorward of 65°, after being tested with non-Gaussian surrogates consistent with the data anomalies. The main emerging independent components and subspaces, supposedly generated by independent forcing, include different variability modes, namely, The East-Pacific, the Central Pacific, and the Atlantic Niños, the Atlantic Multidecadal Oscillation, along with the subtropical dipoles in the Indian, South Pacific, and South-Atlantic oceans. Benefits and usefulness of independent subspaces are then discussed.

Natural Preconditioning and Iterative Methods for Saddle Point Systems

KAUST Repository

Pestana, Jennifer

2015-01-01

© 2015 Society for Industrial and Applied Mathematics. The solution of quadratic or locally quadratic extremum problems subject to linear(ized) constraints gives rise to linear systems in saddle point form. This is true whether in the continuous or the discrete setting, so saddle point systems arising from the discretization of partial differential equation problems, such as those describing electromagnetic problems or incompressible flow, lead to equations with this structure, as do, for example, interior point methods and the sequential quadratic programming approach to nonlinear optimization. This survey concerns iterative solution methods for these problems and, in particular, shows how the problem formulation leads to natural preconditioners which guarantee a fast rate of convergence of the relevant iterative methods. These preconditioners are related to the original extremum problem and their effectiveness - in terms of rapidity of convergence - is established here via a proof of general bounds on the eigenvalues of the preconditioned saddle point matrix on which iteration convergence depends.

Microscopic theory of dynamical subspace for large amplitude collective motion

International Nuclear Information System (INIS)

Sakata, Fumihiko; Marumori, Toshio; Ogura, Masanori.

1986-01-01

A full quantum theory appropriate for describing large amplitude collective motion is proposed by exploiting the basic idea of the semi-classical theory so far developed within the time-depedent Hartree-Fock theory. A central problem of the quantum theory is how to determine an optimal representation called a dynamical representation specific for the collective subspace where the large amplitude collective motion is replicated as precisely as possible. As an extension of the semi-classical theory where the concept of an approximate integral surface played an important role, the collective subspace is properly characterized by introducing a concept of an approximate invariant subspace of the Hamiltonian. (author)

Annual Copper Mountain Conferences on Multigrid and Iterative Methods, Copper Mountain, Colorado

International Nuclear Information System (INIS)

McCormick, Stephen F.

2016-01-01

This project supported the Copper Mountain Conference on Multigrid and Iterative Methods, held from 2007 to 2015, at Copper Mountain, Colorado. The subject of the Copper Mountain Conference Series alternated between Multigrid Methods in odd-numbered years and Iterative Methods in even-numbered years. Begun in 1983, the Series represents an important forum for the exchange of ideas in these two closely related fields. This report describes the Copper Mountain Conference on Multigrid and Iterative Methods, 2007-2015. Information on the conference series is available at http://grandmaster.colorado.edu/~copper/

Annual Copper Mountain Conferences on Multigrid and Iterative Methods, Copper Mountain, Colorado

Energy Technology Data Exchange (ETDEWEB)

McCormick, Stephen F. [Front Range Scientific, Inc., Lake City, CO (United States)

2016-03-25

This project supported the Copper Mountain Conference on Multigrid and Iterative Methods, held from 2007 to 2015, at Copper Mountain, Colorado. The subject of the Copper Mountain Conference Series alternated between Multigrid Methods in odd-numbered years and Iterative Methods in even-numbered years. Begun in 1983, the Series represents an important forum for the exchange of ideas in these two closely related fields. This report describes the Copper Mountain Conference on Multigrid and Iterative Methods, 2007-2015. Information on the conference series is available at http://grandmaster.colorado.edu/~copper/.

Kernel based subspace projection of near infrared hyperspectral images of maize kernels

DEFF Research Database (Denmark)

Larsen, Rasmus; Arngren, Morten; Hansen, Per Waaben

2009-01-01

In this paper we present an exploratory analysis of hyper- spectral 900-1700 nm images of maize kernels. The imaging device is a line scanning hyper spectral camera using a broadband NIR illumi- nation. In order to explore the hyperspectral data we compare a series of subspace projection methods ......- tor transform outperform the linear methods as well as kernel principal components in producing interesting projections of the data.......In this paper we present an exploratory analysis of hyper- spectral 900-1700 nm images of maize kernels. The imaging device is a line scanning hyper spectral camera using a broadband NIR illumi- nation. In order to explore the hyperspectral data we compare a series of subspace projection methods...... including principal component analysis and maximum autocorrelation factor analysis. The latter utilizes the fact that interesting phenomena in images exhibit spatial autocorrelation. However, linear projections often fail to grasp the underlying variability on the data. Therefore we propose to use so...

Detecting anomalies in crowded scenes via locality-constrained affine subspace coding

Science.gov (United States)

Fan, Yaxiang; Wen, Gongjian; Qiu, Shaohua; Li, Deren

2017-07-01

Video anomaly event detection is the process of finding an abnormal event deviation compared with the majority of normal or usual events. The main challenges are the high structure redundancy and the dynamic changes in the scenes that are in surveillance videos. To address these problems, we present a framework for anomaly detection and localization in videos that is based on locality-constrained affine subspace coding (LASC) and a model updating procedure. In our algorithm, LASC attempts to reconstruct the test sample by its top-k nearest subspaces, which are obtained by segmenting the normal samples space using a clustering method. A sample with a large reconstruction cost is detected as abnormal by setting a threshold. To adapt to the scene changes over time, a model updating strategy is proposed. We experiment on two public datasets: the UCSD dataset and the Avenue dataset. The results demonstrate that our method achieves competitive performance at a 700 fps on a single desktop PC.

Milestones in the Development of Iterative Solution Methods

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe

2010-01-01

Roč. 2010, - (2010), s. 1-33 ISSN 2090-0147 Institutional research plan: CEZ:AV0Z30860518 Keywords : iterative solution methods * convergence acceleration methods * linear systems Subject RIV: JC - Computer Hardware ; Software http://www.hindawi.com/journals/jece/2010/972794.html

A new efficient method for the calculation of interior eigenpairs and its application to vibrational structure problems

Science.gov (United States)

Petrenko, Taras; Rauhut, Guntram

2017-03-01

Vibrational configuration interaction theory is a common method for calculating vibrational levels and associated IR and Raman spectra of small and medium-sized molecules. When combined with appropriate configuration selection procedures, the method allows the treatment of configuration spaces with up to 1010 configurations. In general, this approach pursues the construction of the eigenstates with significant contributions of physically relevant configurations. The corresponding eigenfunctions are evaluated in the subspace of selected configurations. However, it can easily reach the dimension which is not tractable for conventional eigenvalue solvers. Although Davidson and Lanczos methods are the methods of choice for calculating exterior eigenvalues, they usually fall into stagnation when applied to interior states. The latter are commonly treated by the Jacobi-Davidson method. This approach in conjunction with matrix factorization for solving the correction equation (CE) is prohibitive for larger problems, and it has limited efficiency if the solution of the CE is based on Krylov's subspace algorithms. We propose an iterative subspace method that targets the eigenvectors with significant contributions to a given reference vector and is based on the optimality condition for the residual norm corresponding to the error in the solution vector. The subspace extraction and expansion are modified according to these principles which allow very efficient calculation of interior vibrational states with a strong multireference character in different vibrational structure problems. The convergence behavior of the method and its performance in comparison with the aforementioned algorithms are investigated in a set of benchmark calculations.

Numerical simulations of microwave heating of liquids: enhancements using Krylov subspace methods

Science.gov (United States)

Lollchund, M. R.; Dookhitram, K.; Sunhaloo, M. S.; Boojhawon, R.

2013-04-01

In this paper, we compare the performances of three iterative solvers for large sparse linear systems arising in the numerical computations of incompressible Navier-Stokes (NS) equations. These equations are employed mainly in the simulation of microwave heating of liquids. The emphasis of this work is on the application of Krylov projection techniques such as Generalized Minimal Residual (GMRES) to solve the Pressure Poisson Equations that result from discretisation of the NS equations. The performance of the GMRES method is compared with the traditional Gauss-Seidel (GS) and point successive over relaxation (PSOR) techniques through their application to simulate the dynamics of water housed inside a vertical cylindrical vessel which is subjected to microwave radiation. It is found that as the mesh size increases, GMRES gives the fastest convergence rate in terms of computational times and number of iterations.

Numerical simulations of microwave heating of liquids: enhancements using Krylov subspace methods

International Nuclear Information System (INIS)

Lollchund, M R; Dookhitram, K; Sunhaloo, M S; Boojhawon, R

2013-01-01

In this paper, we compare the performances of three iterative solvers for large sparse linear systems arising in the numerical computations of incompressible Navier-Stokes (NS) equations. These equations are employed mainly in the simulation of microwave heating of liquids. The emphasis of this work is on the application of Krylov projection techniques such as Generalized Minimal Residual (GMRES) to solve the Pressure Poisson Equations that result from discretisation of the NS equations. The performance of the GMRES method is compared with the traditional Gauss-Seidel (GS) and point successive over relaxation (PSOR) techniques through their application to simulate the dynamics of water housed inside a vertical cylindrical vessel which is subjected to microwave radiation. It is found that as the mesh size increases, GMRES gives the fastest convergence rate in terms of computational times and number of iterations.

On spectral subspaces and their applications to automorphism groups

International Nuclear Information System (INIS)

Olesen, Dorte

1974-03-01

An attempt is made to give a survey of the theory of spectra and spectral subspaces of group representations in an abstract Banach space setting. The theory is applied to the groups of automorphisms of operator algebras (mostly C*-algebras) and some important results of interest for mathematical physicists are proved (restrictions of the bitransposed action, spectral subspaces for the transposed action on a C*-algebra, and positive states and representations of Rsup(n)) [fr

Preconditioning of iterative methods - theory and applications

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe; Blaheta, Radim; Neytcheva, M.; Pultarová, I.

2015-01-01

Roč. 22, č. 6 (2015), s. 901-902 ISSN 1070-5325 Institutional support: RVO:68145535 Keywords : preconditioning * iterative methods * applications Subject RIV: BA - General Mathematics Impact factor: 1.431, year: 2015 http://onlinelibrary.wiley.com/doi/10.1002/nla.2016/epdf

New Parallel Algorithms for Structural Analysis and Design of Aerospace Structures

Science.gov (United States)

Nguyen, Duc T.

1998-01-01

Subspace and Lanczos iterations have been developed, well documented, and widely accepted as efficient methods for obtaining p-lowest eigen-pair solutions of large-scale, practical engineering problems. The focus of this paper is to incorporate recent developments in vectorized sparse technologies in conjunction with Subspace and Lanczos iterative algorithms for computational enhancements. Numerical performance, in terms of accuracy and efficiency of the proposed sparse strategies for Subspace and Lanczos algorithm, is demonstrated by solving for the lowest frequencies and mode shapes of structural problems on the IBM-R6000/590 and SunSparc 20 workstations.

Improved neutron-gamma discrimination for a 3He neutron detector using subspace learning methods

Science.gov (United States)

Wang, C. L.; Funk, L. L.; Riedel, R. A.; Berry, K. D.

2017-05-01

3He gas based neutron Linear-Position-Sensitive Detectors (LPSDs) have been used for many neutron scattering instruments. Traditional Pulse-height Analysis (PHA) for Neutron-Gamma Discrimination (NGD) resulted in the neutron-gamma efficiency ratio (NGD ratio) on the order of 105-106. The NGD ratios of 3He detectors need to be improved for even better scientific results from neutron scattering. Digital Signal Processing (DSP) analyses of waveforms were proposed for obtaining better NGD ratios, based on features extracted from rise-time, pulse amplitude, charge integration, a simplified Wiener filter, and the cross-correlation between individual and template waveforms of neutron and gamma events. Fisher Linear Discriminant Analysis (FLDA) and three Multivariate Analyses (MVAs) of the features were performed. The NGD ratios are improved by about 102-103 times compared with the traditional PHA method. Our results indicate the NGD capabilities of 3He tube detectors can be significantly improved with subspace-learning based methods, which may result in a reduced data-collection time and better data quality for further data reduction.

Variational Iteration Method for Fifth-Order Boundary Value Problems Using He's Polynomials

Directory of Open Access Journals (Sweden)

Muhammad Aslam Noor

2008-01-01

Full Text Available We apply the variational iteration method using He's polynomials (VIMHP for solving the fifth-order boundary value problems. The proposed method is an elegant combination of variational iteration and the homotopy perturbation methods and is mainly due to Ghorbani (2007. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.

Comment on “Variational Iteration Method for Fractional Calculus Using He’s Polynomials”

Directory of Open Access Journals (Sweden)

Ji-Huan He

2012-01-01

boundary value problems. This note concludes that the method is a modified variational iteration method using He’s polynomials. A standard variational iteration algorithm for fractional differential equations is suggested.

NUMERICAL WITHOUT ITERATION METHOD OF MODELING OF ELECTROMECHANICAL PROCESSES IN ASYNCHRONOUS ENGINES

Directory of Open Access Journals (Sweden)

D. G. Patalakh

2018-02-01

Full Text Available Purpose. Development of calculation of electromagnetic and electromechanic transients is in asynchronous engines without iterations. Methodology. Numeral methods of integration of usual differential equations, programming. Findings. As the system of equations, describing the dynamics of asynchronous engine, contents the products of rotor and stator currents and product of rotation frequency of rotor and currents, so this system is nonlinear one. The numeral solution of nonlinear differential equations supposes an iteration process on every step of integration. Time-continuing and badly converging iteration process may be the reason of calculation slowing. The improvement of numeral method by the way of an iteration process removing is offered. As result the modeling time is reduced. The improved numeral method is applied for integration of differential equations, describing the dynamics of asynchronous engine. Originality. The improvement of numeral method allowing to execute numeral integrations of differential equations containing product of functions is offered, that allows to avoid an iteration process on every step of integration and shorten modeling time. Practical value. On the basis of the offered methodology the universal program of modeling of electromechanics processes in asynchronous engines could be developed as taking advantage on fast-acting.

Pseudoinverse preconditioners and iterative methods for large dense linear least-squares problems

Directory of Open Access Journals (Sweden)

Oskar Cahueñas

2013-05-01

Full Text Available We address the issue of approximating the pseudoinverse of the coefficient matrix for dynamically building preconditioning strategies for the numerical solution of large dense linear least-squares problems. The new preconditioning strategies are embedded into simple and well-known iterative schemes that avoid the use of the, usually ill-conditioned, normal equations. We analyze a scheme to approximate the pseudoinverse, based on Schulz iterative method, and also different iterative schemes, based on extensions of Richardson's method, and the conjugate gradient method, that are suitable for preconditioning strategies. We present preliminary numerical results to illustrate the advantages of the proposed schemes.

On varitional iteration method for fractional calculus

Directory of Open Access Journals (Sweden)

Wu Hai-Gen

2017-01-01

Full Text Available Modification of the Das’ variational iteration method for fractional differential equations is discussed, and its main shortcoming involved in the solution process is pointed out and overcome by using fractional power series. The suggested computational procedure is simple and reliable for fractional calculus.

Beamforming using subspace estimation from a diagonally averaged sample covariance.

Science.gov (United States)

Quijano, Jorge E; Zurk, Lisa M

2017-08-01

The potential benefit of a large-aperture sonar array for high resolution target localization is often challenged by the lack of sufficient data required for adaptive beamforming. This paper introduces a Toeplitz-constrained estimator of the clairvoyant signal covariance matrix corresponding to multiple far-field targets embedded in background isotropic noise. The estimator is obtained by averaging along subdiagonals of the sample covariance matrix, followed by covariance extrapolation using the method of maximum entropy. The sample covariance is computed from limited data snapshots, a situation commonly encountered with large-aperture arrays in environments characterized by short periods of local stationarity. Eigenvectors computed from the Toeplitz-constrained covariance are used to construct signal-subspace projector matrices, which are shown to reduce background noise and improve detection of closely spaced targets when applied to subspace beamforming. Monte Carlo simulations corresponding to increasing array aperture suggest convergence of the proposed projector to the clairvoyant signal projector, thereby outperforming the classic projector obtained from the sample eigenvectors. Beamforming performance of the proposed method is analyzed using simulated data, as well as experimental data from the Shallow Water Array Performance experiment.

On iteration-separable method on the multichannel scattering theory

International Nuclear Information System (INIS)

Zubarev, A.L.; Ivlieva, I.N.; Podkopaev, A.P.

1975-01-01

The iteration-separable method for solving the equations of the Lippman-Schwinger type is suggested. Exponential convergency of the method of proven. Numerical convergency is clarified on the e + H scattering. Application of the method to the theory of multichannel scattering is formulated

Numerov iteration method for second order integral-differential equation

International Nuclear Information System (INIS)

Zeng Fanan; Zhang Jiaju; Zhao Xuan

1987-01-01

In this paper, Numerov iterative method for second order integral-differential equation and system of equations are constructed. Numerical examples show that this method is better than direct method (Gauss elimination method) in CPU time and memoy requireing. Therefore, this method is an efficient method for solving integral-differential equation in nuclear physics

Comparison results on preconditioned SOR-type iterative method for Z-matrices linear systems

Science.gov (United States)

Wang, Xue-Zhong; Huang, Ting-Zhu; Fu, Ying-Ding

2007-09-01

In this paper, we present some comparison theorems on preconditioned iterative method for solving Z-matrices linear systems, Comparison results show that the rate of convergence of the Gauss-Seidel-type method is faster than the rate of convergence of the SOR-type iterative method.

Discounted Markov games : generalized policy iteration method

NARCIS (Netherlands)

Wal, van der J.

1978-01-01

In this paper, we consider two-person zero-sum discounted Markov games with finite state and action spaces. We show that the Newton-Raphson or policy iteration method as presented by Pollats-chek and Avi-Itzhak does not necessarily converge, contradicting a proof of Rao, Chandrasekaran, and Nair.

Iterative method of the parameter variation for solution of nonlinear functional equations

International Nuclear Information System (INIS)

Davidenko, D.F.

1975-01-01

The iteration method of parameter variation is used for solving nonlinear functional equations in Banach spaces. The authors consider some methods for numerical integration of ordinary first-order differential equations and construct the relevant iteration methods of parameter variation, both one- and multifactor. They also discuss problems of mathematical substantiation of the method, study the conditions and rate of convergence, estimate the error. The paper considers the application of the method to specific functional equations

A generalized Schwinger boson mapping with a physical subspace

International Nuclear Information System (INIS)

Scholtz, F.G.; Geyer, H.B.

1988-01-01

We investigate the existence of a physical subspace for generalized Schwinger boson mappings of SO(2n+1) contains SO(2n) in view of previous observations by Marshalek and the recent construction of such a mapping and subspace for SO(8) by Kaup. It is shown that Kaup's construction can be attributed to the existence of a unique SO(8) automorphism. We proceed to construct a generalized Schwinger-type mapping for SO(2n+1) contains SO(2n) which, in contrast to a similar attempt by Yamamura and Nishiyama, indeed has a corresponding physical subspace. This new mapping includes in the special case of SO(8) the mapping by Kaup which is equivalent to the one given by Yamamura and Nishiyama for n=4. Nevertheless, we indicate the limitations of the generalized Schwinger mapping regarding its applicability to situations where one seeks to establish a direct link between phenomenological boson models and an underlying fermion microscopy. (orig.)

Optimized iterative decoding method for TPC coded CPM

Science.gov (United States)

Ma, Yanmin; Lai, Penghui; Wang, Shilian; Xie, Shunqin; Zhang, Wei

2018-05-01

Turbo Product Code (TPC) coded Continuous Phase Modulation (CPM) system (TPC-CPM) has been widely used in aeronautical telemetry and satellite communication. This paper mainly investigates the improvement and optimization on the TPC-CPM system. We first add the interleaver and deinterleaver to the TPC-CPM system, and then establish an iterative system to iteratively decode. However, the improved system has a poor convergence ability. To overcome this issue, we use the Extrinsic Information Transfer (EXIT) analysis to find the optimal factors for the system. The experiments show our method is efficient to improve the convergence performance.

Improved magnetic resonance fingerprinting reconstruction with low-rank and subspace modeling.

Science.gov (United States)

Zhao, Bo; Setsompop, Kawin; Adalsteinsson, Elfar; Gagoski, Borjan; Ye, Huihui; Ma, Dan; Jiang, Yun; Ellen Grant, P; Griswold, Mark A; Wald, Lawrence L

2018-02-01

This article introduces a constrained imaging method based on low-rank and subspace modeling to improve the accuracy and speed of MR fingerprinting (MRF). A new model-based imaging method is developed for MRF to reconstruct high-quality time-series images and accurate tissue parameter maps (e.g., T 1 , T 2 , and spin density maps). Specifically, the proposed method exploits low-rank approximations of MRF time-series images, and further enforces temporal subspace constraints to capture magnetization dynamics. This allows the time-series image reconstruction problem to be formulated as a simple linear least-squares problem, which enables efficient computation. After image reconstruction, tissue parameter maps are estimated via dictionary-based pattern matching, as in the conventional approach. The effectiveness of the proposed method was evaluated with in vivo experiments. Compared with the conventional MRF reconstruction, the proposed method reconstructs time-series images with significantly reduced aliasing artifacts and noise contamination. Although the conventional approach exhibits some robustness to these corruptions, the improved time-series image reconstruction in turn provides more accurate tissue parameter maps. The improvement is pronounced especially when the acquisition time becomes short. The proposed method significantly improves the accuracy of MRF, and also reduces data acquisition time. Magn Reson Med 79:933-942, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

An iterative method for determination of a minimal eigenvalue

DEFF Research Database (Denmark)

Kristiansen, G.K.

1968-01-01

Kristiansen (1963) has discussed the convergence of a group of iterative methods (denoted the Equipoise methods) for the solution of reactor criticality problems. The main result was that even though the methods are said to work satisfactorily in all practical cases, examples of divergence can be...

Iterative Equalization and Interference Alignment for Multiuser MIMO HetNets with Imperfect CSI

Directory of Open Access Journals (Sweden)

Daniel Castanheira

2015-01-01

Full Text Available In this paper we consider a scenario, where several small-cells work under the same coverage area and spectrum of a macrocell. The signals stemming from the small-cell (macrocell users if not carefully dealt with will generate harmful interference into the macrocell (small-cell. To tackle this problem interference alignment and iterative equalization techniques are considered. By using IA all interference generated by the small-cell (macrocell users is aligned along a low dimensional subspace, at the macrocell (small-cells. This reduces considerably the amount of resources allocated, to enable the coexistence of the two systems. However, perfect IA requires the availability of error-free channel state information (CSI at the transmitters. Due to CSI errors one can have substantial performance degradation due to imperfect alignments. Since in this work the IA precoders are based on imperfect CSI, an efficient iterative space-frequency equalization is designed at the receiver side to cope with the residual aligned interference. The results demonstrate that iterative equalization is robust to imperfect CSI and removes efficiently the interference generated by the poorly aligned interference. Close to matched filter bound performance is achieved, with a very few number of iterations.

Memory Efficient PCA Methods for Large Group ICA.

Science.gov (United States)

Rachakonda, Srinivas; Silva, Rogers F; Liu, Jingyu; Calhoun, Vince D

2016-01-01

Principal component analysis (PCA) is widely used for data reduction in group independent component analysis (ICA) of fMRI data. Commonly, group-level PCA of temporally concatenated datasets is computed prior to ICA of the group principal components. This work focuses on reducing very high dimensional temporally concatenated datasets into its group PCA space. Existing randomized PCA methods can determine the PCA subspace with minimal memory requirements and, thus, are ideal for solving large PCA problems. Since the number of dataloads is not typically optimized, we extend one of these methods to compute PCA of very large datasets with a minimal number of dataloads. This method is coined multi power iteration (MPOWIT). The key idea behind MPOWIT is to estimate a subspace larger than the desired one, while checking for convergence of only the smaller subset of interest. The number of iterations is reduced considerably (as well as the number of dataloads), accelerating convergence without loss of accuracy. More importantly, in the proposed implementation of MPOWIT, the memory required for successful recovery of the group principal components becomes independent of the number of subjects analyzed. Highly efficient subsampled eigenvalue decomposition techniques are also introduced, furnishing excellent PCA subspace approximations that can be used for intelligent initialization of randomized methods such as MPOWIT. Together, these developments enable efficient estimation of accurate principal components, as we illustrate by solving a 1600-subject group-level PCA of fMRI with standard acquisition parameters, on a regular desktop computer with only 4 GB RAM, in just a few hours. MPOWIT is also highly scalable and could realistically solve group-level PCA of fMRI on thousands of subjects, or more, using standard hardware, limited only by time, not memory. Also, the MPOWIT algorithm is highly parallelizable, which would enable fast, distributed implementations ideal for big

Memory efficient PCA methods for large group ICA

Directory of Open Access Journals (Sweden)

Srinivas eRachakonda

2016-02-01

Full Text Available Principal component analysis (PCA is widely used for data reduction in group independent component analysis (ICA of fMRI data. Commonly, group-level PCA of temporally concatenated datasets is computed prior to ICA of the group principal components. This work focuses on reducing very high dimensional temporally concatenated datasets into its group PCA space. Existing randomized PCA methods can determine the PCA subspace with minimal memory requirements and, thus, are ideal for solving large PCA problems. Since the number of dataloads is not typically optimized, we extend one of these methods to compute PCA of very large datasets with a minimal number of dataloads. This method is coined multi power iteration (MPOWIT. The key idea behind MPOWIT is to estimate a subspace larger than the desired one, while checking for convergence of only the smaller subset of interest. The number of iterations is reduced considerably (as well as the number of dataloads, accelerating convergence without loss of accuracy. More importantly, in the proposed implementation of MPOWIT, the memory required for successful recovery of the group principal components becomes independent of the number of subjects analyzed. Highly efficient subsampled eigenvalue decomposition techniques are also introduced, furnishing excellent PCA subspace approximations that can be used for intelligent initialization of randomized methods such as MPOWIT. Together, these developments enable efficient estimation of accurate principal components, as we illustrate by solving a 1600-subject group-level PCA of fMRI with standard acquisition parameters, on a regular desktop computer with only 4GB RAM, in just a few hours. MPOWIT is also highly scalable and could realistically solve group-level PCA of fMRI on thousands of subjects, or more, using standard hardware, limited only by time, not memory. Also, the MPOWIT algorithm is highly parallelizable, which would enable fast, distributed implementations

Ensemble Kalman methods for inverse problems

International Nuclear Information System (INIS)

Iglesias, Marco A; Law, Kody J H; Stuart, Andrew M

2013-01-01

The ensemble Kalman filter (EnKF) was introduced by Evensen in 1994 (Evensen 1994 J. Geophys. Res. 99 10143–62) as a novel method for data assimilation: state estimation for noisily observed time-dependent problems. Since that time it has had enormous impact in many application domains because of its robustness and ease of implementation, and numerical evidence of its accuracy. In this paper we propose the application of an iterative ensemble Kalman method for the solution of a wide class of inverse problems. In this context we show that the estimate of the unknown function that we obtain with the ensemble Kalman method lies in a subspace A spanned by the initial ensemble. Hence the resulting error may be bounded above by the error found from the best approximation in this subspace. We provide numerical experiments which compare the error incurred by the ensemble Kalman method for inverse problems with the error of the best approximation in A, and with variants on traditional least-squares approaches, restricted to the subspace A. In so doing we demonstrate that the ensemble Kalman method for inverse problems provides a derivative-free optimization method with comparable accuracy to that achieved by traditional least-squares approaches. Furthermore, we also demonstrate that the accuracy is of the same order of magnitude as that achieved by the best approximation. Three examples are used to demonstrate these assertions: inversion of a compact linear operator; inversion of piezometric head to determine hydraulic conductivity in a Darcy model of groundwater flow; and inversion of Eulerian velocity measurements at positive times to determine the initial condition in an incompressible fluid. (paper)

Projection-iteration methods for solving nonlinear operator equations

International Nuclear Information System (INIS)

Nguyen Minh Chuong; Tran thi Lan Anh; Tran Quoc Binh

1989-09-01

In this paper, the authors investigate a nonlinear operator equation in uniformly convex Banach spaces as in metric spaces by using stationary and nonstationary generalized projection-iteration methods. Convergence theorems in the strong and weak sense were established. (author). 7 refs

Different structures on subspaces of OsckM

Directory of Open Access Journals (Sweden)

Čomić Irena

2013-01-01

Full Text Available The geometry of OsckM spaces was introduced by R. Miron and Gh. Atanasiu in [6] and [7]. The theory of these spaces was developed by R. Miron and his cooperators from Romania, Japan and other countries in several books and many papers. Only some of them are mentioned in references. Here we recall the construction of adapted bases in T(OsckM and T*(OsckM, which are comprehensive with the J structure. The theory of two complementary family of subspaces is presented as it was done in [2] and [4]. The operators J,J, θ,θ, p, p* are introduced in the ambient space and subspaces. Some new relations between them are established. The action of these operators on Liouville vector fields are examined.

Accelerating Inexact Newton Schemes for Large Systems of Nonlinear Equations

NARCIS (Netherlands)

Fokkema, D.R.; Sleijpen, G.L.G.; Vorst, H.A. van der

Classical iteration methods for linear systems, such as Jacobi iteration, can be accelerated considerably by Krylov subspace methods like GMRES. In this paper, we describe how inexact Newton methods for nonlinear problems can be accelerated in a similar way and how this leads to a general

Excluding Noise from Short Krylov Subspace Approximations to the Truncated Singular Value Decomposition (SVD)

Science.gov (United States)

2017-09-27

100 times larger for the minimal Krylov subspace. 0 5 10 15 20 25 Krylov subspace dimension 10-2 10-1 100 101 102 103 104 jjĜ ¡ 1 jj F SVD...approximation Kn (G;u(0) ) 0 5 10 15 20 25 Krylov subspace dimension 10-2 10-1 100 101 102 103 104 jjx jj fo r m in x jjĜ x ¡ bjj SVD approximation Kn (G;u(0

Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions

Directory of Open Access Journals (Sweden)

Yuan Li

2013-01-01

Full Text Available This paper presents two-level iteration penalty finite element methods to approximate the solution of the Navier-Stokes equations with friction boundary conditions. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size H in combining with solving a Stokes, Oseen, or linearized Navier-Stokes type variational inequality problem for Stokes, Oseen, or Newton iteration on a fine mesh with mesh size h. The error estimate obtained in this paper shows that if H, h, and ε can be chosen appropriately, then these two-level iteration penalty methods are of the same convergence orders as the usual one-level iteration penalty method.

Krylov iterative methods and synthetic acceleration for transport in binary statistical media

International Nuclear Information System (INIS)

Fichtl, Erin D.; Warsa, James S.; Prinja, Anil K.

2009-01-01

In particle transport applications there are numerous physical constructs in which heterogeneities are randomly distributed. The quantity of interest in these problems is the ensemble average of the flux, or the average of the flux over all possible material 'realizations.' The Levermore-Pomraning closure assumes Markovian mixing statistics and allows a closed, coupled system of equations to be written for the ensemble averages of the flux in each material. Generally, binary statistical mixtures are considered in which there are two (homogeneous) materials and corresponding coupled equations. The solution process is iterative, but convergence may be slow as either or both materials approach the diffusion and/or atomic mix limits. A three-part acceleration scheme is devised to expedite convergence, particularly in the atomic mix-diffusion limit where computation is extremely slow. The iteration is first divided into a series of 'inner' material and source iterations to attenuate the diffusion and atomic mix error modes separately. Secondly, atomic mix synthetic acceleration is applied to the inner material iteration and S 2 synthetic acceleration to the inner source iterations to offset the cost of doing several inner iterations per outer iteration. Finally, a Krylov iterative solver is wrapped around each iteration, inner and outer, to further expedite convergence. A spectral analysis is conducted and iteration counts and computing cost for the new two-step scheme are compared against those for a simple one-step iteration, to which a Krylov iterative method can also be applied.

Adaptive Mesh Iteration Method for Trajectory Optimization Based on Hermite-Pseudospectral Direct Transcription

Directory of Open Access Journals (Sweden)

Humin Lei

2017-01-01

Full Text Available An adaptive mesh iteration method based on Hermite-Pseudospectral is described for trajectory optimization. The method uses the Legendre-Gauss-Lobatto points as interpolation points; then the state equations are approximated by Hermite interpolating polynomials. The method allows for changes in both number of mesh points and the number of mesh intervals and produces significantly smaller mesh sizes with a higher accuracy tolerance solution. The derived relative error estimate is then used to trade the number of mesh points with the number of mesh intervals. The adaptive mesh iteration method is applied successfully to the examples of trajectory optimization of Maneuverable Reentry Research Vehicle, and the simulation experiment results show that the adaptive mesh iteration method has many advantages.

Iterative and range test methods for an inverse source problem for acoustic waves

International Nuclear Information System (INIS)

Alves, Carlos; Kress, Rainer; Serranho, Pedro

2009-01-01

We propose two methods for solving an inverse source problem for time-harmonic acoustic waves. Based on the reciprocity gap principle a nonlinear equation is presented for the locations and intensities of the point sources that can be solved via Newton iterations. To provide an initial guess for this iteration we suggest a range test algorithm for approximating the source locations. We give a mathematical foundation for the range test and exhibit its feasibility in connection with the iteration method by some numerical examples

Variable aperture-based ptychographical iterative engine method

Science.gov (United States)

Sun, Aihui; Kong, Yan; Meng, Xin; He, Xiaoliang; Du, Ruijun; Jiang, Zhilong; Liu, Fei; Xue, Liang; Wang, Shouyu; Liu, Cheng

2018-02-01

A variable aperture-based ptychographical iterative engine (vaPIE) is demonstrated both numerically and experimentally to reconstruct the sample phase and amplitude rapidly. By adjusting the size of a tiny aperture under the illumination of a parallel light beam to change the illumination on the sample step by step and recording the corresponding diffraction patterns sequentially, both the sample phase and amplitude can be faithfully reconstructed with a modified ptychographical iterative engine (PIE) algorithm. Since many fewer diffraction patterns are required than in common PIE and the shape, the size, and the position of the aperture need not to be known exactly, this proposed vaPIE method remarkably reduces the data acquisition time and makes PIE less dependent on the mechanical accuracy of the translation stage; therefore, the proposed technique can be potentially applied for various scientific researches.

Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients

KAUST Repository

Gao, Longfei; Calo, Victor M.

2015-01-01

In this paper, we combine the Alternating Direction Implicit (ADI) algorithm with the concept of preconditioning and apply it to linear systems discretized from the 2D steady-state diffusion equations with orthotropic heterogeneous coefficients by the finite element method assuming tensor product basis functions. Specifically, we adopt the compound iteration idea and use ADI iterations as the preconditioner for the outside Krylov subspace method that is used to solve the preconditioned linear system. An efficient algorithm to perform each ADI iteration is crucial to the efficiency of the overall iterative scheme. We exploit the Kronecker product structure in the matrices, inherited from the tensor product basis functions, to achieve high efficiency in each ADI iteration. Meanwhile, in order to reduce the number of Krylov subspace iterations, we incorporate partially the coefficient information into the preconditioner by exploiting the local support property of the finite element basis functions. Numerical results demonstrated the efficiency and quality of the proposed preconditioner. © 2014 Elsevier B.V. All rights reserved.

Subspace Arrangement Codes and Cryptosystems

Science.gov (United States)

2011-05-09

Signature Date Acceptance for the Trident Scholar Committee Professor Carl E. Wick Associate Director of Midshipmen Research Signature Date SUBSPACE...Professor William Traves. I also thank Professor Carl Wick and the Trident Scholar Committee for providing me with the opportunity to conduct this... Sagan . Why the characteristic polynomial factors. Bulletin of the American Mathematical Society, 36(2):113–133, February 1999. [16] Karen E. Smith

Iterative methods for tomography problems: implementation to a cross-well tomography problem

Science.gov (United States)

Karadeniz, M. F.; Weber, G. W.

2018-01-01

The velocity distribution between two boreholes is reconstructed by cross-well tomography, which is commonly used in geology. In this paper, iterative methods, Kaczmarz’s algorithm, algebraic reconstruction technique (ART), and simultaneous iterative reconstruction technique (SIRT), are implemented to a specific cross-well tomography problem. Convergence to the solution of these methods and their CPU time for the cross-well tomography problem are compared. Furthermore, these three methods for this problem are compared for different tolerance values.

Backtracking-Based Iterative Regularization Method for Image Compressive Sensing Recovery

Directory of Open Access Journals (Sweden)

Lingjun Liu

2017-01-01

Full Text Available This paper presents a variant of the iterative shrinkage-thresholding (IST algorithm, called backtracking-based adaptive IST (BAIST, for image compressive sensing (CS reconstruction. For increasing iterations, IST usually yields a smoothing of the solution and runs into prematurity. To add back more details, the BAIST method backtracks to the previous noisy image using L2 norm minimization, i.e., minimizing the Euclidean distance between the current solution and the previous ones. Through this modification, the BAIST method achieves superior performance while maintaining the low complexity of IST-type methods. Also, BAIST takes a nonlocal regularization with an adaptive regularizor to automatically detect the sparsity level of an image. Experimental results show that our algorithm outperforms the original IST method and several excellent CS techniques.

Linear Subspace Ranking Hashing for Cross-Modal Retrieval.

Science.gov (United States)

Li, Kai; Qi, Guo-Jun; Ye, Jun; Hua, Kien A

2017-09-01

Hashing has attracted a great deal of research in recent years due to its effectiveness for the retrieval and indexing of large-scale high-dimensional multimedia data. In this paper, we propose a novel ranking-based hashing framework that maps data from different modalities into a common Hamming space where the cross-modal similarity can be measured using Hamming distance. Unlike existing cross-modal hashing algorithms where the learned hash functions are binary space partitioning functions, such as the sign and threshold function, the proposed hashing scheme takes advantage of a new class of hash functions closely related to rank correlation measures which are known to be scale-invariant, numerically stable, and highly nonlinear. Specifically, we jointly learn two groups of linear subspaces, one for each modality, so that features' ranking orders in different linear subspaces maximally preserve the cross-modal similarities. We show that the ranking-based hash function has a natural probabilistic approximation which transforms the original highly discontinuous optimization problem into one that can be efficiently solved using simple gradient descent algorithms. The proposed hashing framework is also flexible in the sense that the optimization procedures are not tied up to any specific form of loss function, which is typical for existing cross-modal hashing methods, but rather we can flexibly accommodate different loss functions with minimal changes to the learning steps. We demonstrate through extensive experiments on four widely-used real-world multimodal datasets that the proposed cross-modal hashing method can achieve competitive performance against several state-of-the-arts with only moderate training and testing time.

Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

Directory of Open Access Journals (Sweden)

Ai-Min Yang

2014-01-01

Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

Iterated interactions method. Realistic NN potential

International Nuclear Information System (INIS)

Gorbatov, A.M.; Skopich, V.L.; Kolganova, E.A.

1991-01-01

The method of iterated potential is tested in the case of realistic fermionic systems. As a base for comparison calculations of the 16 O system (using various versions of realistic NN potentials) by means of the angular potential-function method as well as operators of pairing correlation were used. The convergence of genealogical series is studied for the central Malfliet-Tjon potential. In addition the mathematical technique of microscopical calculations is improved: new equations for correlators in odd states are suggested and the technique of leading terms was applied for the first time to calculations of heavy p-shell nuclei in the basis of angular potential functions

Solution of Nonlinear Partial Differential Equations by New Laplace Variational Iteration Method

Directory of Open Access Journals (Sweden)

Eman M. A. Hilal

2014-01-01

Full Text Available The aim of this study is to give a good strategy for solving some linear and nonlinear partial differential equations in engineering and physics fields, by combining Laplace transform and the modified variational iteration method. This method is based on the variational iteration method, Laplace transforms, and convolution integral, introducing an alternative Laplace correction functional and expressing the integral as a convolution. Some examples in physical engineering are provided to illustrate the simplicity and reliability of this method. The solutions of these examples are contingent only on the initial conditions.

An Automated Baseline Correction Method Based on Iterative Morphological Operations.

Science.gov (United States)

Chen, Yunliang; Dai, Liankui

2018-05-01

Raman spectra usually suffer from baseline drift caused by fluorescence or other reasons. Therefore, baseline correction is a necessary and crucial step that must be performed before subsequent processing and analysis of Raman spectra. An automated baseline correction method based on iterative morphological operations is proposed in this work. The method can adaptively determine the structuring element first and then gradually remove the spectral peaks during iteration to get an estimated baseline. Experiments on simulated data and real-world Raman data show that the proposed method is accurate, fast, and flexible for handling different kinds of baselines in various practical situations. The comparison of the proposed method with some state-of-the-art baseline correction methods demonstrates its advantages over the existing methods in terms of accuracy, adaptability, and flexibility. Although only Raman spectra are investigated in this paper, the proposed method is hopefully to be used for the baseline correction of other analytical instrumental signals, such as IR spectra and chromatograms.

Three dimensional iterative beam propagation method for optical waveguide devices

Science.gov (United States)

Ma, Changbao; Van Keuren, Edward

2006-10-01

The finite difference beam propagation method (FD-BPM) is an effective model for simulating a wide range of optical waveguide structures. The classical FD-BPMs are based on the Crank-Nicholson scheme, and in tridiagonal form can be solved using the Thomas method. We present a different type of algorithm for 3-D structures. In this algorithm, the wave equation is formulated into a large sparse matrix equation which can be solved using iterative methods. The simulation window shifting scheme and threshold technique introduced in our earlier work are utilized to overcome the convergence problem of iterative methods for large sparse matrix equation and wide-angle simulations. This method enables us to develop higher-order 3-D wide-angle (WA-) BPMs based on Pade approximant operators and the multistep method, which are commonly used in WA-BPMs for 2-D structures. Simulations using the new methods will be compared to the analytical results to assure its effectiveness and applicability.

Variation Iteration Method for The Approximate Solution of Nonlinear ...

African Journals Online (AJOL)

In this study, we considered the numerical solution of the nonlinear Burgers equation using the Variational Iteration Method (VIM). The method seeks to examine the convergence of solutions of the Burgers equation at the expense of the parameters x and t of which the amount of errors depends. Numerical experimentation ...

Lyapunov vectors and assimilation in the unstable subspace: theory and applications

International Nuclear Information System (INIS)

Palatella, Luigi; Carrassi, Alberto; Trevisan, Anna

2013-01-01

Based on a limited number of noisy observations, estimation algorithms provide a complete description of the state of a system at current time. Estimation algorithms that go under the name of assimilation in the unstable subspace (AUS) exploit the nonlinear stability properties of the forecasting model in their formulation. Errors that grow due to sensitivity to initial conditions are efficiently removed by confining the analysis solution in the unstable and neutral subspace of the system, the subspace spanned by Lyapunov vectors with positive and zero exponents, while the observational noise does not disturb the system along the stable directions. The formulation of the AUS approach in the context of four-dimensional variational assimilation (4DVar-AUS) and the extended Kalman filter (EKF-AUS) and its application to chaotic models is reviewed. In both instances, the AUS algorithms are at least as efficient but simpler to implement and computationally less demanding than their original counterparts. As predicted by the theory when error dynamics is linear, the optimal subspace dimension for 4DVar-AUS is given by the number of positive and null Lyapunov exponents, while the EKF-AUS algorithm, using the same unstable and neutral subspace, recovers the solution of the full EKF algorithm, but dealing with error covariance matrices of a much smaller dimension and significantly reducing the computational burden. Examples of the application to a simplified model of the atmospheric circulation and to the optimal velocity model for traffic dynamics are given. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces

Directory of Open Access Journals (Sweden)

Rabian Wangkeeree

2012-01-01

Full Text Available We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.

SU-D-206-03: Segmentation Assisted Fast Iterative Reconstruction Method for Cone-Beam CT

International Nuclear Information System (INIS)

Wu, P; Mao, T; Gong, S; Wang, J; Niu, T; Sheng, K; Xie, Y

2016-01-01

Purpose: Total Variation (TV) based iterative reconstruction (IR) methods enable accurate CT image reconstruction from low-dose measurements with sparse projection acquisition, due to the sparsifiable feature of most CT images using gradient operator. However, conventional solutions require large amount of iterations to generate a decent reconstructed image. One major reason is that the expected piecewise constant property is not taken into consideration at the optimization starting point. In this work, we propose an iterative reconstruction method for cone-beam CT (CBCT) using image segmentation to guide the optimization path more efficiently on the regularization term at the beginning of the optimization trajectory. Methods: Our method applies general knowledge that one tissue component in the CT image contains relatively uniform distribution of CT number. This general knowledge is incorporated into the proposed reconstruction using image segmentation technique to generate the piecewise constant template on the first-pass low-quality CT image reconstructed using analytical algorithm. The template image is applied as an initial value into the optimization process. Results: The proposed method is evaluated on the Shepp-Logan phantom of low and high noise levels, and a head patient. The number of iterations is reduced by overall 40%. Moreover, our proposed method tends to generate a smoother reconstructed image with the same TV value. Conclusion: We propose a computationally efficient iterative reconstruction method for CBCT imaging. Our method achieves a better optimization trajectory and a faster convergence behavior. It does not rely on prior information and can be readily incorporated into existing iterative reconstruction framework. Our method is thus practical and attractive as a general solution to CBCT iterative reconstruction. This work is supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LR16F010001), National High-tech R

SU-D-206-03: Segmentation Assisted Fast Iterative Reconstruction Method for Cone-Beam CT

Energy Technology Data Exchange (ETDEWEB)

Wu, P; Mao, T; Gong, S; Wang, J; Niu, T [Sir Run Run Shaw Hospital, Zhejiang University School of Medicine, Institute of Translational Medicine, Zhejiang University, Hangzhou, Zhejiang (China); Sheng, K [Department of Radiation Oncology, University of California, Los Angeles, Los Angeles, CA (United States); Xie, Y [Institute of Biomedical and Health Engineering, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, Guangdong (China)

2016-06-15

Purpose: Total Variation (TV) based iterative reconstruction (IR) methods enable accurate CT image reconstruction from low-dose measurements with sparse projection acquisition, due to the sparsifiable feature of most CT images using gradient operator. However, conventional solutions require large amount of iterations to generate a decent reconstructed image. One major reason is that the expected piecewise constant property is not taken into consideration at the optimization starting point. In this work, we propose an iterative reconstruction method for cone-beam CT (CBCT) using image segmentation to guide the optimization path more efficiently on the regularization term at the beginning of the optimization trajectory. Methods: Our method applies general knowledge that one tissue component in the CT image contains relatively uniform distribution of CT number. This general knowledge is incorporated into the proposed reconstruction using image segmentation technique to generate the piecewise constant template on the first-pass low-quality CT image reconstructed using analytical algorithm. The template image is applied as an initial value into the optimization process. Results: The proposed method is evaluated on the Shepp-Logan phantom of low and high noise levels, and a head patient. The number of iterations is reduced by overall 40%. Moreover, our proposed method tends to generate a smoother reconstructed image with the same TV value. Conclusion: We propose a computationally efficient iterative reconstruction method for CBCT imaging. Our method achieves a better optimization trajectory and a faster convergence behavior. It does not rely on prior information and can be readily incorporated into existing iterative reconstruction framework. Our method is thus practical and attractive as a general solution to CBCT iterative reconstruction. This work is supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LR16F010001), National High-tech R

Variable aperture-based ptychographical iterative engine method.

Science.gov (United States)

Sun, Aihui; Kong, Yan; Meng, Xin; He, Xiaoliang; Du, Ruijun; Jiang, Zhilong; Liu, Fei; Xue, Liang; Wang, Shouyu; Liu, Cheng

2018-02-01

A variable aperture-based ptychographical iterative engine (vaPIE) is demonstrated both numerically and experimentally to reconstruct the sample phase and amplitude rapidly. By adjusting the size of a tiny aperture under the illumination of a parallel light beam to change the illumination on the sample step by step and recording the corresponding diffraction patterns sequentially, both the sample phase and amplitude can be faithfully reconstructed with a modified ptychographical iterative engine (PIE) algorithm. Since many fewer diffraction patterns are required than in common PIE and the shape, the size, and the position of the aperture need not to be known exactly, this proposed vaPIE method remarkably reduces the data acquisition time and makes PIE less dependent on the mechanical accuracy of the translation stage; therefore, the proposed technique can be potentially applied for various scientific researches. (2018) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

Subspace-based Inverse Uncertainty Quantification for Nuclear Data Assessment

Energy Technology Data Exchange (ETDEWEB)

Khuwaileh, B.A., E-mail: bakhuwai@ncsu.edu; Abdel-Khalik, H.S.

2015-01-15

Safety analysis and design optimization depend on the accurate prediction of various reactor attributes. Predictions can be enhanced by reducing the uncertainty associated with the attributes of interest. An inverse problem can be defined and solved to assess the sources of uncertainty, and experimental effort can be subsequently directed to further improve the uncertainty associated with these sources. In this work a subspace-based algorithm for inverse sensitivity/uncertainty quantification (IS/UQ) has been developed to enable analysts account for all sources of nuclear data uncertainties in support of target accuracy assessment-type analysis. An approximate analytical solution of the optimization problem is used to guide the search for the dominant uncertainty subspace. By limiting the search to a subspace, the degrees of freedom available for the optimization search are significantly reduced. A quarter PWR fuel assembly is modeled and the accuracy of the multiplication factor and the fission reaction rate are used as reactor attributes whose uncertainties are to be reduced. Numerical experiments are used to demonstrate the computational efficiency of the proposed algorithm. Our ongoing work is focusing on extending the proposed algorithm to account for various forms of feedback, e.g., thermal-hydraulics and depletion effects.

A New Iterative Method for Equilibrium Problems and Fixed Point Problems

Directory of Open Access Journals (Sweden)

Abdul Latif

2013-01-01

Full Text Available Introducing a new iterative method, we study the existence of a common element of the set of solutions of equilibrium problems for a family of monotone, Lipschitz-type continuous mappings and the sets of fixed points of two nonexpansive semigroups in a real Hilbert space. We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. Our results improve and generalize the corresponding recent results of Anh (2012, Cianciaruso et al. (2010, and many others.

Counting Subspaces of a Finite Vector Space

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 15; Issue 11. Counting Subspaces of a Finite Vector Space – 1. Amritanshu Prasad. General Article Volume 15 Issue 11 November 2010 pp 977-987. Fulltext. Click here to view fulltext PDF. Permanent link:

Combining the CORS and BiCORSTAB Iterative Methods with MLFMA and SAI Preconditioning for Solving Large Linear Systems in Electromagnetics

NARCIS (Netherlands)

Carpentieri, Bruno; Jing, Yan-Fei; Huang, Ting-Zhu; Pi, Wei-Chao; Sheng, Xin-Qing

We report on experiments with a novel family of Krylov subspace methods for solving dense, complex, non-Hermitian systems of linear equations arising from the Galerkin discretization of surface integral equation models in Electromagnetics. By some experiments on realistic radar-cross-section

Parallel computation of multigroup reactivity coefficient using iterative method

Science.gov (United States)

Susmikanti, Mike; Dewayatna, Winter

2013-09-01

One of the research activities to support the commercial radioisotope production program is a safety research target irradiation FPM (Fission Product Molybdenum). FPM targets form a tube made of stainless steel in which the nuclear degrees of superimposed high-enriched uranium. FPM irradiation tube is intended to obtain fission. The fission material widely used in the form of kits in the world of nuclear medicine. Irradiation FPM tube reactor core would interfere with performance. One of the disorders comes from changes in flux or reactivity. It is necessary to study a method for calculating safety terrace ongoing configuration changes during the life of the reactor, making the code faster became an absolute necessity. Neutron safety margin for the research reactor can be reused without modification to the calculation of the reactivity of the reactor, so that is an advantage of using perturbation method. The criticality and flux in multigroup diffusion model was calculate at various irradiation positions in some uranium content. This model has a complex computation. Several parallel algorithms with iterative method have been developed for the sparse and big matrix solution. The Black-Red Gauss Seidel Iteration and the power iteration parallel method can be used to solve multigroup diffusion equation system and calculated the criticality and reactivity coeficient. This research was developed code for reactivity calculation which used one of safety analysis with parallel processing. It can be done more quickly and efficiently by utilizing the parallel processing in the multicore computer. This code was applied for the safety limits calculation of irradiated targets FPM with increment Uranium.

On Optimal Short Recurrences for Generating Orthogonal Krylov Subspace Bases. Dedicated to Gene Golub

Czech Academy of Sciences Publication Activity Database

Liesen, J.; Strakoš, Zdeněk

2008-01-01

Roč. 50, č. 3 (2008), s. 485-503 ISSN 0036-1445 R&D Projects: GA AV ČR 1ET400300415; GA AV ČR IAA100300802 Institutional research plan: CEZ:AV0Z10300504 Keywords : Krylov subspace methods * orthogonal bases * short reccurences * conjugate gradient -like methods Subject RIV: IN - Informatics, Computer Science Impact factor: 2.739, year: 2008

Comments on new iterative methods for solving linear systems

Directory of Open Access Journals (Sweden)

Wang Ke

2017-06-01

Full Text Available Some new iterative methods were presented by Du, Zheng and Wang for solving linear systems in [3], where it is shown that the new methods, comparing to the classical Jacobi or Gauss-Seidel method, can be applied to more systems and have faster convergence. This note shows that their methods are suitable for more matrices than positive matrices which the authors suggested through further analysis and numerical examples.

A fast method to emulate an iterative POCS image reconstruction algorithm.

Science.gov (United States)

Zeng, Gengsheng L

2017-10-01

Iterative image reconstruction algorithms are commonly used to optimize an objective function, especially when the objective function is nonquadratic. Generally speaking, the iterative algorithms are computationally inefficient. This paper presents a fast algorithm that has one backprojection and no forward projection. This paper derives a new method to solve an optimization problem. The nonquadratic constraint, for example, an edge-preserving denoising constraint is implemented as a nonlinear filter. The algorithm is derived based on the POCS (projections onto projections onto convex sets) approach. A windowed FBP (filtered backprojection) algorithm enforces the data fidelity. An iterative procedure, divided into segments, enforces edge-enhancement denoising. Each segment performs nonlinear filtering. The derived iterative algorithm is computationally efficient. It contains only one backprojection and no forward projection. Low-dose CT data are used for algorithm feasibility studies. The nonlinearity is implemented as an edge-enhancing noise-smoothing filter. The patient studies results demonstrate its effectiveness in processing low-dose x ray CT data. This fast algorithm can be used to replace many iterative algorithms. © 2017 American Association of Physicists in Medicine.

Application of the perturbation iteration method to boundary layer type problems.

Science.gov (United States)

Pakdemirli, Mehmet

2016-01-01

The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution technique. The inner and outer solutions are determined with the iteration algorithm and matched to construct a composite expansion valid within all parts of the domain. The solutions are contrasted with the available exact or numerical solutions. It is shown that the perturbation-iteration algorithm can be effectively used for solving boundary layer type problems.

Iterative Methods for the Non-LTE Transfer of Polarized Radiation: Resonance Line Polarization in One-dimensional Atmospheres

Science.gov (United States)

Trujillo Bueno, Javier; Manso Sainz, Rafael

1999-05-01

This paper shows how to generalize to non-LTE polarization transfer some operator splitting methods that were originally developed for solving unpolarized transfer problems. These are the Jacobi-based accelerated Λ-iteration (ALI) method of Olson, Auer, & Buchler and the iterative schemes based on Gauss-Seidel and successive overrelaxation (SOR) iteration of Trujillo Bueno and Fabiani Bendicho. The theoretical framework chosen for the formulation of polarization transfer problems is the quantum electrodynamics (QED) theory of Landi Degl'Innocenti, which specifies the excitation state of the atoms in terms of the irreducible tensor components of the atomic density matrix. This first paper establishes the grounds of our numerical approach to non-LTE polarization transfer by concentrating on the standard case of scattering line polarization in a gas of two-level atoms, including the Hanle effect due to a weak microturbulent and isotropic magnetic field. We begin demonstrating that the well-known Λ-iteration method leads to the self-consistent solution of this type of problem if one initializes using the ``exact'' solution corresponding to the unpolarized case. We show then how the above-mentioned splitting methods can be easily derived from this simple Λ-iteration scheme. We show that our SOR method is 10 times faster than the Jacobi-based ALI method, while our implementation of the Gauss-Seidel method is 4 times faster. These iterative schemes lead to the self-consistent solution independently of the chosen initialization. The convergence rate of these iterative methods is very high; they do not require either the construction or the inversion of any matrix, and the computing time per iteration is similar to that of the Λ-iteration method.

Robust Switching Control and Subspace Identification for Flutter of Flexible Wing

Directory of Open Access Journals (Sweden)

Yizhe Wang

2018-01-01

Full Text Available Active flutter suppression and subspace identification for a flexible wing model using micro fiber composite actuator were experimentally studied in a low speed wind tunnel. NACA0006 thin airfoil model was used for the experimental object to verify the performance of identification algorithm and designed controller. The equation of the fluid, vibration, and piezoelectric coupled motion was theoretically analyzed and experimentally identified under the open-loop and closed-loop condition by subspace method for controller design. A robust pole placement algorithm in terms of linear matrix inequality that accommodates the model uncertainty caused by identification deviation and flow speed variation was utilized to stabilize the divergent aeroelastic system. For further enlarging the flutter envelope, additional controllers were designed subject to the models beyond the flutter speed. Wind speed was measured online as the decision parameter of switching between the controllers. To ensure the stability of arbitrary switching, Common Lyapunov function method was applied to design the robust pole placement controllers for different models to ensure that the closed-loop system shared a common Lyapunov function. Wind tunnel result showed that the designed controllers could stabilize the time varying aeroelastic system over a wide range under arbitrary switching.

An Improved EMD-Based Dissimilarity Metric for Unsupervised Linear Subspace Learning

Directory of Open Access Journals (Sweden)

Xiangchun Yu

2018-01-01

Full Text Available We investigate a novel way of robust face image feature extraction by adopting the methods based on Unsupervised Linear Subspace Learning to extract a small number of good features. Firstly, the face image is divided into blocks with the specified size, and then we propose and extract pooled Histogram of Oriented Gradient (pHOG over each block. Secondly, an improved Earth Mover’s Distance (EMD metric is adopted to measure the dissimilarity between blocks of one face image and the corresponding blocks from the rest of face images. Thirdly, considering the limitations of the original Locality Preserving Projections (LPP, we proposed the Block Structure LPP (BSLPP, which effectively preserves the structural information of face images. Finally, an adjacency graph is constructed and a small number of good features of a face image are obtained by methods based on Unsupervised Linear Subspace Learning. A series of experiments have been conducted on several well-known face databases to evaluate the effectiveness of the proposed algorithm. In addition, we construct the noise, geometric distortion, slight translation, slight rotation AR, and Extended Yale B face databases, and we verify the robustness of the proposed algorithm when faced with a certain degree of these disturbances.

View subspaces for indexing and retrieval of 3D models

Science.gov (United States)

Dutagaci, Helin; Godil, Afzal; Sankur, Bülent; Yemez, Yücel

2010-02-01

View-based indexing schemes for 3D object retrieval are gaining popularity since they provide good retrieval results. These schemes are coherent with the theory that humans recognize objects based on their 2D appearances. The viewbased techniques also allow users to search with various queries such as binary images, range images and even 2D sketches. The previous view-based techniques use classical 2D shape descriptors such as Fourier invariants, Zernike moments, Scale Invariant Feature Transform-based local features and 2D Digital Fourier Transform coefficients. These methods describe each object independent of others. In this work, we explore data driven subspace models, such as Principal Component Analysis, Independent Component Analysis and Nonnegative Matrix Factorization to describe the shape information of the views. We treat the depth images obtained from various points of the view sphere as 2D intensity images and train a subspace to extract the inherent structure of the views within a database. We also show the benefit of categorizing shapes according to their eigenvalue spread. Both the shape categorization and data-driven feature set conjectures are tested on the PSB database and compared with the competitor view-based 3D shape retrieval algorithms.

Boosting iterative stochastic ensemble method for nonlinear calibration of subsurface flow models

KAUST Repository

Elsheikh, Ahmed H.

2013-06-01

A novel parameter estimation algorithm is proposed. The inverse problem is formulated as a sequential data integration problem in which Gaussian process regression (GPR) is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen-Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative stochastic ensemble method (ISEM). ISEM employs directional derivatives within a Gauss-Newton iteration for efficient gradient estimation. The resulting update equation relies on the inverse of the output covariance matrix which is rank deficient.In the proposed algorithm we use an iterative regularization based on the ℓ2 Boosting algorithm. ℓ2 Boosting iteratively fits the residual and the amount of regularization is controlled by the number of iterations. A termination criteria based on Akaike information criterion (AIC) is utilized. This regularization method is very attractive in terms of performance and simplicity of implementation. The proposed algorithm combining ISEM and ℓ2 Boosting is evaluated on several nonlinear subsurface flow parameter estimation problems. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier B.V.

Visual characterization and diversity quantification of chemical libraries: 2. Analysis and selection of size-independent, subspace-specific diversity indices.

Science.gov (United States)

Colliandre, Lionel; Le Guilloux, Vincent; Bourg, Stephane; Morin-Allory, Luc

2012-02-27

High Throughput Screening (HTS) is a standard technique widely used to find hit compounds in drug discovery projects. The high costs associated with such experiments have highlighted the need to carefully design screening libraries in order to avoid wasting resources. Molecular diversity is an established concept that has been used to this end for many years. In this article, a new approach to quantify the molecular diversity of screening libraries is presented. The approach is based on the Delimited Reference Chemical Subspace (DRCS) methodology, a new method that can be used to delimit the densest subspace spanned by a reference library in a reduced 2D continuous space. A total of 22 diversity indices were implemented or adapted to this methodology, which is used here to remove outliers and obtain a relevant cell-based partition of the subspace. The behavior of these indices was assessed and compared in various extreme situations and with respect to a set of theoretical rules that a diversity function should satisfy when libraries of different sizes have to be compared. Some gold standard indices are found inappropriate in such a context, while none of the tested indices behave perfectly in all cases. Five DRCS-based indices accounting for different aspects of diversity were finally selected, and a simple framework is proposed to use them effectively. Various libraries have been profiled with respect to more specific subspaces, which further illustrate the interest of the method.

Outlier Ranking via Subspace Analysis in Multiple Views of the Data

DEFF Research Database (Denmark)

Muller, Emmanuel; Assent, Ira; Iglesias, Patricia

2012-01-01

, a novel outlier ranking concept. Outrank exploits subspace analysis to determine the degree of outlierness. It considers different subsets of the attributes as individual outlier properties. It compares clustered regions in arbitrary subspaces and derives an outlierness score for each object. Its...... principled integration of multiple views into an outlierness measure uncovers outliers that are not detectable in the full attribute space. Our experimental evaluation demonstrates that Outrank successfully determines a high quality outlier ranking, and outperforms state-of-the-art outlierness measures....

Iterative reconstruction methods for Thermo-acoustic Tomography

International Nuclear Information System (INIS)

Marinesque, Sebastien

2012-01-01

We define, study and implement various iterative reconstruction methods for Thermo-acoustic Tomography (TAT): the Back and Forth Nudging (BFN), easy to implement and to use, a variational technique (VT) and the Back and Forth SEEK (BF-SEEK), more sophisticated, and a coupling method between Kalman filter (KF) and Time Reversal (TR). A unified formulation is explained for the sequential techniques aforementioned that defines a new class of inverse problem methods: the Back and Forth Filters (BFF). In addition to existence and uniqueness (particularly for backward solutions), we study many frameworks that ensure and characterize the convergence of the algorithms. Thus we give a general theoretical framework for which the BFN is a well-posed problem. Then, in application to TAT, existence and uniqueness of its solutions and geometrical convergence of the algorithm are proved, and an explicit convergence rate and a description of its numerical behaviour are given. Next, theoretical and numerical studies of more general and realistic framework are led, namely different objects, speeds (with or without trapping), various sensor configurations and samplings, attenuated equations or external sources. Then optimal control and best estimate tools are used to characterize the BFN convergence and converging feedbacks for BFF, under observability assumptions. Finally, we compare the most flexible and efficient current techniques (TR and an iterative variant) with our various BFF and the VT in several experiments. Thus, robust, with different possible complexities and flexible, the methods that we propose are very interesting reconstruction techniques, particularly in TAT and when observations are degraded. (author) [fr

Quantum Zeno subspaces induced by temperature

Energy Technology Data Exchange (ETDEWEB)

Militello, B.; Scala, M.; Messina, A. [Dipartimento di Fisica dell' Universita di Palermo, Via Archirafi 36, I-90123 Palermo (Italy)

2011-08-15

We discuss the partitioning of the Hilbert space of a quantum system induced by the interaction with another system at thermal equilibrium, showing that the higher the temperature the more effective is the formation of Zeno subspaces. We show that our analysis keeps its validity even in the case of interaction with a bosonic reservoir, provided appropriate limitations of the relevant bandwidth.

Shrinkage-thresholding enhanced born iterative method for solving 2D inverse electromagnetic scattering problem

KAUST Repository

Desmal, Abdulla; Bagci, Hakan

2014-01-01

A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST

EVD Dualdating Based Online Subspace Learning

Directory of Open Access Journals (Sweden)

Bo Jin

2014-01-01

Full Text Available Conventional incremental PCA methods usually only discuss the situation of adding samples. In this paper, we consider two different cases: deleting samples and simultaneously adding and deleting samples. To avoid the NP-hard problem of downdating SVD without right singular vectors and specific position information, we choose to use EVD instead of SVD, which is used by most IPCA methods. First, we propose an EVD updating and downdating algorithm, called EVD dualdating, which permits simultaneous arbitrary adding and deleting operation, via transforming the EVD of the covariance matrix into a SVD updating problem plus an EVD of a small autocorrelation matrix. A comprehensive analysis is delivered to express the essence, expansibility, and computation complexity of EVD dualdating. A mathematical theorem proves that if the whole data matrix satisfies the low-rank-plus-shift structure, EVD dualdating is an optimal rank-k estimator under the sequential environment. A selection method based on eigenvalues is presented to determine the optimal rank k of the subspace. Then, we propose three incremental/decremental PCA methods: EVDD-IPCA, EVDD-DPCA, and EVDD-IDPCA, which are adaptive to the varying mean. Finally, plenty of comparative experiments demonstrate that EVDD-based methods outperform conventional incremental/decremental PCA methods in both efficiency and accuracy.

Analysis of Diffusion Problems using Homotopy Perturbation and Variational Iteration Methods

DEFF Research Database (Denmark)

Barari, Amin; Poor, A. Tahmasebi; Jorjani, A.

2010-01-01

In this paper, variational iteration method and homotopy perturbation method are applied to different forms of diffusion equation. The diffusion equations have found wide applications in heat transfer problems, theory of consolidation and many other problems in engineering. The methods proposed...

Laplace transform overcoming principle drawbacks in application of the variational iteration method to fractional heat equations

Directory of Open Access Journals (Sweden)

Wu Guo-Cheng

2012-01-01

Full Text Available This note presents a Laplace transform approach in the determination of the Lagrange multiplier when the variational iteration method is applied to time fractional heat diffusion equation. The presented approach is more straightforward and allows some simplification in application of the variational iteration method to fractional differential equations, thus improving the convergence of the successive iterations.

Iterative resonance self-shielding methods using resonance integral table in heterogeneous transport lattice calculations

International Nuclear Information System (INIS)

Hong, Ser Gi; Kim, Kang-Seog

2011-01-01

This paper describes the iteration methods using resonance integral tables to estimate the effective resonance cross sections in heterogeneous transport lattice calculations. Basically, these methods have been devised to reduce an effort to convert resonance integral table into subgroup data to be used in the physical subgroup method. Since these methods do not use subgroup data but only use resonance integral tables directly, these methods do not include an error in converting resonance integral into subgroup data. The effective resonance cross sections are estimated iteratively for each resonance nuclide through the heterogeneous fixed source calculations for the whole problem domain to obtain the background cross sections. These methods have been implemented in the transport lattice code KARMA which uses the method of characteristics (MOC) to solve the transport equation. The computational results show that these iteration methods are quite promising in the practical transport lattice calculations.

An iterative method for selecting degenerate multiplex PCR primers.

Science.gov (United States)

Souvenir, Richard; Buhler, Jeremy; Stormo, Gary; Zhang, Weixiong

2007-01-01

Single-nucleotide polymorphism (SNP) genotyping is an important molecular genetics process, which can produce results that will be useful in the medical field. Because of inherent complexities in DNA manipulation and analysis, many different methods have been proposed for a standard assay. One of the proposed techniques for performing SNP genotyping requires amplifying regions of DNA surrounding a large number of SNP loci. To automate a portion of this particular method, it is necessary to select a set of primers for the experiment. Selecting these primers can be formulated as the Multiple Degenerate Primer Design (MDPD) problem. The Multiple, Iterative Primer Selector (MIPS) is an iterative beam-search algorithm for MDPD. Theoretical and experimental analyses show that this algorithm performs well compared with the limits of degenerate primer design. Furthermore, MIPS outperforms an existing algorithm that was designed for a related degenerate primer selection problem.

Formulations to overcome the divergence of iterative method of fixed-point in nonlinear equations solution

Directory of Open Access Journals (Sweden)

Wilson Rodríguez Calderón

2015-04-01

Full Text Available When we need to determine the solution of a nonlinear equation there are two options: closed-methods which use intervals that contain the root and during the iterative process reduce the size of natural way, and, open-methods that represent an attractive option as they do not require an initial interval enclosure. In general, we know open-methods are more efficient computationally though they do not always converge. In this paper we are presenting a divergence case analysis when we use the method of fixed point iteration to find the normal height in a rectangular channel using the Manning equation. To solve this problem, we propose applying two strategies (developed by authors that allow to modifying the iteration function making additional formulations of the traditional method and its convergence theorem. Although Manning equation is solved with other methods like Newton when we use the iteration method of fixed-point an interesting divergence situation is presented which can be solved with a convergence higher than quadratic over the initial iterations. The proposed strategies have been tested in two cases; a study of divergence of square root of real numbers was made previously by authors for testing. Results in both cases have been successful. We present comparisons because are important for seeing the advantage of proposed strategies versus the most representative open-methods.

Subspace in Linear Algebra: Investigating Students' Concept Images and Interactions with the Formal Definition

Science.gov (United States)

Wawro, Megan; Sweeney, George F.; Rabin, Jeffrey M.

2011-01-01

This paper reports on a study investigating students' ways of conceptualizing key ideas in linear algebra, with the particular results presented here focusing on student interactions with the notion of subspace. In interviews conducted with eight undergraduates, we found students' initial descriptions of subspace often varied substantially from…

Contribution to regularizing iterative method development for attenuation correction in gamma emission tomography

International Nuclear Information System (INIS)

Cao, A.

1981-07-01

This study is concerned with the transverse axial gamma emission tomography. The problem of self-attenuation of radiations in biologic tissues is raised. The regularizing iterative method is developed, as a reconstruction method of 3 dimensional images. The different steps from acquisition to results, necessary to its application, are described. Organigrams relative to each step are explained. Comparison notion between two reconstruction methods is introduced. Some methods used for the comparison or to bring about the characteristics of a reconstruction technique are defined. The studies realized to test the regularizing iterative method are presented and results are analyzed [fr

Matrix completion-based reconstruction for undersampled magnetic resonance fingerprinting data.

Science.gov (United States)

Doneva, Mariya; Amthor, Thomas; Koken, Peter; Sommer, Karsten; Börnert, Peter

2017-09-01

An iterative reconstruction method for undersampled magnetic resonance fingerprinting data is presented. The method performs the reconstruction entirely in k-space and is related to low rank matrix completion methods. A low dimensional data subspace is estimated from a small number of k-space locations fully sampled in the temporal direction and used to reconstruct the missing k-space samples before MRF dictionary matching. Performing the iterations in k-space eliminates the need for applying a forward and an inverse Fourier transform in each iteration required in previously proposed iterative reconstruction methods for undersampled MRF data. A projection onto the low dimensional data subspace is performed as a matrix multiplication instead of a singular value thresholding typically used in low rank matrix completion, further reducing the computational complexity of the reconstruction. The method is theoretically described and validated in phantom and in-vivo experiments. The quality of the parameter maps can be significantly improved compared to direct matching on undersampled data. Copyright © 2017 Elsevier Inc. All rights reserved.

Plasma flow to a surface using the iterative Monte Carlo method

International Nuclear Information System (INIS)

Pitcher, C.S.

1994-01-01

The iterative Monte Carlo (IMC) method is applied to a number of one-dimensional plasma flow problems, which encompass a wide range of conditions typical of those present in the boundary of magnetic fusion devices. The kinetic IMC method of solving plasma flow to a surface consists of launching and following particles within a grid of 'bins' into which weights are left according to the time a particle spends within a bin. The density and potential distributions within the plasma are iterated until the final solution is arrived at. The IMC results are compared with analytical treatments of these problems and, in general, good agreement is obtained. (author)

Detailed Design and Fabrication Method of the ITER Vacuum Vessel Ports

International Nuclear Information System (INIS)

Hee-Jae Ahn; Kwon, T.H.; Hong, Y.S.

2006-01-01

The engineering design of the ITER vacuum vessel (VV) has been progressed by the ITER International Team (IT) with the cooperation of several participant teams (PT). The VV and ports are the components allocated to Korea for the construction of the ITER. Hyundai Heavy Industries has been involved in the structural analysis, detailed design and development of the fabrication method of the upper and lower ports within the framework of the ITER transitional arrangements (ITA). The design of the port structures has been investigated to validate and to improve the conceptual designs of the ITER IT and other PT. The special emphasis was laid on the flange joint between the port extension and the in-port plug to develop the design of the upper port. The modified design with a pure friction type flange with forty-eight pieces of bolts instead of the tangential key is recommended. Furthermore, the alternative flange designs developed by the ITER IT have been analyzed in detail to simplify the lip seal maintenance into the port flange. The structural analyses of the lower RH port have been also performed to verify the capacity for supporting the VV. The maximum stress exceeds the allowable value at the reinforcing block and basement. More elaborate local models have been developed to mitigate the stress concentration and to modify the component design. The fabrication method and the sequence of the detailed fabrication for the ports are developed focusing on the cost reduction as well as the simplification. A typical port structure includes a port stub, a stub extension and a port extension with a connecting duct. The fabrication sequence consists of surface treatment, cutting, forming, cleaning, welding, machining, and non-destructive inspection and test. Tolerance study has been performed to avoid the mismatch of each fabricated component and to obtain the suitable tolerances in the assembly at the shop and site. This study is based on the experience in the fabrication of

Reducing the effects of acoustic heterogeneity with an iterative reconstruction method from experimental data in microwave induced thermoacoustic tomography

International Nuclear Information System (INIS)

Wang, Jinguo; Zhao, Zhiqin; Song, Jian; Chen, Guoping; Nie, Zaiping; Liu, Qing-Huo

2015-01-01

Purpose: An iterative reconstruction method has been previously reported by the authors of this paper. However, the iterative reconstruction method was demonstrated by solely using the numerical simulations. It is essential to apply the iterative reconstruction method to practice conditions. The objective of this work is to validate the capability of the iterative reconstruction method for reducing the effects of acoustic heterogeneity with the experimental data in microwave induced thermoacoustic tomography. Methods: Most existing reconstruction methods need to combine the ultrasonic measurement technology to quantitatively measure the velocity distribution of heterogeneity, which increases the system complexity. Different to existing reconstruction methods, the iterative reconstruction method combines time reversal mirror technique, fast marching method, and simultaneous algebraic reconstruction technique to iteratively estimate the velocity distribution of heterogeneous tissue by solely using the measured data. Then, the estimated velocity distribution is used subsequently to reconstruct the highly accurate image of microwave absorption distribution. Experiments that a target placed in an acoustic heterogeneous environment are performed to validate the iterative reconstruction method. Results: By using the estimated velocity distribution, the target in an acoustic heterogeneous environment can be reconstructed with better shape and higher image contrast than targets that are reconstructed with a homogeneous velocity distribution. Conclusions: The distortions caused by the acoustic heterogeneity can be efficiently corrected by utilizing the velocity distribution estimated by the iterative reconstruction method. The advantage of the iterative reconstruction method over the existing correction methods is that it is successful in improving the quality of the image of microwave absorption distribution without increasing the system complexity

Iterative methods for photoacoustic tomography in attenuating acoustic media

Science.gov (United States)

Haltmeier, Markus; Kowar, Richard; Nguyen, Linh V.

2017-11-01

The development of efficient and accurate reconstruction methods is an important aspect of tomographic imaging. In this article, we address this issue for photoacoustic tomography. To this aim, we use models for acoustic wave propagation accounting for frequency dependent attenuation according to a wide class of attenuation laws that may include memory. We formulate the inverse problem of photoacoustic tomography in attenuating medium as an ill-posed operator equation in a Hilbert space framework that is tackled by iterative regularization methods. Our approach comes with a clear convergence analysis. For that purpose we derive explicit expressions for the adjoint problem that can efficiently be implemented. In contrast to time reversal, the employed adjoint wave equation is again damping and, thus has a stable solution. This stability property can be clearly seen in our numerical results. Moreover, the presented numerical results clearly demonstrate the efficiency and accuracy of the derived iterative reconstruction algorithms in various situations including the limited view case.

On a new iterative method for solving linear systems and comparison results

Science.gov (United States)

Jing, Yan-Fei; Huang, Ting-Zhu

2008-10-01

In Ujevic [A new iterative method for solving linear systems, Appl. Math. Comput. 179 (2006) 725-730], the author obtained a new iterative method for solving linear systems, which can be considered as a modification of the Gauss-Seidel method. In this paper, we show that this is a special case from a point of view of projection techniques. And a different approach is established, which is both theoretically and numerically proven to be better than (at least the same as) Ujevic's. As the presented numerical examples show, in most cases, the convergence rate is more than one and a half that of Ujevic.

Computation of saddle-type slow manifolds using iterative methods

DEFF Research Database (Denmark)

Kristiansen, Kristian Uldall

2015-01-01

with respect to , appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples, including a model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables, and the computation of homoclinic connections in the Fitz......This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, which require mesh refinements to ensure uniform convergence...

Design and fabrication methods of FW/blanket and vessel for ITER-FEAT

Energy Technology Data Exchange (ETDEWEB)

Ioki, K. E-mail: iokik@itereu.de; Barabash, V.; Cardella, A.; Elio, F.; Kalinin, G.; Miki, N.; Onozuka, M.; Osaki, T.; Rozov, V.; Sannazzaro, G.; Utin, Y.; Yamada, M.; Yoshimura, H

2001-11-01

Design has progressed on the vacuum vessel and FW/blanket for ITER-FEAT. The basic functions and structures are the same as for the 1998 ITER design. Detailed blanket module designs of the radially cooled shield block with flat separable FW panels have been developed. The ITER blanket R and D program covers different materials and fabrication methods in order make a final selection based on the results. Separate manifolds have been designed and analysed for the blanket cooling. The vessel design with flexible support housings has been improved to minimise the number of continuous poloidal ribs. Most of the R and D performed so far during EDA are still applicable.

Design and fabrication methods of FW/blanket and vessel for ITER-FEAT

International Nuclear Information System (INIS)

Ioki, K.; Barabash, V.; Cardella, A.; Elio, F.; Kalinin, G.; Miki, N.; Onozuka, M.; Osaki, T.; Rozov, V.; Sannazzaro, G.; Utin, Y.; Yamada, M.; Yoshimura, H.

2001-01-01

Design has progressed on the vacuum vessel and FW/blanket for ITER-FEAT. The basic functions and structures are the same as for the 1998 ITER design. Detailed blanket module designs of the radially cooled shield block with flat separable FW panels have been developed. The ITER blanket R and D program covers different materials and fabrication methods in order make a final selection based on the results. Separate manifolds have been designed and analysed for the blanket cooling. The vessel design with flexible support housings has been improved to minimise the number of continuous poloidal ribs. Most of the R and D performed so far during EDA are still applicable

Variational iteration method for solving coupled-KdV equations

International Nuclear Information System (INIS)

Assas, Laila M.B.

2008-01-01

In this paper, the He's variational iteration method is applied to solve the non-linear coupled-KdV equations. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This technique provides a sequence of functions which converge to the exact solution of the coupled-KdV equations. This procedure is a powerful tool for solving coupled-KdV equations

A connection between the asymptotic iteration method and the continued fractions formalism

International Nuclear Information System (INIS)

Matamala, A.R.; Gutierrez, F.A.; Diaz-Valdes, J.

2007-01-01

In this work, we show that there is a connection between the asymptotic iteration method (a method to solve second order linear ordinary differential equations) and the older method of continued fractions to solve differential equations

Solution of problems in calculus of variations via He's variational iteration method

International Nuclear Information System (INIS)

Tatari, Mehdi; Dehghan, Mehdi

2007-01-01

In the modeling of a large class of problems in science and engineering, the minimization of a functional is appeared. Finding the solution of these problems needs to solve the corresponding ordinary differential equations which are generally nonlinear. In recent years He's variational iteration method has been attracted a lot of attention of the researchers for solving nonlinear problems. This method finds the solution of the problem without any discretization of the equation. Since this method gives a closed form solution of the problem and avoids the round off errors, it can be considered as an efficient method for solving various kinds of problems. In this research He's variational iteration method will be employed for solving some problems in calculus of variations. Some examples are presented to show the efficiency of the proposed technique

MO-DE-207A-07: Filtered Iterative Reconstruction (FIR) Via Proximal Forward-Backward Splitting: A Synergy of Analytical and Iterative Reconstruction Method for CT

International Nuclear Information System (INIS)

Gao, H

2016-01-01

Purpose: This work is to develop a general framework, namely filtered iterative reconstruction (FIR) method, to incorporate analytical reconstruction (AR) method into iterative reconstruction (IR) method, for enhanced CT image quality. Methods: FIR is formulated as a combination of filtered data fidelity and sparsity regularization, and then solved by proximal forward-backward splitting (PFBS) algorithm. As a result, the image reconstruction decouples data fidelity and image regularization with a two-step iterative scheme, during which an AR-projection step updates the filtered data fidelity term, while a denoising solver updates the sparsity regularization term. During the AR-projection step, the image is projected to the data domain to form the data residual, and then reconstructed by certain AR to a residual image which is in turn weighted together with previous image iterate to form next image iterate. Since the eigenvalues of AR-projection operator are close to the unity, PFBS based FIR has a fast convergence. Results: The proposed FIR method is validated in the setting of circular cone-beam CT with AR being FDK and total-variation sparsity regularization, and has improved image quality from both AR and IR. For example, AIR has improved visual assessment and quantitative measurement in terms of both contrast and resolution, and reduced axial and half-fan artifacts. Conclusion: FIR is proposed to incorporate AR into IR, with an efficient image reconstruction algorithm based on PFBS. The CBCT results suggest that FIR synergizes AR and IR with improved image quality and reduced axial and half-fan artifacts. The authors was partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000), and the Shanghai Pujiang Talent Program (#14PJ1404500).

A non-iterative method for fitting decay curves with background

International Nuclear Information System (INIS)

Mukoyama, T.

1982-01-01

A non-iterative method for fitting a decay curve with background is presented. The sum of an exponential function and a constant term is linearized by the use of the difference equation and parameters are determined by the standard linear least-squares fitting. The validity of the present method has been tested against pseudo-experimental data. (orig.)

Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

Czech Academy of Sciences Publication Activity Database

Bru, R.; Marín, J.; Mas, J.; Tůma, Miroslav

2014-01-01

Roč. 36, č. 4 (2014), A2002-A2022 ISSN 1064-8275 Institutional support: RVO:67985807 Keywords : preconditioned iterative methods * incomplete decompositions * approximate inverses * linear least squares Subject RIV: BA - General Mathematics Impact factor: 1.854, year: 2014

Persymmetric Adaptive Detectors of Subspace Signals in Homogeneous and Partially Homogeneous Clutter

Directory of Open Access Journals (Sweden)

Ding Hao

2015-08-01

Full Text Available In the field of adaptive radar detection, an effective strategy to improve the detection performance is to exploit the structural information of the covariance matrix, especially in the case of insufficient reference cells. Thus, in this study, the problem of detecting multidimensional subspace signals is discussed by considering the persymmetric structure of the clutter covariance matrix, which implies that the covariance matrix is persymmetric about its cross diagonal. Persymmetric adaptive detectors are derived on the basis of the one-step principle as well as the two-step Generalized Likelihood Ratio Test (GLRT in homogeneous and partially homogeneous clutter. The proposed detectors consider the structural information of the covariance matrix at the design stage. Simulation results suggest performance improvement compared with existing detectors when reference cells are insufficient. Moreover, the detection performance is assessed with respect to the effects of the covariance matrix, signal subspace dimension, and mismatched performance of signal subspace as well as signal fluctuations.

MULTI-LABEL ASRS DATASET CLASSIFICATION USING SEMI-SUPERVISED SUBSPACE CLUSTERING

Data.gov (United States)

National Aeronautics and Space Administration — MULTI-LABEL ASRS DATASET CLASSIFICATION USING SEMI-SUPERVISED SUBSPACE CLUSTERING MOHAMMAD SALIM AHMED, LATIFUR KHAN, NIKUNJ OZA, AND MANDAVA RAJESWARI Abstract....

Uncertainty calculation for modal parameters used with stochastic subspace identification: an application to a bridge structure

Science.gov (United States)

Hsu, Wei-Ting; Loh, Chin-Hsiung; Chao, Shu-Hsien

2015-03-01

Stochastic subspace identification method (SSI) has been proven to be an efficient algorithm for the identification of liner-time-invariant system using multivariate measurements. Generally, the estimated modal parameters through SSI may be afflicted with statistical uncertainty, e.g. undefined measurement noises, non-stationary excitation, finite number of data samples etc. Therefore, the identified results are subjected to variance errors. Accordingly, the concept of the stabilization diagram can help users to identify the correct model, i.e. through removing the spurious modes. Modal parameters are estimated at successive model orders where the physical modes of the system are extracted and separated from the spurious modes. Besides, an uncertainty computation scheme was derived for the calculation of uncertainty bounds for modal parameters at some given model order. The uncertainty bounds of damping ratios are particularly interesting, as the estimation of damping ratios are difficult to obtain. In this paper, an automated stochastic subspace identification algorithm is addressed. First, the identification of modal parameters through covariance-driven stochastic subspace identification from the output-only measurements is used for discussion. A systematic way of investigation on the criteria for the stabilization diagram is presented. Secondly, an automated algorithm of post-processing on stabilization diagram is demonstrated. Finally, the computation of uncertainty bounds for each mode with all model order in the stabilization diagram is utilized to determine system natural frequencies and damping ratios. Demonstration of this study on the system identification of a three-span steel bridge under operation condition is presented. It is shown that the proposed new operation procedure for the automated covariance-driven stochastic subspace identification can enhance the robustness and reliability in structural health monitoring.

Analysis of the iteratively regularized Gauss-Newton method under a heuristic rule

Science.gov (United States)

Jin, Qinian; Wang, Wei

2018-03-01

The iteratively regularized Gauss-Newton method is one of the most prominent regularization methods for solving nonlinear ill-posed inverse problems when the data is corrupted by noise. In order to produce a useful approximate solution, this iterative method should be terminated properly. The existing a priori and a posteriori stopping rules require accurate information on the noise level, which may not be available or reliable in practical applications. In this paper we propose a heuristic selection rule for this regularization method, which requires no information on the noise level. By imposing certain conditions on the noise, we derive a posteriori error estimates on the approximate solutions under various source conditions. Furthermore, we establish a convergence result without using any source condition. Numerical results are presented to illustrate the performance of our heuristic selection rule.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

Science.gov (United States)

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite

A novel iterative energy calibration method for composite germanium detectors

International Nuclear Information System (INIS)

Pattabiraman, N.S.; Chintalapudi, S.N.; Ghugre, S.S.

2004-01-01

An automatic method for energy calibration of the observed experimental spectrum has been developed. The method presented is based on an iterative algorithm and presents an efficient way to perform energy calibrations after establishing the weights of the calibration data. An application of this novel technique for data acquired using composite detectors in an in-beam γ-ray spectroscopy experiment is presented

A novel iterative energy calibration method for composite germanium detectors

Energy Technology Data Exchange (ETDEWEB)

Pattabiraman, N.S.; Chintalapudi, S.N.; Ghugre, S.S. E-mail: ssg@alpha.iuc.res.in

2004-07-01

An automatic method for energy calibration of the observed experimental spectrum has been developed. The method presented is based on an iterative algorithm and presents an efficient way to perform energy calibrations after establishing the weights of the calibration data. An application of this novel technique for data acquired using composite detectors in an in-beam {gamma}-ray spectroscopy experiment is presented.

Evaluating Clustering in Subspace Projections of High Dimensional Data

DEFF Research Database (Denmark)

Müller, Emmanuel; Günnemann, Stephan; Assent, Ira

2009-01-01

Clustering high dimensional data is an emerging research field. Subspace clustering or projected clustering group similar objects in subspaces, i.e. projections, of the full space. In the past decade, several clustering paradigms have been developed in parallel, without thorough evaluation...... and comparison between these paradigms on a common basis. Conclusive evaluation and comparison is challenged by three major issues. First, there is no ground truth that describes the "true" clusters in real world data. Second, a large variety of evaluation measures have been used that reflect different aspects...... of the clustering result. Finally, in typical publications authors have limited their analysis to their favored paradigm only, while paying other paradigms little or no attention. In this paper, we take a systematic approach to evaluate the major paradigms in a common framework. We study representative clustering...

A hyperpower iterative method for computing the generalized Drazin ...

Indian Academy of Sciences (India)

Shwetabh Srivastava

[6, 7]. A number of direct and iterative methods for com- putation of the Drazin inverse were developed in [8–12]. Its extension to Banach algebras is known as the generalized Drazin inverse and was established in [13]. Let J denote the complex. Banach algebra with the unit 1. The generalized Drazin inverse of an element ...

Copper Mountain conference on iterative methods: Proceedings: Volume 1

Energy Technology Data Exchange (ETDEWEB)

NONE

1996-10-01

This volume (one of two) contains information presented during the first three days of the Copper Mountain Conference on Iterative Methods held April 9-13, 1996 at Copper Mountain, Colorado. Topics of the sessions held these three days included nonlinear systems, parallel processing, preconditioning, sparse matrix test collections, first-order system least squares, Arnoldi`s method, integral equations, software, Navier-Stokes equations, Euler equations, Krylov methods, and eigenvalues. The top three papers from a student competition are also included. Selected papers indexed separately for the Energy Science and Technology Database.

Subspace Dimensionality: A Tool for Automated QC in Seismic Array Processing

Science.gov (United States)

Rowe, C. A.; Stead, R. J.; Begnaud, M. L.

2013-12-01

Because of the great resolving power of seismic arrays, the application of automated processing to array data is critically important in treaty verification work. A significant problem in array analysis is the inclusion of bad sensor channels in the beamforming process. We are testing an approach to automated, on-the-fly quality control (QC) to aid in the identification of poorly performing sensor channels prior to beam-forming in routine event detection or location processing. The idea stems from methods used for large computer servers, when monitoring traffic at enormous numbers of nodes is impractical on a node-by node basis, so the dimensionality of the node traffic is instead monitoried for anomalies that could represent malware, cyber-attacks or other problems. The technique relies upon the use of subspace dimensionality or principal components of the overall system traffic. The subspace technique is not new to seismology, but its most common application has been limited to comparing waveforms to an a priori collection of templates for detecting highly similar events in a swarm or seismic cluster. In the established template application, a detector functions in a manner analogous to waveform cross-correlation, applying a statistical test to assess the similarity of the incoming data stream to known templates for events of interest. In our approach, we seek not to detect matching signals, but instead, we examine the signal subspace dimensionality in much the same way that the method addresses node traffic anomalies in large computer systems. Signal anomalies recorded on seismic arrays affect the dimensional structure of the array-wide time-series. We have shown previously that this observation is useful in identifying real seismic events, either by looking at the raw signal or derivatives thereof (entropy, kurtosis), but here we explore the effects of malfunctioning channels on the dimension of the data and its derivatives, and how to leverage this effect for

Polynomial factor models : non-iterative estimation via method-of-moments

NARCIS (Netherlands)

Schuberth, Florian; Büchner, Rebecca; Schermelleh-Engel, Karin; Dijkstra, Theo K.

2017-01-01

We introduce a non-iterative method-of-moments estimator for non-linear latent variable (LV) models. Under the assumption of joint normality of all exogenous variables, we use the corrected moments of linear combinations of the observed indicators (proxies) to obtain consistent path coefficient and

Note: interpreting iterative methods convergence with diffusion point of view

OpenAIRE

Hong, Dohy

2013-01-01

In this paper, we explain the convergence speed of different iteration schemes with the fluid diffusion view when solving a linear fixed point problem. This interpretation allows one to better understand why power iteration or Jacobi iteration may converge faster or slower than Gauss-Seidel iteration.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

Science.gov (United States)

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

A New General Iterative Method for a Finite Family of Nonexpansive Mappings in Hilbert Spaces

Directory of Open Access Journals (Sweden)

Singthong Urailuk

2010-01-01

Full Text Available We introduce a new general iterative method by using the -mapping for finding a common fixed point of a finite family of nonexpansive mappings in the framework of Hilbert spaces. A strong convergence theorem of the purposed iterative method is established under some certain control conditions. Our results improve and extend the results announced by many others.

More on Generalizations and Modifications of Iterative Methods for Solving Large Sparse Indefinite Linear Systems

Directory of Open Access Journals (Sweden)

Jen-Yuan Chen

2014-01-01

Full Text Available Continuing from the works of Li et al. (2014, Li (2007, and Kincaid et al. (2000, we present more generalizations and modifications of iterative methods for solving large sparse symmetric and nonsymmetric indefinite systems of linear equations. We discuss a variety of iterative methods such as GMRES, MGMRES, MINRES, LQ-MINRES, QR MINRES, MMINRES, MGRES, and others.

Development of Subspace-based Hybrid Monte Carlo-Deterministric Algorithms for Reactor Physics Calculations

International Nuclear Information System (INIS)

Abdel-Khalik, Hany S.; Zhang, Qiong

2014-01-01

The development of hybrid Monte-Carlo-Deterministic (MC-DT) approaches, taking place over the past few decades, have primarily focused on shielding and detection applications where the analysis requires a small number of responses, i.e. at the detector locations(s). This work further develops a recently introduced global variance reduction approach, denoted by the SUBSPACE approach is designed to allow the use of MC simulation, currently limited to benchmarking calculations, for routine engineering calculations. By way of demonstration, the SUBSPACE approach is applied to assembly level calculations used to generate the few-group homogenized cross-sections. These models are typically expensive and need to be executed in the order of 10 3 - 10 5 times to properly characterize the few-group cross-sections for downstream core-wide calculations. Applicability to k-eigenvalue core-wide models is also demonstrated in this work. Given the favorable results obtained in this work, we believe the applicability of the MC method for reactor analysis calculations could be realized in the near future.

Gauss-Seidel Iterative Method as a Real-Time Pile-Up Solver of Scintillation Pulses

Science.gov (United States)

Novak, Roman; Vencelj, Matja¿

2009-12-01

The pile-up rejection in nuclear spectroscopy has been confronted recently by several pile-up correction schemes that compensate for distortions of the signal and subsequent energy spectra artifacts as the counting rate increases. We study here a real-time capability of the event-by-event correction method, which at the core translates to solving many sets of linear equations. Tight time limits and constrained front-end electronics resources make well-known direct solvers inappropriate. We propose a novel approach based on the Gauss-Seidel iterative method, which turns out to be a stable and cost-efficient solution to improve spectroscopic resolution in the front-end electronics. We show the method convergence properties for a class of matrices that emerge in calorimetric processing of scintillation detector signals and demonstrate the ability of the method to support the relevant resolutions. The sole iteration-based error component can be brought below the sliding window induced errors in a reasonable number of iteration steps, thus allowing real-time operation. An area-efficient hardware implementation is proposed that fully utilizes the method's inherent parallelism.

Nonlinear acceleration of SN transport calculations

Energy Technology Data Exchange (ETDEWEB)

Fichtl, Erin D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Calef, Matthew T [Los Alamos National Laboratory

2010-12-20

The use of nonlinear iterative methods, Jacobian-Free Newton-Krylov (JFNK) in particular, for solving eigenvalue problems in transport applications has recently become an active subject of research. While JFNK has been shown to be effective for k-eigenvalue problems, there are a number of input parameters that impact computational efficiency, making it difficult to implement efficiently in a production code using a single set of default parameters. We show that different selections for the forcing parameter in particular can lead to large variations in the amount of computational work for a given problem. In contrast, we present a nonlinear subspace method that sits outside and effectively accelerates nonlinear iterations of a given form and requires only a single input parameter, the subspace size. It is shown to consistently and significantly reduce the amount of computational work when applied to fixed-point iteration, and this combination of methods is shown to be more efficient than JFNK for our application.

Nonlinear acceleration of S_n transport calculations

International Nuclear Information System (INIS)

Fichtl, Erin D.; Warsa, James S.; Calef, Matthew T.

2011-01-01

The use of nonlinear iterative methods, Jacobian-Free Newton-Krylov (JFNK) in particular, for solving eigenvalue problems in transport applications has recently become an active subject of research. While JFNK has been shown to be effective for k-eigenvalue problems, there are a number of input parameters that impact computational efficiency, making it difficult to implement efficiently in a production code using a single set of default parameters. We show that different selections for the forcing parameter in particular can lead to large variations in the amount of computational work for a given problem. In contrast, we employ a nonlinear subspace method that sits outside and effectively accelerates nonlinear iterations of a given form and requires only a single input parameter, the subspace size. It is shown to consistently and significantly reduce the amount of computational work when applied to fixed-point iteration, and this combination of methods is shown to be more efficient than JFNK for our application. (author)

A Posteriori Error Estimation for Finite Element Methods and Iterative Linear Solvers

Energy Technology Data Exchange (ETDEWEB)

Melboe, Hallgeir

2001-10-01

This thesis addresses a posteriori error estimation for finite element methods and iterative linear solvers. Adaptive finite element methods have gained a lot of popularity over the last decades due to their ability to produce accurate results with limited computer power. In these methods a posteriori error estimates play an essential role. Not only do they give information about how large the total error is, they also indicate which parts of the computational domain should be given a more sophisticated treatment in order to reduce the error. A posteriori error estimates are traditionally aimed at estimating the global error, but more recently so called goal oriented error estimators have been shown a lot of interest. The name reflects the fact that they estimate the error in user-defined local quantities. In this thesis the main focus is on global error estimators for highly stretched grids and goal oriented error estimators for flow problems on regular grids. Numerical methods for partial differential equations, such as finite element methods and other similar techniques, typically result in a linear system of equations that needs to be solved. Usually such systems are solved using some iterative procedure which due to a finite number of iterations introduces an additional error. Most such algorithms apply the residual in the stopping criterion, whereas the control of the actual error may be rather poor. A secondary focus in this thesis is on estimating the errors that are introduced during this last part of the solution procedure. The thesis contains new theoretical results regarding the behaviour of some well known, and a few new, a posteriori error estimators for finite element methods on anisotropic grids. Further, a goal oriented strategy for the computation of forces in flow problems is devised and investigated. Finally, an approach for estimating the actual errors associated with the iterative solution of linear systems of equations is suggested. (author)

Phase reconstruction by a multilevel iteratively regularized Gauss–Newton method

International Nuclear Information System (INIS)

Langemann, Dirk; Tasche, Manfred

2008-01-01

In this paper we consider the numerical solution of a phase retrieval problem for a compactly supported, linear spline f : R → C with the Fourier transform f-circumflex, where values of |f| and |f-circumflex| at finitely many equispaced nodes are given. The unknown phases of complex spline coefficients fulfil a well-structured system of nonlinear equations. Thus the phase reconstruction leads to a nonlinear inverse problem, which is solved by a multilevel strategy and iterative Tikhonov regularization. The multilevel strategy concentrates the main effort of the solution of the phase retrieval problem in the coarse, less expensive levels and provides convenient initial guesses at the next finer level. On each level, the corresponding nonlinear system is solved by an iteratively regularized Gauss–Newton method. The multilevel strategy is motivated by convergence results of IRGN. This method is applicable to a wide range of examples as shown in several numerical tests for noiseless and noisy data

Study of a Biparametric Family of Iterative Methods

Directory of Open Access Journals (Sweden)

B. Campos

2014-01-01

Full Text Available The dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the c-iterative methods and the well-known Chebyshev-Halley family. We find the analytical expressions for the fixed and critical points by solving 6-degree polynomials. We use the free critical points to get the parameter planes and, by observing them, we specify some values of (α, c with clear stable and unstable behaviors.

Non-iterative method to calculate the periodical distribution of temperature in reactors with thermal regeneration

International Nuclear Information System (INIS)

Sanchez de Alsina, O.L.; Scaricabarozzi, R.A.

1982-01-01

A matrix non-iterative method to calculate the periodical distribution in reactors with thermal regeneration is presented. In case of exothermic reaction, a source term will be included. A computer code was developed to calculate the final temperature distribution in solids and in the outlet temperatures of the gases. The results obtained from ethane oxidation calculation in air, using the Dietrich kinetic data are presented. This method is more advantageous than iterative methods. (E.G.) [pt

Speech Denoising in White Noise Based on Signal Subspace Low-rank Plus Sparse Decomposition

Directory of Open Access Journals (Sweden)

yuan Shuai

2017-01-01

Full Text Available In this paper, a new subspace speech enhancement method using low-rank and sparse decomposition is presented. In the proposed method, we firstly structure the corrupted data as a Toeplitz matrix and estimate its effective rank for the underlying human speech signal. Then the low-rank and sparse decomposition is performed with the guidance of speech rank value to remove the noise. Extensive experiments have been carried out in white Gaussian noise condition, and experimental results show the proposed method performs better than conventional speech enhancement methods, in terms of yielding less residual noise and lower speech distortion.

Analyzing the Impacts of Alternated Number of Iterations in Multiple Imputation Method on Explanatory Factor Analysis

Directory of Open Access Journals (Sweden)

Duygu KOÇAK

2017-11-01

Full Text Available The study aims to identify the effects of iteration numbers used in multiple iteration method, one of the methods used to cope with missing values, on the results of factor analysis. With this aim, artificial datasets of different sample sizes were created. Missing values at random and missing values at complete random were created in various ratios by deleting data. For the data in random missing values, a second variable was iterated at ordinal scale level and datasets with different ratios of missing values were obtained based on the levels of this variable. The data were generated using “psych” program in R software, while “dplyr” program was used to create codes that would delete values according to predetermined conditions of missing value mechanism. Different datasets were generated by applying different iteration numbers. Explanatory factor analysis was conducted on the datasets completed and the factors and total explained variances are presented. These values were first evaluated based on the number of factors and total variance explained of the complete datasets. The results indicate that multiple iteration method yields a better performance in cases of missing values at random compared to datasets with missing values at complete random. Also, it was found that increasing the number of iterations in both missing value datasets decreases the difference in the results obtained from complete datasets.

Iteratively-coupled propagating exterior complex scaling method for electron-hydrogen collisions

International Nuclear Information System (INIS)

Bartlett, Philip L; Stelbovics, Andris T; Bray, Igor

2004-01-01

A newly-derived iterative coupling procedure for the propagating exterior complex scaling (PECS) method is used to efficiently calculate the electron-impact wavefunctions for atomic hydrogen. An overview of this method is given along with methods for extracting scattering cross sections. Differential scattering cross sections at 30 eV are presented for the electron-impact excitation to the n = 1, 2, 3 and 4 final states, for both PECS and convergent close coupling (CCC), which are in excellent agreement with each other and with experiment. PECS results are presented at 27.2 eV and 30 eV for symmetric and asymmetric energy-sharing triple differential cross sections, which are in excellent agreement with CCC and exterior complex scaling calculations, and with experimental data. At these intermediate energies, the efficiency of the PECS method with iterative coupling has allowed highly accurate partial-wave solutions of the full Schroedinger equation, for L ≤ 50 and a large number of coupled angular momentum states, to be obtained with minimal computing resources. (letter to the editor)

Quantum theory of dynamical collective subspace for large-amplitude collective motion

International Nuclear Information System (INIS)

Sakata, Fumihiko; Marumori, Toshio; Ogura, Masanori.

1986-03-01

By placing emphasis on conceptual correspondence to the ''classical'' theory which has been developed within the framework of the time-dependent Hartree-Fock theory, a full quantum theory appropriate for describing large-amplitude collective motion is proposed. A central problem of the quantum theory is how to determine an optimal representation called a dynamical representation; the representation is specific for the collective subspace where the large-amplitude collective motion is replicated as satisfactorily as possible. As an extension of the classical theory where the concept of an approximate integral surface plays an important role, the dynamical representation is properly characterized by introducing a concept of an approximate invariant subspace of the Hamiltonian. (author)

Newton-sor iterative method for solving the two-dimensional porous ...

African Journals Online (AJOL)

In this paper, we consider the application of the Newton-SOR iterative method in obtaining the approximate solution of the two-dimensional porous medium equation (2D PME). The nonlinear finite difference approximation equation to the 2D PME is derived by using the implicit finite difference scheme. The developed ...

Comparison between the Variational Iteration Method and the Homotopy Perturbation Method for the Sturm-Liouville Differential Equation

OpenAIRE

Darzi R; Neamaty A

2010-01-01

We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.

A sparsity-regularized Born iterative method for reconstruction of two-dimensional piecewise continuous inhomogeneous domains

KAUST Repository

Sandhu, Ali Imran; Desmal, Abdulla; Bagci, Hakan

2016-01-01

A sparsity-regularized Born iterative method (BIM) is proposed for efficiently reconstructing two-dimensional piecewise-continuous inhomogeneous dielectric profiles. Such profiles are typically not spatially sparse, which reduces the efficiency of the sparsity-promoting regularization. To overcome this problem, scattered fields are represented in terms of the spatial derivative of the dielectric profile and reconstruction is carried out over samples of the dielectric profile's derivative. Then, like the conventional BIM, the nonlinear problem is iteratively converted into a sequence of linear problems (in derivative samples) and sparsity constraint is enforced on each linear problem using the thresholded Landweber iterations. Numerical results, which demonstrate the efficiency and accuracy of the proposed method in reconstructing piecewise-continuous dielectric profiles, are presented.

An iterative method for the solution of nonlinear systems using the Faber polynomials for annular sectors

Energy Technology Data Exchange (ETDEWEB)

Myers, N.J. [Univ. of Durham (United Kingdom)

1994-12-31

The author gives a hybrid method for the iterative solution of linear systems of equations Ax = b, where the matrix (A) is nonsingular, sparse and nonsymmetric. As in a method developed by Starke and Varga the method begins with a number of steps of the Arnoldi method to produce some information on the location of the spectrum of A. This method then switches to an iterative method based on the Faber polynomials for an annular sector placed around these eigenvalue estimates. The Faber polynomials for an annular sector are used because, firstly an annular sector can easily be placed around any eigenvalue estimates bounded away from zero, and secondly the Faber polynomials are known analytically for an annular sector. Finally the author gives three numerical examples, two of which allow comparison with Starke and Varga`s results. The third is an example of a matrix for which many iterative methods would fall, but this method converges.

ITER radio frequency systems

International Nuclear Information System (INIS)

Bosia, G.

1998-01-01

Neutral Beam Injection and RF heating are two of the methods for heating and current drive in ITER. The three ITER RF systems, which have been developed during the EDA, offer several complementary services and are able to fulfil ITER operational requirements

Environmental dose rate assessment of ITER using the Monte Carlo method

Directory of Open Access Journals (Sweden)

Karimian Alireza

2014-01-01

Full Text Available Exposure to radiation is one of the main sources of risk to staff employed in reactor facilities. The staff of a tokamak is exposed to a wide range of neutrons and photons around the tokamak hall. The International Thermonuclear Experimental Reactor (ITER is a nuclear fusion engineering project and the most advanced experimental tokamak in the world. From the radiobiological point of view, ITER dose rates assessment is particularly important. The aim of this study is the assessment of the amount of radiation in ITER during its normal operation in a radial direction from the plasma chamber to the tokamak hall. To achieve this goal, the ITER system and its components were simulated by the Monte Carlo method using the MCNPX 2.6.0 code. Furthermore, the equivalent dose rates of some radiosensitive organs of the human body were calculated by using the medical internal radiation dose phantom. Our study is based on the deuterium-tritium plasma burning by 14.1 MeV neutron production and also photon radiation due to neutron activation. As our results show, the total equivalent dose rate on the outside of the bioshield wall of the tokamak hall is about 1 mSv per year, which is less than the annual occupational dose rate limit during the normal operation of ITER. Also, equivalent dose rates of radiosensitive organs have shown that the maximum dose rate belongs to the kidney. The data may help calculate how long the staff can stay in such an environment, before the equivalent dose rates reach the whole-body dose limits.

A novel EMD selecting thresholding method based on multiple iteration for denoising LIDAR signal

Science.gov (United States)

Li, Meng; Jiang, Li-hui; Xiong, Xing-long

2015-06-01

Empirical mode decomposition (EMD) approach has been believed to be potentially useful for processing the nonlinear and non-stationary LIDAR signals. To shed further light on its performance, we proposed the EMD selecting thresholding method based on multiple iteration, which essentially acts as a development of EMD interval thresholding (EMD-IT), and randomly alters the samples of noisy parts of all the corrupted intrinsic mode functions to generate a better effect of iteration. Simulations on both synthetic signals and LIDAR signals from real world support this method.

Breaking of separability condition for dynamical collective subspace; Onset of quantum chaos in large-amplitude collective motion

Energy Technology Data Exchange (ETDEWEB)

Sakata, Fumihiko [Tokyo Univ., Tanashi (Japan). Inst. for Nuclear Study; Yamamoto, Yoshifumi; Marumori, Toshio; Iida, Shinji; Tsukuma, Hidehiko

1989-11-01

It is the purpose of the present paper to study 'global structure' of the state space of an N-body interacting fermion system, which exhibits regular, transient and stochastic phases depending on strength of the interaction. An optimum representation called a dynamical representation plays an essential role in this investigation. The concept of the dynamical representation has been introduced in the quantum theory of dynamical subspace in our previous paper, in order to determine self-consistently an optimum collective subspace as well as an optimum collective Hamiltonian. In the theory, furthermore, dynamical conditions called separability and stability conditions have been provided in order to identify the optimum collective subspace as an approximate invariant subspace of the Hamiltonian. Physical meaning of these conditions are clarified from a viewpoint to relate breaking of them with bifurcation of the collectivity and an onset of quantum chaos from the regular collective motion, by illustrating the general idea with numerical results obtained for a simple soluble model. It turns out that the onset of the stochastic phase is associated with dissolution of the quantum numbers to specify the collective subspace and this dissolution is induced by the breaking of the separability condition in the dynamical representation. (author).

Rank-defective millimeter-wave channel estimation based on subspace-compressive sensing

Directory of Open Access Journals (Sweden)

Majid Shakhsi Dastgahian

2016-11-01

Full Text Available Millimeter-wave communication (mmWC is considered as one of the pioneer candidates for 5G indoor and outdoor systems in E-band. To subdue the channel propagation characteristics in this band, high dimensional antenna arrays need to be deployed at both the base station (BS and mobile sets (MS. Unlike the conventional MIMO systems, Millimeter-wave (mmW systems lay away to employ the power predatory equipment such as ADC or RF chain in each branch of MIMO system because of hardware constraints. Such systems leverage to the hybrid precoding (combining architecture for downlink deployment. Because there is a large array at the transceiver, it is impossible to estimate the channel by conventional methods. This paper develops a new algorithm to estimate the mmW channel by exploiting the sparse nature of the channel. The main contribution is the representation of a sparse channel model and the exploitation of a modified approach based on Multiple Measurement Vector (MMV greedy sparse framework and subspace method of Multiple Signal Classification (MUSIC which work together to recover the indices of non-zero elements of an unknown channel matrix when the rank of the channel matrix is defected. In practical rank-defective channels, MUSIC fails, and we need to propose new extended MUSIC approaches based on subspace enhancement to compensate the limitation of MUSIC. Simulation results indicate that our proposed extended MUSIC algorithms will have proper performances and moderate computational speeds, and that they are even able to work in channels with an unknown sparsity level.

Chatter suppression methods of a robot machine for ITER vacuum vessel assembly and maintenance

International Nuclear Information System (INIS)

Wu, Huapeng; Wang, Yongbo; Li, Ming; Al-Saedi, Mazin; Handroos, Heikki

2014-01-01

Highlights: •A redundant 10-DOF serial-parallel hybrid robot for ITER assembly and maintains is presented. •A dynamic model of the robot is developed. •A feedback and feedforward controller is presented to suppress machining vibration of the robot. -- Abstract: In the process of assembly and maintenance of ITER vacuum vessel (ITER VV), various machining tasks including threading, milling, welding-defects cutting and flexible hose boring are required to be performed from inside of ITER VV by on-site machining tools. Robot machine is a promising option for these tasks, but great chatter (machine vibration) would happen in the machining process. The chatter vibration will deteriorate the robot accuracy and surface quality, and even cause some damages on the end-effector tools and the robot structure itself. This paper introduces two vibration control methods, one is passive and another is active vibration control. For the passive vibration control, a parallel mechanism is presented to increase the stiffness of robot machine; for the active vibration control, a hybrid control method combining feedforward controller and nonlinear feedback controller is introduced for chatter suppression. A dynamic model and its chatter vibration phenomena of a hybrid robot is demonstrated. Simulation results are given based on the proposed hybrid robot machine which is developed for the ITER VV assembly and maintenance

Chatter suppression methods of a robot machine for ITER vacuum vessel assembly and maintenance

Energy Technology Data Exchange (ETDEWEB)

Wu, Huapeng; Wang, Yongbo, E-mail: yongbo.wang@lut.fi; Li, Ming; Al-Saedi, Mazin; Handroos, Heikki

2014-10-15

Highlights: •A redundant 10-DOF serial-parallel hybrid robot for ITER assembly and maintains is presented. •A dynamic model of the robot is developed. •A feedback and feedforward controller is presented to suppress machining vibration of the robot. -- Abstract: In the process of assembly and maintenance of ITER vacuum vessel (ITER VV), various machining tasks including threading, milling, welding-defects cutting and flexible hose boring are required to be performed from inside of ITER VV by on-site machining tools. Robot machine is a promising option for these tasks, but great chatter (machine vibration) would happen in the machining process. The chatter vibration will deteriorate the robot accuracy and surface quality, and even cause some damages on the end-effector tools and the robot structure itself. This paper introduces two vibration control methods, one is passive and another is active vibration control. For the passive vibration control, a parallel mechanism is presented to increase the stiffness of robot machine; for the active vibration control, a hybrid control method combining feedforward controller and nonlinear feedback controller is introduced for chatter suppression. A dynamic model and its chatter vibration phenomena of a hybrid robot is demonstrated. Simulation results are given based on the proposed hybrid robot machine which is developed for the ITER VV assembly and maintenance.

Comparison between the Variational Iteration Method and the Homotopy Perturbation Method for the Sturm-Liouville Differential Equation

Directory of Open Access Journals (Sweden)

R. Darzi

2010-01-01

Full Text Available We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.

A Subspace Approach to the Structural Decomposition and Identification of Ankle Joint Dynamic Stiffness.

Science.gov (United States)

Jalaleddini, Kian; Tehrani, Ehsan Sobhani; Kearney, Robert E

2017-06-01

The purpose of this paper is to present a structural decomposition subspace (SDSS) method for decomposition of the joint torque to intrinsic, reflexive, and voluntary torques and identification of joint dynamic stiffness. First, it formulates a novel state-space representation for the joint dynamic stiffness modeled by a parallel-cascade structure with a concise parameter set that provides a direct link between the state-space representation matrices and the parallel-cascade parameters. Second, it presents a subspace method for the identification of the new state-space model that involves two steps: 1) the decomposition of the intrinsic and reflex pathways and 2) the identification of an impulse response model of the intrinsic pathway and a Hammerstein model of the reflex pathway. Extensive simulation studies demonstrate that SDSS has significant performance advantages over some other methods. Thus, SDSS was more robust under high noise conditions, converging where others failed; it was more accurate, giving estimates with lower bias and random errors. The method also worked well in practice and yielded high-quality estimates of intrinsic and reflex stiffnesses when applied to experimental data at three muscle activation levels. The simulation and experimental results demonstrate that SDSS accurately decomposes the intrinsic and reflex torques and provides accurate estimates of physiologically meaningful parameters. SDSS will be a valuable tool for studying joint stiffness under functionally important conditions. It has important clinical implications for the diagnosis, assessment, objective quantification, and monitoring of neuromuscular diseases that change the muscle tone.

Subspace-Based Noise Reduction for Speech Signals via Diagonal and Triangular Matrix Decompositions

DEFF Research Database (Denmark)

Hansen, Per Christian; Jensen, Søren Holdt

We survey the definitions and use of rank-revealing matrix decompositions in single-channel noise reduction algorithms for speech signals. Our algorithms are based on the rank-reduction paradigm and, in particular, signal subspace techniques. The focus is on practical working algorithms, using both...... diagonal (eigenvalue and singular value) decompositions and rank-revealing triangular decompositions (ULV, URV, VSV, ULLV and ULLIV). In addition we show how the subspace-based algorithms can be evaluated and compared by means of simple FIR filter interpretations. The algorithms are illustrated...... with working Matlab code and applications in speech processing....

An iterative method for obtaining the optimum lightning location on a spherical surface

Science.gov (United States)

Chao, Gao; Qiming, MA

1991-01-01

A brief introduction to the basic principles of an eigen method used to obtain the optimum source location of lightning is presented. The location of the optimum source is obtained by using multiple direction finders (DF's) on a spherical surface. An improvement of this method, which takes the distance of source-DF's as a constant, is presented. It is pointed out that using a weight factor of signal strength is not the most ideal method because of the inexact inverse signal strength-distance relation and the inaccurate signal amplitude. An iterative calculation method is presented using the distance from the source to the DF as a weight factor. This improved method has higher accuracy and needs only a little more calculation time. Some computer simulations for a 4DF system are presented to show the improvement of location through use of the iterative method.

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

Science.gov (United States)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management

Science.gov (United States)

Koleva, M. N.

2011-11-01

In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.

A Comparative Study for Orthogonal Subspace Projection and Constrained Energy Minimization

National Research Council Canada - National Science Library

Du, Qian; Ren, Hsuan; Chang, Chein-I

2003-01-01

...: orthogonal subspace projection (OSP) and constrained energy minimization (CEM). It is shown that they are closely related and essentially equivalent provided that the noise is white with large SNR...

N-screen aware multicriteria hybrid recommender system using weight based subspace clustering.

Science.gov (United States)

Ullah, Farman; Sarwar, Ghulam; Lee, Sungchang

2014-01-01

This paper presents a recommender system for N-screen services in which users have multiple devices with different capabilities. In N-screen services, a user can use various devices in different locations and time and can change a device while the service is running. N-screen aware recommendation seeks to improve the user experience with recommended content by considering the user N-screen device attributes such as screen resolution, media codec, remaining battery time, and access network and the user temporal usage pattern information that are not considered in existing recommender systems. For N-screen aware recommendation support, this work introduces a user device profile collaboration agent, manager, and N-screen control server to acquire and manage the user N-screen devices profile. Furthermore, a multicriteria hybrid framework is suggested that incorporates the N-screen devices information with user preferences and demographics. In addition, we propose an individual feature and subspace weight based clustering (IFSWC) to assign different weights to each subspace and each feature within a subspace in the hybrid framework. The proposed system improves the accuracy, precision, scalability, sparsity, and cold start issues. The simulation results demonstrate the effectiveness and prove the aforementioned statements.

Worst-case Analysis of Strategy Iteration and the Simplex Method

DEFF Research Database (Denmark)

Hansen, Thomas Dueholm

In this dissertation we study strategy iteration (also known as policy iteration) algorithms for solving Markov decision processes (MDPs) and two-player turn-based stochastic games (2TBSGs). MDPs provide a mathematical model for sequential decision making under uncertainty. They are widely used...... to model stochastic optimization problems in various areas ranging from operations research, machine learning, artificial intelligence, economics and game theory. The class of two-player turn-based stochastic games is a natural generalization of Markov decision processes that is obtained by introducing...... in the size of the problem (the bounds have subexponential form). Utilizing a tight connection between MDPs and linear programming, it is shown that the same bounds apply to the corresponding pivoting rules for the simplex method for solving linear programs. Prior to this result no super-polynomial lower...

Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes.

Science.gov (United States)

Hudson, H M; Ma, J; Green, P

1994-01-01

Many algorithms for medical image reconstruction adopt versions of the expectation-maximization (EM) algorithm. In this approach, parameter estimates are obtained which maximize a complete data likelihood or penalized likelihood, in each iteration. Implicitly (and sometimes explicitly) penalized algorithms require smoothing of the current reconstruction in the image domain as part of their iteration scheme. In this paper, we discuss alternatives to EM which adapt Fisher's method of scoring (FS) and other methods for direct maximization of the incomplete data likelihood. Jacobi and Gauss-Seidel methods for non-linear optimization provide efficient algorithms applying FS in tomography. One approach uses smoothed projection data in its iterations. We investigate the convergence of Jacobi and Gauss-Seidel algorithms with clinical tomographic projection data.

An efficient iterative method for the generalized Stokes problem

Energy Technology Data Exchange (ETDEWEB)

Sameh, A. [Univ. of Minnesota, Twin Cities, MN (United States); Sarin, V. [Univ. of Illinois, Urbana, IL (United States)

1996-12-31

This paper presents an efficient iterative scheme for the generalized Stokes problem, which arises frequently in the simulation of time-dependent Navier-Stokes equations for incompressible fluid flow. The general form of the linear system is where A = {alpha}M + vT is an n x n symmetric positive definite matrix, in which M is the mass matrix, T is the discrete Laplace operator, {alpha} and {nu} are positive constants proportional to the inverses of the time-step {Delta}t and the Reynolds number Re respectively, and B is the discrete gradient operator of size n x k (k < n). Even though the matrix A is symmetric and positive definite, the system is indefinite due to the incompressibility constraint (B{sup T}u = 0). This causes difficulties both for iterative methods and commonly used preconditioners. Moreover, depending on the ratio {alpha}/{nu}, A behaves like the mass matrix M at one extreme and the Laplace operator T at the other, thus complicating the issue of preconditioning.

He's variational iteration method applied to the solution of the prey and predator problem with variable coefficients

International Nuclear Information System (INIS)

Yusufoglu, Elcin; Erbas, Baris

2008-01-01

In this Letter, a mathematical model of the problem of prey and predator is presented and He's variational iteration method is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. The results are compared with the results obtained by Adomian decomposition method and homotopy perturbation method. Comparison of the methods show that He's variational iteration method is a powerful method for obtaining approximate solutions to nonlinear equations and their systems

A sparsity-regularized Born iterative method for reconstruction of two-dimensional piecewise continuous inhomogeneous domains

KAUST Repository

Sandhu, Ali Imran

2016-04-10

A sparsity-regularized Born iterative method (BIM) is proposed for efficiently reconstructing two-dimensional piecewise-continuous inhomogeneous dielectric profiles. Such profiles are typically not spatially sparse, which reduces the efficiency of the sparsity-promoting regularization. To overcome this problem, scattered fields are represented in terms of the spatial derivative of the dielectric profile and reconstruction is carried out over samples of the dielectric profile\\'s derivative. Then, like the conventional BIM, the nonlinear problem is iteratively converted into a sequence of linear problems (in derivative samples) and sparsity constraint is enforced on each linear problem using the thresholded Landweber iterations. Numerical results, which demonstrate the efficiency and accuracy of the proposed method in reconstructing piecewise-continuous dielectric profiles, are presented.

Lie n-derivations on 7 -subspace lattice algebras

Indian Academy of Sciences (India)

all x ∈ K and all A ∈ Alg L. Based on this result, a complete characterization of linear n-Lie derivations on Alg L is obtained. Keywords. J -subspace lattice algebras; Lie derivations; Lie n-derivations; derivations. 2010 Mathematics Subject Classification. 47B47, 47L35. 1. Introduction. Let A be an algebra. Recall that a linear ...

Reverse time migration by Krylov subspace reduced order modeling

Science.gov (United States)

Basir, Hadi Mahdavi; Javaherian, Abdolrahim; Shomali, Zaher Hossein; Firouz-Abadi, Roohollah Dehghani; Gholamy, Shaban Ali

2018-04-01

Imaging is a key step in seismic data processing. To date, a myriad of advanced pre-stack depth migration approaches have been developed; however, reverse time migration (RTM) is still considered as the high-end imaging algorithm. The main limitations associated with the performance cost of reverse time migration are the intensive computation of the forward and backward simulations, time consumption, and memory allocation related to imaging condition. Based on the reduced order modeling, we proposed an algorithm, which can be adapted to all the aforementioned factors. Our proposed method benefit from Krylov subspaces method to compute certain mode shapes of the velocity model computed by as an orthogonal base of reduced order modeling. Reverse time migration by reduced order modeling is helpful concerning the highly parallel computation and strongly reduces the memory requirement of reverse time migration. The synthetic model results showed that suggested method can decrease the computational costs of reverse time migration by several orders of magnitudes, compared with reverse time migration by finite element method.

An angle-based subspace anomaly detection approach to high-dimensional data: With an application to industrial fault detection

International Nuclear Information System (INIS)

Zhang, Liangwei; Lin, Jing; Karim, Ramin

2015-01-01

The accuracy of traditional anomaly detection techniques implemented on full-dimensional spaces degrades significantly as dimensionality increases, thereby hampering many real-world applications. This work proposes an approach to selecting meaningful feature subspace and conducting anomaly detection in the corresponding subspace projection. The aim is to maintain the detection accuracy in high-dimensional circumstances. The suggested approach assesses the angle between all pairs of two lines for one specific anomaly candidate: the first line is connected by the relevant data point and the center of its adjacent points; the other line is one of the axis-parallel lines. Those dimensions which have a relatively small angle with the first line are then chosen to constitute the axis-parallel subspace for the candidate. Next, a normalized Mahalanobis distance is introduced to measure the local outlier-ness of an object in the subspace projection. To comprehensively compare the proposed algorithm with several existing anomaly detection techniques, we constructed artificial datasets with various high-dimensional settings and found the algorithm displayed superior accuracy. A further experiment on an industrial dataset demonstrated the applicability of the proposed algorithm in fault detection tasks and highlighted another of its merits, namely, to provide preliminary interpretation of abnormality through feature ordering in relevant subspaces. - Highlights: • An anomaly detection approach for high-dimensional reliability data is proposed. • The approach selects relevant subspaces by assessing vectorial angles. • The novel ABSAD approach displays superior accuracy over other alternatives. • Numerical illustration approves its efficacy in fault detection applications

Multiple Revolution Solutions for the Perturbed Lambert Problem using the Method of Particular Solutions and Picard Iteration

Science.gov (United States)

Woollands, Robyn M.; Read, Julie L.; Probe, Austin B.; Junkins, John L.

2017-12-01

We present a new method for solving the multiple revolution perturbed Lambert problem using the method of particular solutions and modified Chebyshev-Picard iteration. The method of particular solutions differs from the well-known Newton-shooting method in that integration of the state transition matrix (36 additional differential equations) is not required, and instead it makes use of a reference trajectory and a set of n particular solutions. Any numerical integrator can be used for solving two-point boundary problems with the method of particular solutions, however we show that using modified Chebyshev-Picard iteration affords an avenue for increased efficiency that is not available with other step-by-step integrators. We take advantage of the path approximation nature of modified Chebyshev-Picard iteration (nodes iteratively converge to fixed points in space) and utilize a variable fidelity force model for propagating the reference trajectory. Remarkably, we demonstrate that computing the particular solutions with only low fidelity function evaluations greatly increases the efficiency of the algorithm while maintaining machine precision accuracy. Our study reveals that solving the perturbed Lambert's problem using the method of particular solutions with modified Chebyshev-Picard iteration is about an order of magnitude faster compared with the classical shooting method and a tenth-twelfth order Runge-Kutta integrator. It is well known that the solution to Lambert's problem over multiple revolutions is not unique and to ensure that all possible solutions are considered we make use of a reliable preexisting Keplerian Lambert solver to warm start our perturbed algorithm.

Recursive subspace identification for in flight modal analysis of airplanes

OpenAIRE

De Cock , Katrien; Mercère , Guillaume; De Moor , Bart

2006-01-01

International audience; In this paper recursive subspace identification algorithms are applied to track the modal parameters of airplanes on-line during test flights. The ability to track changes in the damping ratios and the influence of the forgetting factor are studied through simulations.

AN ITERATIVE SEGMENTATION METHOD FOR REGION OF INTEREST EXTRACTION

Directory of Open Access Journals (Sweden)

Volkan CETIN

2013-01-01

Full Text Available In this paper, a method is presented for applications which include mammographic image segmentation and region of interest extraction. Segmentation is a very critical and difficult stage to accomplish in computer aided detection systems. Although the presented segmentation method is developed for mammographic images, it can be used for any medical image which resembles the same statistical characteristics with mammograms. Fundamentally, the method contains iterative automatic thresholding and masking operations which is applied to the original or enhanced mammograms. Also the effect of image enhancement to the segmentation process was observed. A version of histogram equalization was applied to the images for enhancement. Finally, the results show that enhanced version of the proposed segmentation method is preferable because of its better success rate.

A superlinear iteration method for calculation of finite length journal bearing's static equilibrium position

Science.gov (United States)

Zhou, Wenjie; Wei, Xuesong; Wang, Leqin; Wu, Guangkuan

2017-05-01

Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method-twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length.

Design and fabrication methods of FW/blanket, divertor and vacuum vessel for ITER

Science.gov (United States)

Ioki, K.; Barabash, V.; Cardella, A.; Elio, F.; Ibbott, C.; Janeschitz, G.; Johnson, G.; Kalinin, G.; Miki, N.; Onozuka, M.; Sannazzaro, G.; Tivey, R.; Utin, Y.; Yamada, M.

2000-12-01

Design has progressed on the vacuum vessel, FW/blanket and Divertor for the Reduced Technical Objective/Reduced Cost (RTO/RC) ITER. The basic functions and structures are the same as for the 1998 ITER design [K. Ioki et al., J. Nucl. Mater. 258-263 (1998) 74]. Design and fabrication methods of the components have been improved to achieve ˜50% reduction of the construction cost. Detailed blanket module designs with flat separable FW panels have been developed to reduce the fabrication cost and the future radioactive waste. Most of the R&D performed so far during the Engineering Design Activities (EDAs) are still applicable. Further cost reduction methods are also being investigated and additional R&D is being performed.

Iterative convergence acceleration of neutral particle transport methods via adjacent-cell preconditioners

International Nuclear Information System (INIS)

Azmy, Y.Y.

1999-01-01

The author proposes preconditioning as a viable acceleration scheme for the inner iterations of transport calculations in slab geometry. In particular he develops Adjacent-Cell Preconditioners (AP) that have the same coupling stencil as cell-centered diffusion schemes. For lowest order methods, e.g., Diamond Difference, Step, and 0-order Nodal Integral Method (ONIM), cast in a Weighted Diamond Difference (WDD) form, he derives AP for thick (KAP) and thin (NAP) cells that for model problems are unconditionally stable and efficient. For the First-Order Nodal Integral Method (INIM) he derives a NAP that possesses similarly excellent spectral properties for model problems. The two most attractive features of the new technique are:(1) its cell-centered coupling stencil, which makes it more adequate for extension to multidimensional, higher order situations than the standard edge-centered or point-centered Diffusion Synthetic Acceleration (DSA) methods; and (2) its decreasing spectral radius with increasing cell thickness to the extent that immediate pointwise convergence, i.e., in one iteration, can be achieved for problems with sufficiently thick cells. He implemented these methods, augmented with appropriate boundary conditions and mixing formulas for material heterogeneities, in the test code APID that he uses to successfully verify the analytical spectral properties for homogeneous problems. Furthermore, he conducts numerical tests to demonstrate the robustness of the KAP and NAP in the presence of sharp mesh or material discontinuities. He shows that the AP for WDD is highly resilient to such discontinuities, but for INIM a few cases occur in which the scheme does not converge; however, when it converges, AP greatly reduces the number of iterations required to achieve convergence

A study on linear and nonlinear Schrodinger equations by the variational iteration method

International Nuclear Information System (INIS)

Wazwaz, Abdul-Majid

2008-01-01

In this work, we introduce a framework to obtain exact solutions to linear and nonlinear Schrodinger equations. The He's variational iteration method (VIM) is used for analytic treatment of these equations. Numerical examples are tested to show the pertinent features of this method

The Davidson Method as an alternative to power iterations for criticality calculations

International Nuclear Information System (INIS)

Subramanian, C.; Van Criekingen, S.; Heuveline, V.; Nataf, F.; Have, P.

2011-01-01

The Davidson method is implemented within the neutron transport core solver parafish to solve k-eigenvalue criticality transport problems. The parafish solver is based on domain decomposition, uses spherical harmonics (P_N method) for angular discretization, and nonconforming finite elements for spatial discretization. The Davidson method is compared to the traditional power iteration method in that context. Encouraging numerical results are obtained with both sequential and parallel calculations. (author)

Iterative solutions of finite difference diffusion equations

International Nuclear Information System (INIS)

Menon, S.V.G.; Khandekar, D.C.; Trasi, M.S.

1981-01-01

The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)

Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction.

Science.gov (United States)

Nikazad, T; Davidi, R; Herman, G T

2012-03-01

We study the convergence of a class of accelerated perturbation-resilient block-iterative projection methods for solving systems of linear equations. We prove convergence to a fixed point of an operator even in the presence of summable perturbations of the iterates, irrespective of the consistency of the linear system. For a consistent system, the limit point is a solution of the system. In the inconsistent case, the symmetric version of our method converges to a weighted least squares solution. Perturbation resilience is utilized to approximate the minimum of a convex functional subject to the equations. A main contribution, as compared to previously published approaches to achieving similar aims, is a more than an order of magnitude speed-up, as demonstrated by applying the methods to problems of image reconstruction from projections. In addition, the accelerated algorithms are illustrated to be better, in a strict sense provided by the method of statistical hypothesis testing, than their unaccelerated versions for the task of detecting small tumors in the brain from X-ray CT projection data.

An iterative stochastic ensemble method for parameter estimation of subsurface flow models

International Nuclear Information System (INIS)

Elsheikh, Ahmed H.; Wheeler, Mary F.; Hoteit, Ibrahim

2013-01-01

Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss–Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates

An iterative stochastic ensemble method for parameter estimation of subsurface flow models

KAUST Repository

Elsheikh, Ahmed H.

2013-06-01

Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss-Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier Inc.

Double folding model of nucleus-nucleus potential: formulae, iteration method and computer code

International Nuclear Information System (INIS)

Luk'yanov, K.V.

2008-01-01

Method of construction of the nucleus-nucleus double folding potential is described. Iteration procedure for the corresponding integral equation is presented. Computer code and numerical results are presented

Joint 2D-DOA and Frequency Estimation for L-Shaped Array Using Iterative Least Squares Method

Directory of Open Access Journals (Sweden)

Ling-yun Xu

2012-01-01

Full Text Available We introduce an iterative least squares method (ILS for estimating the 2D-DOA and frequency based on L-shaped array. The ILS iteratively finds direction matrix and delay matrix, then 2D-DOA and frequency can be obtained by the least squares method. Without spectral peak searching and pairing, this algorithm works well and pairs the parameters automatically. Moreover, our algorithm has better performance than conventional ESPRIT algorithm and propagator method. The useful behavior of the proposed algorithm is verified by simulations.

Removing Ocular Movement Artefacts by a Joint Smoothened Subspace Estimator

Directory of Open Access Journals (Sweden)

Ronald Phlypo

2007-01-01

Full Text Available To cope with the severe masking of background cerebral activity in the electroencephalogram (EEG by ocular movement artefacts, we present a method which combines lower-order, short-term and higher-order, long-term statistics. The joint smoothened subspace estimator (JSSE calculates the joint information in both statistical models, subject to the constraint that the resulting estimated source should be sufficiently smooth in the time domain (i.e., has a large autocorrelation or self predictive power. It is shown that the JSSE is able to estimate a component from simulated data that is superior with respect to methodological artefact suppression to those of FastICA, SOBI, pSVD, or JADE/COM1 algorithms used for blind source separation (BSS. Interference and distortion suppression are of comparable order when compared with the above-mentioned methods. Results on patient data demonstrate that the method is able to suppress blinking and saccade artefacts in a fully automated way.

Multiscale optical simulation settings: challenging applications handled with an iterative ray-tracing FDTD interface method.

Science.gov (United States)

Leiner, Claude; Nemitz, Wolfgang; Schweitzer, Susanne; Kuna, Ladislav; Wenzl, Franz P; Hartmann, Paul; Satzinger, Valentin; Sommer, Christian

2016-03-20

We show that with an appropriate combination of two optical simulation techniques-classical ray-tracing and the finite difference time domain method-an optical device containing multiple diffractive and refractive optical elements can be accurately simulated in an iterative simulation approach. We compare the simulation results with experimental measurements of the device to discuss the applicability and accuracy of our iterative simulation procedure.

Quantum cloning of mixed states in symmetric subspaces

International Nuclear Information System (INIS)

Fan Heng

2003-01-01

Quantum-cloning machine for arbitrary mixed states in symmetric subspaces is proposed. This quantum-cloning machine can be used to copy part of the output state of another quantum-cloning machine and is useful in quantum computation and quantum information. The shrinking factor of this quantum cloning achieves the well-known upper bound. When the input is identical pure states, two different fidelities of this cloning machine are optimal

A holistic calibration method with iterative distortion compensation for stereo deflectometry

Science.gov (United States)

Xu, Yongjia; Gao, Feng; Zhang, Zonghua; Jiang, Xiangqian

2018-07-01

This paper presents a novel holistic calibration method for stereo deflectometry system to improve the system measurement accuracy. The reconstruction result of stereo deflectometry is integrated with the calculated normal data of the measured surface. The calculation accuracy of the normal data is seriously influenced by the calibration accuracy of the geometrical relationship of the stereo deflectometry system. Conventional calibration approaches introduce form error to the system due to inaccurate imaging model and distortion elimination. The proposed calibration method compensates system distortion based on an iterative algorithm instead of the conventional distortion mathematical model. The initial value of the system parameters are calculated from the fringe patterns displayed on the systemic LCD screen through a reflection of a markless flat mirror. An iterative algorithm is proposed to compensate system distortion and optimize camera imaging parameters and system geometrical relation parameters based on a cost function. Both simulation work and experimental results show the proposed calibration method can significantly improve the calibration and measurement accuracy of a stereo deflectometry. The PV (peak value) of measurement error of a flat mirror can be reduced to 69.7 nm by applying the proposed method from 282 nm obtained with the conventional calibration approach.

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

Application of He's variational iteration method to the fifth-order boundary value problems

International Nuclear Information System (INIS)

Shen, S

2008-01-01

Variational iteration method is introduced to solve the fifth-order boundary value problems. This method provides an efficient approach to solve this type of problems without discretization and the computation of the Adomian polynomials. Numerical results demonstrate that this method is a promising and powerful tool for solving the fifth-order boundary value problems

Design and fabrication methods of FW/blanket, divertor and vacuum vessel for ITER

International Nuclear Information System (INIS)

Ioki, K.; Barabash, V.; Cardella, A.; Elio, F.; Ibbott, C.; Janeschitz, G.; Johnson, G.; Kalinin, G.; Miki, N.; Onozuka, M.; Sannazzaro, G.; Tivey, R.; Utin, Y.; Yamada, M.

2000-01-01

Design has progressed on the vacuum vessel, FW/blanket and Divertor for the Reduced Technical Objective/Reduced Cost (RTO/RC) ITER. The basic functions and structures are the same as for the 1998 ITER design [K. Ioki et al., J. Nucl. Mater. 258-263 (1998) 74]. Design and fabrication methods of the components have been improved to achieve ∼50% reduction of the construction cost. Detailed blanket module designs with flat separable FW panels have been developed to reduce the fabrication cost and the future radioactive waste. Most of the R and D performed so far during the Engineering Design Activities (EDAs) are still applicable. Further cost reduction methods are also being investigated and additional R and D is being performed

Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

International Nuclear Information System (INIS)

Dmitriy Y. Anistratov; Adrian Constantinescu; Loren Roberts; William Wieselquist

2007-01-01

This is a project in the field of fundamental research on numerical methods for solving the particle transport equation. Numerous practical problems require to use unstructured meshes, for example, detailed nuclear reactor assembly-level calculations, large-scale reactor core calculations, radiative hydrodynamics problems, where the mesh is determined by hydrodynamic processes, and well-logging problems in which the media structure has very complicated geometry. Currently this is an area of very active research in numerical transport theory. main issues in developing numerical methods for solving the transport equation are the accuracy of the numerical solution and effectiveness of iteration procedure. The problem in case of unstructured grids is that it is very difficult to derive an iteration algorithm that will be unconditionally stable

Design and fabrication methods of FW/blanket, divertor and vacuum vessel for ITER

Energy Technology Data Exchange (ETDEWEB)

Ioki, K. E-mail: iokik@itereu.deiokik@ipp.mpg.de; Barabash, V.; Cardella, A.; Elio, F.; Ibbott, C.; Janeschitz, G.; Johnson, G.; Kalinin, G.; Miki, N.; Onozuka, M.; Sannazzaro, G.; Tivey, R.; Utin, Y.; Yamada, M

2000-12-01

Design has progressed on the vacuum vessel, FW/blanket and Divertor for the Reduced Technical Objective/Reduced Cost (RTO/RC) ITER. The basic functions and structures are the same as for the 1998 ITER design [K. Ioki et al., J. Nucl. Mater. 258-263 (1998) 74]. Design and fabrication methods of the components have been improved to achieve {approx}50% reduction of the construction cost. Detailed blanket module designs with flat separable FW panels have been developed to reduce the fabrication cost and the future radioactive waste. Most of the R and D performed so far during the Engineering Design Activities (EDAs) are still applicable. Further cost reduction methods are also being investigated and additional R and D is being performed.

Maxwell iteration for the lattice Boltzmann method with diffusive scaling

Science.gov (United States)

Zhao, Weifeng; Yong, Wen-An

2017-03-01

In this work, we present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook models of the lattice Boltzmann method with diffusive scaling. This derivation is based on the Maxwell iteration and can expose certain important features of the lattice Boltzmann solutions. Moreover, it will be seen to be much more straightforward and logically clearer than the existing approaches including the Chapman-Enskog expansion.

Vinayaka : A Semi-Supervised Projected Clustering Method Using Differential Evolution

OpenAIRE

Satish Gajawada; Durga Toshniwal

2012-01-01

Differential Evolution (DE) is an algorithm for evolutionary optimization. Clustering problems have beensolved by using DE based clustering methods but these methods may fail to find clusters hidden insubspaces of high dimensional datasets. Subspace and projected clustering methods have been proposed inliterature to find subspace clusters that are present in subspaces of dataset. In this paper we proposeVINAYAKA, a semi-supervised projected clustering method based on DE. In this method DE opt...

The Regularized Iteratively Reweighted MAD Method for Change Detection in Multi- and Hyperspectral Data

DEFF Research Database (Denmark)

Nielsen, Allan Aasbjerg

2007-01-01

This paper describes new extensions to the previously published multivariate alteration detection (MAD) method for change detection in bi-temporal, multi- and hypervariate data such as remote sensing imagery. Much like boosting methods often applied in data mining work, the iteratively reweighted...... to observations that show little change, i.e., for which the sum of squared, standardized MAD variates is small, and small weights are assigned to observations for which the sum is large. Like the original MAD method, the iterative extension is invariant to linear (affine) transformations of the original...... an agricultural region in Kenya, and hyperspectral airborne HyMap data from a small rural area in southeastern Germany are given. The latter case demonstrates the need for regularization....

Iterative solution of the inverse Cauchy problem for an elliptic equation by the conjugate gradient method

Science.gov (United States)

Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.

2017-10-01

This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution

Improved fixed point iterative method for blade element momentum computations

DEFF Research Database (Denmark)

Sun, Zhenye; Shen, Wen Zhong; Chen, Jin

2017-01-01

The blade element momentum (BEM) theory is widely used in aerodynamic performance calculations and optimization applications for wind turbines. The fixed point iterative method is the most commonly utilized technique to solve the BEM equations. However, this method sometimes does not converge...... are addressed through both theoretical analysis and numerical tests. A term from the BEM equations equals to zero at a critical inflow angle is the source of the convergence problems. When the initial inflow angle is set larger than the critical inflow angle and the relaxation methodology is adopted...

Acceleration of the AFEN method by two-node nonlinear iteration

Energy Technology Data Exchange (ETDEWEB)

Moon, Kap Suk; Cho, Nam Zin; Noh, Jae Man; Hong, Ser Gi [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1999-12-31

A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AFEN method and the computing time is significantly reduced in comparison with the original AFEN method. 7 refs., 1 fig., 1 tab. (Author)

Acceleration of the AFEN method by two-node nonlinear iteration

Energy Technology Data Exchange (ETDEWEB)

Moon, Kap Suk; Cho, Nam Zin; Noh, Jae Man; Hong, Ser Gi [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1998-12-31

A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AFEN method and the computing time is significantly reduced in comparison with the original AFEN method. 7 refs., 1 fig., 1 tab. (Author)

Iterative methods for dose reduction and image enhancement in tomography

Science.gov (United States)

Miao, Jianwei; Fahimian, Benjamin Pooya

2012-09-18

A system and method for creating a three dimensional cross sectional image of an object by the reconstruction of its projections that have been iteratively refined through modification in object space and Fourier space is disclosed. The invention provides systems and methods for use with any tomographic imaging system that reconstructs an object from its projections. In one embodiment, the invention presents a method to eliminate interpolations present in conventional tomography. The method has been experimentally shown to provide higher resolution and improved image quality parameters over existing approaches. A primary benefit of the method is radiation dose reduction since the invention can produce an image of a desired quality with a fewer number projections than seen with conventional methods.

Von Neumann algebras as complemented subspaces of B(H)

DEFF Research Database (Denmark)

Christensen, Erik; Wang, Liguang

2014-01-01

Let M be a von Neumann algebra of type II1 which is also a complemented subspace of B( H). We establish an algebraic criterion, which ensures that M is an injective von Neumann algebra. As a corollary we show that if M is a complemented factor of type II1 on a Hilbert space H, then M is injective...

Embeddings of model subspaces of the Hardy space: compactness and Schatten-von Neumann ideals

International Nuclear Information System (INIS)

Baranov, Anton D

2009-01-01

We study properties of the embedding operators of model subspaces K p Θ (defined by inner functions) in the Hardy space H p (coinvariant subspaces of the shift operator). We find a criterion for the embedding of K p Θ in L p (μ) to be compact similar to the Volberg-Treil theorem on bounded embeddings, and give a positive answer to a question of Cima and Matheson. The proof is based on Bernstein-type inequalities for functions in K p Θ . We investigate measures μ such that the embedding operator belongs to some Schatten-von Neumann ideal.

An iterative method for Tikhonov regularization with a general linear regularization operator

NARCIS (Netherlands)

Hochstenbach, M.E.; Reichel, L.

2010-01-01

Tikhonov regularization is one of the most popular approaches to solve discrete ill-posed problems with error-contaminated data. A regularization operator and a suitable value of a regularization parameter have to be chosen. This paper describes an iterative method, based on Golub-Kahan

ITER...ation

International Nuclear Information System (INIS)

Troyon, F.

1997-01-01

Recurrent attacks against ITER, the new generation of tokamak are a mix of political and scientific arguments. This short article draws a historical review of the European fusion program. This program has allowed to build and manage several installations in the aim of getting experimental results necessary to lead the program forwards. ITER will bring together a fusion reactor core with technologies such as materials, superconductive coils, heating devices and instrumentation in order to validate and delimit the operating range. ITER will be a logical and decisive step towards the use of controlled fusion. (A.C.)

Application of Earthquake Subspace Detectors at Kilauea and Mauna Loa Volcanoes, Hawai`i

Science.gov (United States)

Okubo, P.; Benz, H.; Yeck, W.

2016-12-01

Recent studies have demonstrated the capabilities of earthquake subspace detectors for detailed cataloging and tracking of seismicity in a number of regions and settings. We are exploring the application of subspace detectors at the United States Geological Survey's Hawaiian Volcano Observatory (HVO) to analyze seismicity at Kilauea and Mauna Loa volcanoes. Elevated levels of microseismicity and occasional swarms of earthquakes associated with active volcanism here present cataloging challenges due the sheer numbers of earthquakes and an intrinsically low signal-to-noise environment featuring oceanic microseism and volcanic tremor in the ambient seismic background. With high-quality continuous recording of seismic data at HVO, we apply subspace detectors (Harris and Dodge, 2011, Bull. Seismol. Soc. Am., doi: 10.1785/0120100103) during intervals of noteworthy seismicity. Waveform templates are drawn from Magnitude 2 and larger earthquakes within clusters of earthquakes cataloged in the HVO seismic database. At Kilauea, we focus on seismic swarms in the summit caldera region where, despite continuing eruptions from vents in the summit region and in the east rift zone, geodetic measurements reflect a relatively inflated volcanic state. We also focus on seismicity beneath and adjacent to Mauna Loa's summit caldera that appears to be associated with geodetic expressions of gradual volcanic inflation, and where precursory seismicity clustered prior to both Mauna Loa's most recent eruptions in 1975 and 1984. We recover several times more earthquakes with the subspace detectors - down to roughly 2 magnitude units below the templates, based on relative amplitudes - compared to the numbers of cataloged earthquakes. The increased numbers of detected earthquakes in these clusters, and the ability to associate and locate them, allow us to infer details of the spatial and temporal distributions and possible variations in stresses within these key regions of the volcanoes.

Discrete-State Stochastic Models of Calcium-Regulated Calcium Influx and Subspace Dynamics Are Not Well-Approximated by ODEs That Neglect Concentration Fluctuations

Science.gov (United States)

Weinberg, Seth H.; Smith, Gregory D.

2012-01-01

Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough (e.g., 10−17 liters) that local signaling may involve 1–100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result that accounts for the small subspace volume) with the corresponding deterministic model (an approximation that assumes large system size). When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers. PMID:23509597

Preconditioned iterations to calculate extreme eigenvalues

Energy Technology Data Exchange (ETDEWEB)

Brand, C.W.; Petrova, S. [Institut fuer Angewandte Mathematik, Leoben (Austria)

1994-12-31

Common iterative algorithms to calculate a few extreme eigenvalues of a large, sparse matrix are Lanczos methods or power iterations. They converge at a rate proportional to the separation of the extreme eigenvalues from the rest of the spectrum. Appropriate preconditioning improves the separation of the eigenvalues. Davidson`s method and its generalizations exploit this fact. The authors examine a preconditioned iteration that resembles a truncated version of Davidson`s method with a different preconditioning strategy.

An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

Science.gov (United States)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

Comparing performance of standard and iterative linear unmixing methods for hyperspectral signatures

Science.gov (United States)

Gault, Travis R.; Jansen, Melissa E.; DeCoster, Mallory E.; Jansing, E. David; Rodriguez, Benjamin M.

2016-05-01

Linear unmixing is a method of decomposing a mixed signature to determine the component materials that are present in sensor's field of view, along with the abundances at which they occur. Linear unmixing assumes that energy from the materials in the field of view is mixed in a linear fashion across the spectrum of interest. Traditional unmixing methods can take advantage of adjacent pixels in the decomposition algorithm, but is not the case for point sensors. This paper explores several iterative and non-iterative methods for linear unmixing, and examines their effectiveness at identifying the individual signatures that make up simulated single pixel mixed signatures, along with their corresponding abundances. The major hurdle addressed in the proposed method is that no neighboring pixel information is available for the spectral signature of interest. Testing is performed using two collections of spectral signatures from the Johns Hopkins University Applied Physics Laboratory's Signatures Database software (SigDB): a hand-selected small dataset of 25 distinct signatures from a larger dataset of approximately 1600 pure visible/near-infrared/short-wave-infrared (VIS/NIR/SWIR) spectra. Simulated spectra are created with three and four material mixtures randomly drawn from a dataset originating from SigDB, where the abundance of one material is swept in 10% increments from 10% to 90%with the abundances of the other materials equally divided amongst the remainder. For the smaller dataset of 25 signatures, all combinations of three or four materials are used to create simulated spectra, from which the accuracy of materials returned, as well as the correctness of the abundances, is compared to the inputs. The experiment is expanded to include the signatures from the larger dataset of almost 1600 signatures evaluated using a Monte Carlo scheme with 5000 draws of three or four materials to create the simulated mixed signatures. The spectral similarity of the inputs to the

The steady performance prediction of propeller-rudder-bulb system based on potential iterative method

International Nuclear Information System (INIS)

Liu, Y B; Su, Y M; Ju, L; Huang, S L

2012-01-01

A new numerical method was developed for predicting the steady hydrodynamic performance of propeller-rudder-bulb system. In the calculation, the rudder and bulb was taken into account as a whole, the potential based surface panel method was applied both to propeller and rudder-bulb system. The interaction between propeller and rudder-bulb was taken into account by velocity potential iteration in which the influence of propeller rotation was considered by the average influence coefficient. In the influence coefficient computation, the singular value should be found and deleted. Numerical results showed that the method presented is effective for predicting the steady hydrodynamic performance of propeller-rudder system and propeller-rudder-bulb system. Comparing with the induced velocity iterative method, the method presented can save programming and calculation time. Changing dimensions, the principal parameter—bulb size that affect energy-saving effect was studied, the results show that the bulb on rudder have a optimal size at the design advance coefficient.

A convergence analysis of the iteratively regularized Gauss–Newton method under the Lipschitz condition

International Nuclear Information System (INIS)

Jin Qinian

2008-01-01

In this paper we consider the iteratively regularized Gauss–Newton method for solving nonlinear ill-posed inverse problems. Under merely the Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an order optimal regularization method if the solution is regular in some suitable sense

Time-domain simulations for metallic nano-structures - a Krylov-subspace approach beyond the limitations of FDTD

Energy Technology Data Exchange (ETDEWEB)

Koenig, Michael [Institut fuer Theoretische Festkoerperphysik, Universitaet Karlsruhe (Germany); Karlsruhe School of Optics and Photonics (KSOP), Universitaet Karlsruhe (Germany); Niegemann, Jens; Tkeshelashvili, Lasha; Busch, Kurt [Institut fuer Theoretische Festkoerperphysik, Universitaet Karlsruhe (Germany); DFG Forschungszentrum Center for Functional Nanostructures (CFN), Universitaet Karlsruhe (Germany); Karlsruhe School of Optics and Photonics (KSOP), Universitaet Karlsruhe (Germany)

2008-07-01

Numerical simulations of metallic nano-structures are crucial for the efficient design of plasmonic devices. Conventional time-domain solvers such as FDTD introduce large numerical errors especially at metallic surfaces. Our approach combines a discontinuous Galerkin method on an adaptive mesh for the spatial discretisation with a Krylov-subspace technique for the time-stepping procedure. Thus, the higher-order accuracy in both time and space is supported by unconditional stability. As illustrative examples, we compare numerical results obtained with our method against analytical reference solutions and results from FDTD calculations.

Diffeomorphic Iterative Centroid Methods for Template Estimation on Large Datasets

OpenAIRE

Cury , Claire; Glaunès , Joan Alexis; Colliot , Olivier

2014-01-01

International audience; A common approach for analysis of anatomical variability relies on the stimation of a template representative of the population. The Large Deformation Diffeomorphic Metric Mapping is an attractive framework for that purpose. However, template estimation using LDDMM is computationally expensive, which is a limitation for the study of large datasets. This paper presents an iterative method which quickly provides a centroid of the population in the shape space. This centr...

Index Formulae for Subspaces of Kreĭn Spaces

NARCIS (Netherlands)

Dijksma, Aad; Gheondea, Aurelian

1996-01-01

For a subspace S of a Kreĭn space K and an arbitrary fundamental decomposition K = K-[+]K+ of K, we prove the index formula κ-(S) + dim(S⊥ ∩ K+) = κ+(S⊥) + dim(S ∩ K-), where κ±(S) stands for the positive/negative signature of S. The difference dim(S ∩ K-) - dim(S⊥ ∩ K+), provided it is well

Iterative Method of Regularization with Application of Advanced Technique for Detection of Contours

International Nuclear Information System (INIS)

Niedziela, T.; Stankiewicz, A.

2000-01-01

This paper proposes a novel iterative method of regularization with application of an advanced technique for detection of contours. To eliminate noises, the properties of convolution of functions are utilized. The method can be accomplished in a simple neural cellular network, which creates the possibility of extraction of contours by automatic image recognition equipment. (author)

Iterative numerical solution of scattering problems

International Nuclear Information System (INIS)

Tomio, L.; Adhikari, S.K.

1995-05-01

An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10 10 after some-8-10 iterations. (author). 31 refs, 2 tabs

Iterative methods used in overlap astrometric reduction techniques do not always converge

Science.gov (United States)

Rapaport, M.; Ducourant, C.; Colin, J.; Le Campion, J. F.

1993-04-01

In this paper we prove that the classical Gauss-Seidel type iterative methods used for the solution of the reduced normal equations occurring in overlapping reduction methods of astrometry do not always converge. We exhibit examples of divergence. We then analyze an alternative algorithm proposed by Wang (1985). We prove the consistency of this algorithm and verify that it can be convergent while the Gauss-Seidel method is divergent. We conjecture the convergence of Wang method for the solution of astrometric problems using overlap techniques.

Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

Science.gov (United States)

Lavery, N.; Taylor, C.

1999-07-01

Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright

A comparison between progressive extension method (PEM) and iterative method (IM) for magnetic field extrapolations in the solar atmosphere

Science.gov (United States)

Wu, S. T.; Sun, M. T.; Sakurai, Takashi

1990-01-01

This paper presents a comparison between two numerical methods for the extrapolation of nonlinear force-free magnetic fields, viz the Iterative Method (IM) and the Progressive Extension Method (PEM). The advantages and disadvantages of these two methods are summarized, and the accuracy and numerical instability are discussed. On the basis of this investigation, it is claimed that the two methods do resemble each other qualitatively.

Output-only cyclo-stationary linear-parameter time-varying stochastic subspace identification method for rotating machinery and spinning structures

Science.gov (United States)

Velazquez, Antonio; Swartz, R. Andrew

2015-02-01

Economical maintenance and operation are critical issues for rotating machinery and spinning structures containing blade elements, especially large slender dynamic beams (e.g., wind turbines). Structural health monitoring systems represent promising instruments to assure reliability and good performance from the dynamics of the mechanical systems. However, such devices have not been completely perfected for spinning structures. These sensing technologies are typically informed by both mechanistic models coupled with data-driven identification techniques in the time and/or frequency domain. Frequency response functions are popular but are difficult to realize autonomously for structures of higher order, especially when overlapping frequency content is present. Instead, time-domain techniques have shown to possess powerful advantages from a practical point of view (i.e. low-order computational effort suitable for real-time or embedded algorithms) and also are more suitable to differentiate closely-related modes. Customarily, time-varying effects are often neglected or dismissed to simplify this analysis, but such cannot be the case for sinusoidally loaded structures containing spinning multi-bodies. A more complex scenario is constituted when dealing with both periodic mechanisms responsible for the vibration shaft of the rotor-blade system and the interaction of the supporting substructure. Transformations of the cyclic effects on the vibrational data can be applied to isolate inertial quantities that are different from rotation-generated forces that are typically non-stationary in nature. After applying these transformations, structural identification can be carried out by stationary techniques via data-correlated eigensystem realizations. In this paper, an exploration of a periodic stationary or cyclo-stationary subspace identification technique is presented here for spinning multi-blade systems by means of a modified Eigensystem Realization Algorithm (ERA) via

Iterative numerical solution of scattering problems

Energy Technology Data Exchange (ETDEWEB)

Tomio, L; Adhikari, S K

1995-05-01

An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10{sup 10} after some-8-10 iterations. (author). 31 refs, 2 tabs.

Margin-Wide Earthquake Subspace Scanning Along the Cascadia Subduction Zone Using the Cascadia Initiative Amphibious Dataset

Science.gov (United States)

Morton, E.; Bilek, S. L.; Rowe, C. A.

2017-12-01

Understanding the spatial extent and behavior of the interplate contact in the Cascadia Subduction Zone (CSZ) may prove pivotal to preparation for future great earthquakes, such as the M9 event of 1700. Current and historic seismic catalogs are limited in their integrity by their short duration, given the recurrence rate of great earthquakes, and by their rather high magnitude of completeness for the interplate seismic zone, due to its offshore distance from these land-based networks. This issue is addressed via the 2011-2015 Cascadia Initiative (CI) amphibious seismic array deployment, which combined coastal land seismometers with more than 60 ocean-bottom seismometers (OBS) situated directly above the presumed plate interface. We search the CI dataset for small, previously undetected interplate earthquakes to identify seismic patches on the megathrust. Using the automated subspace detection method, we search for previously undetected events. Our subspace comprises eigenvectors derived from CI OBS and on-land waveforms extracted for existing catalog events that appear to have occurred on the plate interface. Previous work focused on analysis of two repeating event clusters off the coast of Oregon spanning all 4 years of deployment. Here we expand earlier results to include detection and location analysis to the entire CSZ margin during the first year of CI deployment, with more than 200 new events detected for the central portion of the margin. Template events used for subspace scanning primarily occurred beneath the land surface along the coast, at the downdip edge of modeled high slip patches for the 1700 event, with most concentrated at the northwestern edge of the Olympic Peninsula.

ITER-FEAT operation

International Nuclear Information System (INIS)

Shimomura, Y.; Huguet, M.; Mizoguchi, T.; Murakami, Y.; Polevoi, A.R.; Shimada, M.; Aymar, R.; Chuyanov, V.A.; Matsumoto, H.

2001-01-01

ITER is planned to be the first fusion experimental reactor in the world operating for research in physics and engineering. The first ten years of operation will be devoted primarily to physics issues at low neutron fluence and the following ten years of operation to engineering testing at higher fluence. ITER can accommodate various plasma configurations and plasma operation modes, such as inductive high Q modes, long pulse hybrid modes and non-inductive steady state modes, with large ranges of plasma current, density, beta and fusion power, and with various heating and current drive methods. This flexibility will provide an advantage for coping with uncertainties in the physics database, in studying burning plasmas, in introducing advanced features and in optimizing the plasma performance for the different programme objectives. Remote sites will be able to participate in the ITER experiment. This concept will provide an advantage not only in operating ITER for 24 hours a day but also in involving the worldwide fusion community and in promoting scientific competition among the ITER Parties. (author)

Statistics of electron multiplication in multiplier phototube: iterative method

International Nuclear Information System (INIS)

Grau Malonda, A.; Ortiz Sanchez, J.F.

1985-01-01

An iterative method is applied to study the variation of dynode response in the multiplier phototube. Three different situations are considered that correspond to the following ways of electronic incidence on the first dynode: incidence of exactly one electron, incidence of exactly r electrons and incidence of an average anti-r electrons. The responses are given for a number of steps between 1 and 5, and for values of the multiplication factor of 2.1, 2.5, 3 and 5. We study also the variance, the skewness and the excess of jurtosis for different multiplication factors. (author)

An iterative method for the analysis of Cherenkov rings in the HERA-B RICH

International Nuclear Information System (INIS)

Staric, M.; Krizan, P.

1999-01-01

A new method is presented for the analysis of data recorded with a Ring Imaging Cherenkov (RICH) counter. The method, an iterative sorting of hits on the photon detector, is particularly useful for events where rings overlap considerably. The algorithm was tested on simulated data for the HERA-B experiment

Monte Carlo methods in PageRank computation: When one iteration is sufficient

NARCIS (Netherlands)

Avrachenkov, K.; Litvak, Nelli; Nemirovsky, D.; Osipova, N.

2005-01-01

PageRank is one of the principle criteria according to which Google ranks Web pages. PageRank can be interpreted as a frequency of visiting a Web page by a random surfer and thus it reflects the popularity of a Web page. Google computes the PageRank using the power iteration method which requires

Monte Carlo methods in PageRank computation: When one iteration is sufficient

NARCIS (Netherlands)

Avrachenkov, K.; Litvak, Nelli; Nemirovsky, D.; Osipova, N.

PageRank is one of the principle criteria according to which Google ranks Web pages. PageRank can be interpreted as a frequency of visiting a Web page by a random surfer, and thus it reflects the popularity of a Web page. Google computes the PageRank using the power iteration method, which requires

Iterative raw measurements restoration method with penalized weighted least squares approach for low-dose CT

Science.gov (United States)

Takahashi, Hisashi; Goto, Taiga; Hirokawa, Koichi; Miyazaki, Osamu

2014-03-01

Statistical iterative reconstruction and post-log data restoration algorithms for CT noise reduction have been widely studied and these techniques have enabled us to reduce irradiation doses while maintaining image qualities. In low dose scanning, electronic noise becomes obvious and it results in some non-positive signals in raw measurements. The nonpositive signal should be converted to positive signal so that it can be log-transformed. Since conventional conversion methods do not consider local variance on the sinogram, they have difficulty of controlling the strength of the filtering. Thus, in this work, we propose a method to convert the non-positive signal to the positive signal by mainly controlling the local variance. The method is implemented in two separate steps. First, an iterative restoration algorithm based on penalized weighted least squares is used to mitigate the effect of electronic noise. The algorithm preserves the local mean and reduces the local variance induced by the electronic noise. Second, smoothed raw measurements by the iterative algorithm are converted to the positive signal according to a function which replaces the non-positive signal with its local mean. In phantom studies, we confirm that the proposed method properly preserves the local mean and reduce the variance induced by the electronic noise. Our technique results in dramatically reduced shading artifacts and can also successfully cooperate with the post-log data filter to reduce streak artifacts.

A new ART iterative method and a comparison of performance among various ART methods

International Nuclear Information System (INIS)

Tan, Yufeng; Sato, Shunsuke

1993-01-01

Many algebraic reconstruction techniques (ART) image reconstruction algorithms, for instance, simultaneous iterative reconstruction technique (SIRT), the relaxation method and multiplicative ART (MART), have been proposed and their convergent properties have been studied. SIRT and the underrelaxed relaxation method converge to the least-squares solution, but the convergent speeds are very slow. The Kaczmarz method converges very quickly, but the reconstructed images contain a lot of noise. The comparative studies between these algorithms have been done by Gilbert and others, but are not adequate. In this paper, we (1) propose a new method which is a modified Kaczmarz method and prove its convergence property, (2) study performance of 7 algorithms including the one proposed here by computer simulation for 3 kinds of typical phantoms. The method proposed here does not give the least-square solution, but the root mean square errors of its reconstructed images decrease very quickly after few interations. The result shows that the method proposed here gives a better reconstructed image. (author)

Bi Sparsity Pursuit: A Paradigm for Robust Subspace Recovery

Science.gov (United States)

2016-09-27

Bian, Student Member, IEEE, and Hamid Krim, Fellow, IEEE Abstract The success of sparse models in computer vision and machine learning is due to the...16. SECURITY CLASSIFICATION OF: The success of sparse models in computer vision and machine learning is due to the fact that, high dimensional data...vision and machine learning is due to the fact that, high dimensional data is distributed in a union of low dimensional subspaces in many real-world

An iterative method for accelerated degradation testing data of smart electricity meter

Science.gov (United States)

Wang, Xiaoming; Xie, Jinzhe

2017-01-01

In order to evaluate the performance of smart electricity meter (SEM), we must spend a lot of time censoring its status. For example, if we assess to the meter stability of the SEM which needs several years at least according to the standards. So accelerated degradation testing (ADT) is a useful method to assess the performance of the SEM. As we known, the Wiener process is a prevalent method to interpret the performance degradation. This paper proposes an iterative method for ADT data of SEM. The simulation study verifies the application and superiority of the proposed model than other ADT methods.

Development of an iterative 3D reconstruction method for the control of heavy-ion oncotherapy with PET

International Nuclear Information System (INIS)

Lauckner, K.

1999-06-01

The dissertation reports the approach and work for developing and implementing an image space reconstruction method that allows to check the 3D activity distribution and detect possible deviations from irradiation planning data. Other than usual PET scanners, the BASTEI instrument is equipped with two detectors positioned at opposite sides above and below the patient, so that there is enough space for suitable positioning of patient and radiation source. Due to the restricted field of view of the positron camera, the 3D imaging process is subject to displacement-dependent variations, creating bad reconstruction conditions. In addition, the counting rate is lower by two or three orders of magnitude than the usual counting rates of nuclear-medicine PET applications. This is why an iterative 3D algorithm is needed. Two iterative methods known from conventional PET were examined for their suitability and compared with respect to results. The MLEM algorithm proposed by Shepp and Vardi interprets the measured data as a random sample of independent variables of Poisson distributions, to be used for assessing the unknown activity distribution. A disadvantage of this algorithm is the considerable calculation effort required. For minimizing the calculation effort, and in order to make iterative statistical methods applicable to measured 3D data, Daube-Whitherspoon and Muehllehner developed the Iterative Image Space Reconstruction Algorithm, ISRA, derived through modification of the sequence of development steps of the MLEM algorithm. Problem solution with ISRA is based on least square deviation method, other than with the MLEM algorithm which uses the best probability method. (orig./CB) [de

Solving Ratio-Dependent Predatorprey System with Constant Effort Harvesting Using Variational Iteration Method

DEFF Research Database (Denmark)

Ghotbi, Abdoul R; Barari, Amin

2009-01-01

Due to wide range of interest in use of bio-economic models to gain insight in to the scientific management of renewable resources like fisheries and forestry, variational iteration method (VIM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort...

Optimised Iteration in Coupled Monte Carlo - Thermal-Hydraulics Calculations

Science.gov (United States)

Hoogenboom, J. Eduard; Dufek, Jan

2014-06-01

This paper describes an optimised iteration scheme for the number of neutron histories and the relaxation factor in successive iterations of coupled Monte Carlo and thermal-hydraulic reactor calculations based on the stochastic iteration method. The scheme results in an increasing number of neutron histories for the Monte Carlo calculation in successive iteration steps and a decreasing relaxation factor for the spatial power distribution to be used as input to the thermal-hydraulics calculation. The theoretical basis is discussed in detail and practical consequences of the scheme are shown, among which a nearly linear increase per iteration of the number of cycles in the Monte Carlo calculation. The scheme is demonstrated for a full PWR type fuel assembly. Results are shown for the axial power distribution during several iteration steps. A few alternative iteration method are also tested and it is concluded that the presented iteration method is near optimal.

Optimized iteration in coupled Monte-Carlo - Thermal-hydraulics calculations

International Nuclear Information System (INIS)

Hoogenboom, J.E.; Dufek, J.

2013-01-01

This paper describes an optimised iteration scheme for the number of neutron histories and the relaxation factor in successive iterations of coupled Monte Carlo and thermal-hydraulic reactor calculations based on the stochastic iteration method. The scheme results in an increasing number of neutron histories for the Monte Carlo calculation in successive iteration steps and a decreasing relaxation factor for the spatial power distribution to be used as input to the thermal-hydraulics calculation. The theoretical basis is discussed in detail and practical consequences of the scheme are shown, among which a nearly linear increase per iteration of the number of cycles in the Monte Carlo calculation. The scheme is demonstrated for a full PWR type fuel assembly. Results are shown for the axial power distribution during several iteration steps. A few alternative iteration methods are also tested and it is concluded that the presented iteration method is near optimal. (authors)

A Comparison of Iterative 2D-3D Pose Estimation Methods for Real-Time Applications

DEFF Research Database (Denmark)