The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces
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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.
Comment on an application of the asymptotic iteration method to a perturbed Coulomb model
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Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (Conicet, UNLP), Blvd. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2006-08-18
We discuss a recent application of the asymptotic iteration method (AIM) to a perturbed Coulomb model. Contrary to what was argued before we show that the AIM converges and yields accurate energies for that model. We also consider alternative perturbation approaches and show that one of them is equivalent to that recently proposed by another author.
On iterative procedures of asymptotic inference
K.O. Dzhaparidze (Kacha)
1983-01-01
textabstractAbstract An informal discussion is given on performing an unconstrained maximization or solving non‐linear equations of statistics by iterative methods with the quadratic termination property. It is shown that if a miximized function, e.g. likelihood, is asymptotically quadratic, then
DEFF Research Database (Denmark)
Farrokhzad, F.; Mowlaee, P.; Barari, Amin
2011-01-01
The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has its own problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differential equations used in engineering problems are simplified......, and this process produces noise in the obtained answers. This paper deals with solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Optimal Homotopy Asymptotic...... Method (OHAM). The comparisons of the results reveal that these methods are very effective, convenient and quite accurate to systems of non-linear differential equation....
A note on properties of iterative procedures of asymptotic evidence
Paardekooper, H.C.H.; Steens, H.B.A.; Van der Hoek, G.
1989-01-01
The theoretical results obtained by Dzhaparidze (1983) are based on a theorem dealing with the asymptotically normality of an estimator which is the result of a Newton-like iteration method. The paper establishes a new theorem that supports the use of a more robust BFGS Quasi Newton method with
Kisoglu, H. F.; Ciftci, Hakan
2017-04-01
In mathematical physics the main goal of quantum mechanics is to obtain the energy spectrum of an atomic system. In many practices, Schrödinger equation which is a second order and linear differential equation is solved to do this analysis. There are many theoretic mathematical methods serving this purpose. We use Asymptotic Iteration Method (AIM) to obtain the energy eigenvalues of Schrödinger equation in N-dimensional euclidean space for a potential class given as α {r}2d-2-β {r}d-2. We also obtain a restriction on the eigenvalues that gives degeneracies. Besides, we crosscheck the eigenvalues and degeneracies using the perturbation theory in the view of the AIM.
Asymptotic Methods for Solitary Solutions and Compactons
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Ji-Huan He
2012-01-01
Full Text Available This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this paper are first appeared.
The optimal homotopy asymptotic method engineering applications
Marinca, Vasile
2015-01-01
This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011, and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five application...
Hageman, Louis A
1981-01-01
This graduate-level text examines the practical use of iterative methods in solving large, sparse systems of linear algebraic equations and in resolving multidimensional boundary-value problems. Assuming minimal mathematical background, it profiles the relative merits of several general iterative procedures. Topics include polynomial acceleration of basic iterative methods, Chebyshev and conjugate gradient acceleration procedures applicable to partitioning the linear system into a "red/black" block form, adaptive computational algorithms for the successive overrelaxation (SOR) method, and comp
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Saadd, Y.
1994-12-31
In spite of the tremendous progress achieved in recent years in the general area of iterative solution techniques, there are still a few obstacles to the acceptance of iterative methods in a number of applications. These applications give rise to very indefinite or highly ill-conditioned non Hermitian matrices. Trying to solve these systems with the simple-minded standard preconditioned Krylov subspace methods can be a frustrating experience. With the mathematical and physical models becoming more sophisticated, the typical linear systems which we encounter today are far more difficult to solve than those of just a few years ago. This trend is likely to accentuate. This workshop will discuss (1) these applications and the types of problems that they give rise to; and (2) recent progress in solving these problems with iterative methods. The workshop will end with a hopefully stimulating panel discussion with the speakers.
Directory of Open Access Journals (Sweden)
Xiaolong Qin
2011-01-01
Full Text Available An implicit iterative process is considered. Strong and weak convergence theorems of common fixed points of a finite family of asymptotically pseudocontractive mappings in the intermediate sense are established in a real Hilbert space.
Conformable variational iteration method
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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.
Asymptotic methods for wave and quantum problems
Karasev, M V
2003-01-01
The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper "Quantization and Intrinsic Dynamics" a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approxi
Large Deviations and Asymptotic Methods in Finance
Gatheral, Jim; Gulisashvili, Archil; Jacquier, Antoine; Teichmann, Josef
2015-01-01
Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find th...
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Haizhen Sun
2013-01-01
Full Text Available Our aim in this paper is to illustrate that the proof of main theorem of Rhoades and Şoltuz (2003 concerning the equivalence between the convergences of Ishikawa and Mann iterations for uniformly L-Lipschitzian asymptotically pseudocontractive maps is incorrect and to provide its correct version.
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.
Baranwal, Vipul K; Pandey, Ram K; Singh, Om P
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations
Baranwal, Vipul K.; Pandey, Ram K.
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems. PMID:27437484
The Asymptotic Expansion Method via Symbolic Computation
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Juan F. Navarro
2012-01-01
Full Text Available This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.
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Mukhamedov Farrukh
2010-01-01
Full Text Available We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi- -nonexpansive mapping and an asymptotically quasi-nonexpansive mapping , defined on a nonempty closed convex subset of a Banach space.
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Farrukh Mukhamedov
2010-01-01
Full Text Available We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.
Asymptotic methods in mechanics of solids
Bauer, Svetlana M; Smirnov, Andrei L; Tovstik, Petr E; Vaillancourt, Rémi
2015-01-01
The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russi...
Electromagnetic simulations of JET ICRF ITER-like antenna with TOPICA and SSWICH asymptotic codes
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Křivská Alena
2017-01-01
Full Text Available Multi-megawatt Ion Cyclotron Range of Frequencies (ICRF heating is routinely used in the JET tokamak. To increase the ICRF heating power available from the A2 antennas, the ICRF ITER-Like Antenna (ILA was reinstalled for the 2015 JET ITER-like wall experimental campaign. The application of high levels of ICRF power typically results in increased plasma wall interaction which leads to the observation of enhanced influx of metallic impurities in the plasma edge. It is assumed that the impurity production is mainly driven by the parallel component of the Radio-Frequency (RF antenna electric near-field, E// (parallel to the confinement magnetic field of the tokamak, that is rectified in a thin boundary layer (RF sheath. Torino Polytechnic Ion Cyclotron Antenna (TOPICA code was used to compute E// field maps in front of the ILA and between its poloidal limiters in the presence of plasma using measured density profiles and various antenna feedings. E// field maps calculated between the poloidal limiters were used to estimate the poloidal distribution of RF-sheath Direct Current (DC potential in this private region of the ILA and make relative comparison of various antenna electrical settings. For this purpose we used the asymptotic version of the Self-consistent Sheaths and Waves for Ion Cyclotron Heating Slow-Wave (SSWICH-SW code. These estimations can help to study the formation of RF sheaths around the antenna and even at distant locations (∼3m away.
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Gurucharan Singh Saluja
2010-01-01
Full Text Available In this paper, we give some necessary and sufficient conditions for an implicit iteration process with errors for a finite family of asymptotically quasi-nonexpansive mappings converging to a common fixed of the mappings in convex metric spaces. Our results extend and improve some recent results of Sun, Wittmann, Xu and Ori, and Zhou and Chang.
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Javed Ali
2012-01-01
Full Text Available We solve some higher-order boundary value problems by the optimal homotopy asymptotic method (OHAM. The proposed method is capable to handle a wide variety of linear and nonlinear problems effectively. The numerical results given by OHAM are compared with the exact solutions and the solutions obtained by Adomian decomposition (ADM, variational iteration (VIM, homotopy perturbation (HPM, and variational iteration decomposition method (VIDM. The results show that the proposed method is more effective and reliable.
Asymptotic-induced numerical methods for conservation laws
Garbey, Marc; Scroggs, Jeffrey S.
1990-01-01
Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.
New concurrent iterative methods with monotonic convergence
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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.
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
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...
Iterative methods for weighted least-squares
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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.
Selected asymptotic methods with applications to electromagnetics and antennas
Fikioris, George; Bakas, Odysseas N
2013-01-01
This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include som
A Family of Newton Type Iterative Methods for Solving Nonlinear Equations
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Xiaofeng Wang
2015-09-01
Full Text Available In this paper, a general family of n-point Newton type iterative methods for solving nonlinear equations is constructed by using direct Hermite interpolation. The order of convergence of the new n-point iterative methods without memory is 2n requiring the evaluations of n functions and one first-order derivative in per full iteration, which implies that this family is optimal according to Kung and Traub’s conjecture (1974. Its error equations and asymptotic convergence constants are obtained. The n-point iterative methods with memory are obtained by using a self-accelerating parameter, which achieve much faster convergence than the corresponding n-point methods without memory. The increase of convergence order is attained without any additional calculations so that the n-point Newton type iterative methods with memory possess a very high computational efficiency. Numerical examples are demonstrated to confirm theoretical results.
Advances in iterative methods for nonlinear equations
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...
Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers
Marinca, Vasile; Ene, Remus-Daniel; Bereteu, Liviu
2017-10-01
Dynamic response time is an important feature for determining the performance of magnetorheological (MR) dampers in practical civil engineering applications. The objective of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to give approximate analytical solutions of the nonlinear differential equation of a modified Bingham model with non-viscous exponential damping. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. OHAM is very efficient in practice for ensuring very rapid convergence of the solution after only one iteration and with a small number of steps.
An Extension of the Optimal Homotopy Asymptotic Method to Coupled Schrödinger-KdV Equation
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Hakeem Ullah
2014-01-01
Full Text Available We consider the approximate solution of the coupled Schrödinger-KdV equation by using the extended optimal homotopy asymptotic method (OHAM. We obtained the extended OHAM solution of the problem and compared with the exact, variational iteration method (VIM and homotopy perturbation method (HPM solutions. The obtained solution shows that extended OHAM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution.
An Iterative Method for Problems with Multiscale Conductivity
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Hyea Hyun Kim
2012-01-01
Full Text Available A model with its conductivity varying highly across a very thin layer will be considered. It is related to a stable phantom model, which is invented to generate a certain apparent conductivity inside a region surrounded by a thin cylinder with holes. The thin cylinder is an insulator and both inside and outside the thin cylinderare filled with the same saline. The injected current can enter only through the holes adopted to the thin cylinder. The model has a high contrast of conductivity discontinuity across the thin cylinder and the thickness of the layer and the size of holes are very small compared to the domain of the model problem. Numerical methods for such a model require a very fine mesh near the thin layer to resolve the conductivity discontinuity. In this work, an efficient numerical method for such a model problem is proposed by employing a uniform mesh, which need not resolve the conductivity discontinuity. The discrete problem is then solved by an iterative method, where the solution is improved by solving a simple discrete problem with a uniform conductivity. At each iteration, the right-hand side is updated by integrating the previous iterate over the thin cylinder. This process results in a certain smoothing effect on microscopic structures and our discrete model can provide a more practical tool for simulating the apparent conductivity. The convergence of the iterative method is analyzed regarding the contrast in the conductivity and the relative thickness of the layer. In numerical experiments, solutions of our method are compared to reference solutions obtained from COMSOL, where very fine meshes are used to resolve the conductivity discontinuity in the model. Errors of the voltage in L2 norm follow O(h asymptotically and the current density matches quitewell those from the reference solution for a sufficiently small mesh size h. The experimental results present a promising feature of our approach for simulating the apparent
Asymptotic and Numerical Methods for Rapidly Rotating Buoyant Flow
Grooms, Ian G.
This thesis documents three investigations carried out in pursuance of a doctoral degree in applied mathematics at the University of Colorado (Boulder). The first investigation concerns the properties of rotating Rayleigh-Benard convection -- thermal convection in a rotating infinite plane layer between two constant-temperature boundaries. It is noted that in certain parameter regimes convective Taylor columns appear which dominate the dynamics, and a semi-analytical model of these is presented. Investigation of the columns and of various other properties of the flow is ongoing. The second investigation concerns the interactions between planetary-scale and mesoscale dynamics in the oceans. Using multiple-scale asymptotics the possible connections between planetary geostrophic and quasigeostrophic dynamics are investigated, and three different systems of coupled equations are derived. Possible use of these equations in conjunction with the method of superparameterization, and extension of the asymptotic methods to the interactions between mesoscale and submesoscale dynamics is ongoing. The third investigation concerns the linear stability properties of semi-implicit methods for the numerical integration of ordinary differential equations, focusing in particular on the linear stability of IMEX (Implicit-Explicit) methods and exponential integrators applied to systems of ordinary differential equations arising in the numerical solution of spatially discretized nonlinear partial differential equations containing both dispersive and dissipative linear terms. While these investigations may seem unrelated at first glance, some reflection shows that they are in fact closely linked. The investigation of rotating convection makes use of single-space, multiple-time-scale asymptotics to deal with dynamics strongly constrained by rotation. Although the context of thermal convection in an infinite layer seems somewhat removed from large-scale ocean dynamics, the asymptotic
Newton iterative methods for large scale nonlinear systems
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Walker, H.F.; Turner, K.
1993-01-01
Objective is to develop robust, efficient Newton iterative methods for general large scale problems well suited for discretizations of partial differential equations, integral equations, and other continuous problems. A concomitant objective is to develop improved iterative linear algebra methods. We first outline research on Newton iterative methods and then review work on iterative linear algebra methods. (DLC)
Monotone iterative method for fractional differential equations
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Zhanbing Bai
2016-01-01
Full Text Available In this article, by using the lower and upper solution method, we prove the existence of iterative solutions for a class of fractional initial value problem with non-monotone term $$\\displaylines{ D_{0+}^\\alpha u(t=f(t, u(t, \\quad t \\in (0, h, \\cr t^{1-\\alpha}u(t\\big|_{t=0} = u_0 \
Iterative regularization method in generalized inverse beamforming
Zhang, Zhifei; Chen, Si; Xu, Zhongming; He, Yansong; Li, Shu
2017-05-01
Beamforming based on microphone array is a method to identify sound sources. It can visualize the sound field of the source plane and reveal interesting acoustic information. Generalized inverse beamforming (GIB) is one important branch of beamforming techniques due to its high identification accuracy and computational efficiency. However, in real testing situation, errors caused by measurement noise and configuration problems may seriously reduce the beamforming accuracy. As an inverse problem, the stability of GIB can be improved with regularization methods. We proposed a new iterative regularization method for GIB by iteratively redefining the form of regularization matrix and calculating the corresponding solution. Moreover, the new method is applied to functional beamforming and double-layer antenna beamforming respectively. Numerical simulations and experiments are implemented. The results show that the proposed regularization method leads to more robust beamforming output and higher accuracy in both the two applications.
Ke, Zijun; Zhang, Zhiyong Johnny
2017-09-12
Autocorrelation and partial autocorrelation, which provide a mathematical tool to understand repeating patterns in time series data, are often used to facilitate the identification of model orders of time series models (e.g., moving average and autoregressive models). Asymptotic methods for testing autocorrelation and partial autocorrelation such as the 1/T approximation method and the Bartlett's formula method may fail in finite samples and are vulnerable to non-normality. Resampling techniques such as the moving block bootstrap and the surrogate data method are competitive alternatives. In this study, we use a Monte Carlo simulation study and a real data example to compare asymptotic methods with the aforementioned resampling techniques. For each resampling technique, we consider both the percentile method and the bias-corrected and accelerated method for interval construction. Simulation results show that the surrogate data method with percentile intervals yields better performance than the other methods. An R package pautocorr is used to carry out tests evaluated in this study. © 2017 The British Psychological Society.
Application of the Asymptotic Taylor Expansion Method to Bistable Potentials
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Okan Ozer
2013-01-01
Full Text Available A recent method called asymptotic Taylor expansion (ATEM is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.
Iterative regularization with minimum-residual methods
DEFF Research Database (Denmark)
Jensen, Toke Koldborg; Hansen, Per Christian
2006-01-01
subspaces. We provide a combination of theory and numerical examples, and our analysis confirms the experience that MINRES and MR-II can work as general regularization methods. We also demonstrate theoretically and experimentally that the same is not true, in general, for GMRES and RRGMRES - their success......We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these Krylov...... as regularization methods is highly problem dependent....
Iterative Regularization with Minimum-Residual Methods
DEFF Research Database (Denmark)
Jensen, Toke Koldborg; Hansen, Per Christian
2007-01-01
subspaces. We provide a combination of theory and numerical examples, and our analysis confirms the experience that MINRES and MR-II can work as general regularization methods. We also demonstrate theoretically and experimentally that the same is not true, in general, for GMRES and RRGMRES their success......We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these Krylov...... as regularization methods is highly problem dependent....
Asymptotic approximation method of force reconstruction: Proof of concept
Sanchez, J.; Benaroya, H.
2017-08-01
An important problem in engineering is the determination of the system input based on the system response. This type of problem is difficult to solve as it is often ill-defined, and produces inaccurate or non-unique results. Current reconstruction techniques typically involve the employment of optimization methods or additional constraints to regularize the problem, but these methods are not without their flaws as they may be sub-optimally applied and produce inadequate results. An alternative approach is developed that draws upon concepts from control systems theory, the equilibrium analysis of linear dynamical systems with time-dependent inputs, and asymptotic approximation analysis. This paper presents the theoretical development of the proposed method. A simple application of the method is presented to demonstrate the procedure. A more complex application to a continuous system is performed to demonstrate the applicability of the method.
Fields Institute International Symposium on Asymptotic Methods in Stochastics
Kulik, Rafal; Haye, Mohamedou; Szyszkowicz, Barbara; Zhao, Yiqiang
2015-01-01
This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.
Conference on Boundary and Interior Layers : Computational and Asymptotic Methods
Stynes, Martin; Zhang, Zhimin
2017-01-01
This volume collects papers associated with lectures that were presented at the BAIL 2016 conference, which was held from 14 to 19 August 2016 at Beijing Computational Science Research Center and Tsinghua University in Beijing, China. It showcases the variety and quality of current research into numerical and asymptotic methods for theoretical and practical problems whose solutions involve layer phenomena. The BAIL (Boundary And Interior Layers) conferences, held usually in even-numbered years, bring together mathematicians and engineers/physicists whose research involves layer phenomena, with the aim of promoting interaction between these often-separate disciplines. These layers appear as solutions of singularly perturbed differential equations of various types, and are common in physical problems, most notably in fluid dynamics. This book is of interest for current researchers from mathematics, engineering and physics whose work involves the accurate app roximation of solutions of singularly perturbed diffe...
Methods used for research regarding iteration in instructional design
Verstegen, D.M.L.
2004-01-01
This paper focuses on the search for suitable research methods for research regarding iteration in instructional design. More specifically my research concerned the question how instructional designers can be supported during an iterative design process. Although instructional design and development
Optimal Homotopy Asymptotic Method for Solving System of Fredholm Integral Equations
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Bahman Ghazanfari
2013-08-01
Full Text Available In this paper, optimal homotopy asymptotic method (OHAM is applied to solve system of Fredholm integral equations. The effectiveness of optimal homotopy asymptotic method is presented. This method provides easy tools to control the convergence region of approximating solution series wherever necessary. The results of OHAM are compared with homotopy perturbation method (HPM and Taylor series expansion method (TSEM.
An efficient iterative thresholding method for image segmentation
Wang, Dong; Li, Haohan; Wei, Xiaoyu; Wang, Xiao-Ping
2017-12-01
We proposed an efficient iterative thresholding method for multi-phase image segmentation. The algorithm is based on minimizing piecewise constant Mumford-Shah functional in which the contour length (or perimeter) is approximated by a non-local multi-phase energy. The minimization problem is solved by an iterative method. Each iteration consists of computing simple convolutions followed by a thresholding step. The algorithm is easy to implement and has the optimal complexity O (Nlog N) per iteration. We also show that the iterative algorithm has the total energy decaying property. We present some numerical results to show the efficiency of our method.
Directory of Open Access Journals (Sweden)
Mahmoud Bayat
Full Text Available This review features a survey of some recent developments in asymptotic techniques and new developments, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the achieved approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to over-come the shortcomings.In this review we have applied different powerful analytical methods to solve high nonlinear problems in engineering vibrations. Some patterns are given to illustrate the effectiveness and convenience of the methodologies.
Iterative methods for Toeplitz-like matrices
Energy Technology Data Exchange (ETDEWEB)
Huckle, T. [Universitaet Wurzburg (Germany)
1994-12-31
In this paper the author will give a survey on iterative methods for solving linear equations with Toeplitz matrices, Block Toeplitz matrices, Toeplitz plus Hankel matrices, and matrices with low displacement rank. He will treat the following subjects: (1) optimal (w)-circulant preconditioners is a generalization of circulant preconditioners; (2) Optimal implementation of circulant-like preconditioners in the complex and real case; (3) preconditioning of near-singular matrices; what kind of preconditioners can be used in this case; (4) circulant preconditioning for more general classes of Toeplitz matrices; what can be said about matrices with coefficients that are not l{sub 1}-sequences; (5) preconditioners for Toeplitz least squares problems, for block Toeplitz matrices, and for Toeplitz plus Hankel matrices.
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.
Explanation of Second-Order Asymptotic Theory Via Information Spectrum Method
Hayashi, Masahito
We explain second-order asymptotic theory via the information spectrum method. From a unified viewpoint based on the generality of the information spectrum method, we consider second-order asymptotic theory for use in fixed-length data compression, uniform random number generation, and channel coding. Additionally, we discuss its application to quantum cryptography, folklore in source coding, and security analysis.
A new automatic baseline correction method based on iterative method
Bao, Qingjia; Feng, Jiwen; Chen, Fang; Mao, Wenping; Liu, Zao; Liu, Kewen; Liu, Chaoyang
2012-05-01
A new automatic baseline correction method for Nuclear Magnetic Resonance (NMR) spectra is presented. It is based on an improved baseline recognition method and a new iterative baseline modeling method. The presented baseline recognition method takes advantages of three baseline recognition algorithms in order to recognize all signals in spectra. While in the iterative baseline modeling method, besides the well-recognized baseline points in signal-free regions, the 'quasi-baseline points' in the signal-crowded regions are also identified and then utilized to improve robustness by preventing the negative regions. The experimental results on both simulated data and real metabolomics spectra with over-crowded peaks show the efficiency of this automatic method.
Variation Iteration Method for The Approximate Solution of Nonlinear ...
African Journals Online (AJOL)
Results obtained with the Variational Iteration Method (VIM) on the Burgers equation were compared with the exact found in literature. All computational framework of the research were performed with the aid of Maple 18 software. Keywords: Variational Iteration Method, Burgers Equation, Partial Differential Equations, ...
Second degree generalized gauss-Seidel iteration method for ...
African Journals Online (AJOL)
In this paper, a second degree generalized Gauss –Seidel iteration (SDGGS) method for solving linear system of equations whose iterative matrix has real and complex eigenvalues are less than unity in magnitude is presented. Few numerical examples are considered to show the efficiency of the new method compared to ...
Iteration of Complex Functions and Newton's Method
Dwyer, Jerry; Barnard, Roger; Cook, David; Corte, Jennifer
2009-01-01
This paper discusses some common iterations of complex functions. The presentation is such that similar processes can easily be implemented and understood by undergraduate students. The aim is to illustrate some of the beauty of complex dynamics in an informal setting, while providing a couple of results that are not otherwise readily available in…
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.
Leapfrog variants of iterative methods for linear algebra equations
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.
Asymptotic Solutions of Time-Space Fractional Coupled Systems by Residual Power Series Method
Directory of Open Access Journals (Sweden)
Wenjin Li
2017-01-01
Full Text Available This paper focuses on the asymptotic solutions to time-space fractional coupled systems, where the fractional derivative and integral are described in the sense of Caputo derivative and Riemann-Liouville integral. We introduce the Residual Power Series (for short RPS method to construct the desired asymptotic solutions. Furthermore, we apply this method to some time-space fractional coupled systems. The simplicity and efficiency of RPS method are shown by the application.
A hyperpower iterative method for computing the generalized Drazin ...
Indian Academy of Sciences (India)
Shwetabh Srivastava
Abstract. A quadratically convergent Newton-type iterative scheme is proposed for approximating the gen- eralized Drazin inverse bd of the Banach algebra element b. Further, its extension into the form of the hyper- power iterative method of arbitrary order p ! 2 is presented. Convergence criteria along with the estimation of.
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.
Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems
Energy Technology Data Exchange (ETDEWEB)
Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)
1996-12-31
A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.
Iterative Methods for MPC on Graphical Processing Units
DEFF Research Database (Denmark)
2012-01-01
on their applicability for GPUs. We examine published techniques for iterative methods in interior points methods (IPMs) by applying them to simple test cases, such as a system of masses connected by springs. Iterative methods allows us deal with the ill-conditioning occurring in the later iterations of the IPM as well...... reevaluating existing algorithms with respect to this new architecture. This is of particular interest to large-scale constrained optimization problems with real-time requirements. The aim of this study is to investigate dierent methods for solving large-scale optimization problems with focus...
Iterative regularization methods for nonlinear ill-posed problems
Scherzer, Otmar; Kaltenbacher, Barbara
2008-01-01
Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.
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...
Energy Technology Data Exchange (ETDEWEB)
Corcelli, S.A.; Kress, J.D.; Pratt, L.R.
1995-08-07
This paper develops and characterizes mixed direct-iterative methods for boundary integral formulations of continuum dielectric solvation models. We give an example, the Ca{sup ++}{hor_ellipsis}Cl{sup {minus}} pair potential of mean force in aqueous solution, for which a direct solution at thermal accuracy is difficult and, thus for which mixed direct-iterative methods seem necessary to obtain the required high resolution. For the simplest such formulations, Gauss-Seidel iteration diverges in rare cases. This difficulty is analyzed by obtaining the eigenvalues and the spectral radius of the non-symmetric iteration matrix. This establishes that those divergences are due to inaccuracies of the asymptotic approximations used in evaluation of the matrix elements corresponding to accidental close encounters of boundary elements on different atomic spheres. The spectral radii are then greater than one for those diverging cases. This problem is cured by checking for boundary element pairs closer than the typical spatial extent of the boundary elements and for those cases performing an ``in-line`` Monte Carlo integration to evaluate the required matrix elements. These difficulties are not expected and have not been observed for the thoroughly coarsened equations obtained when only a direct solution is sought. Finally, we give an example application of hybrid quantum-classical methods to deprotonation of orthosilicic acid in water.
Conference on iterative methods for large linear systems
Energy Technology Data Exchange (ETDEWEB)
Kincaid, D.R. (comp.)
1988-12-01
This conference is dedicated to providing an overview of the state of the art in the use of iterative methods for solving sparse linear systems with an eye to contributions of the past, present and future. The emphasis is on identifying current and future research directions in the mainstream of modern scientific computing. Recently, the use of iterative methods for solving linear systems has experienced a resurgence of activity as scientists attach extremely complicated three-dimensional problems using vector and parallel supercomputers. Many research advances in the development of iterative methods for high-speed computers over the past forty years are reviewed, as well as focusing on current research.
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 convergence ability of the iterative method will be greatly enhanced. Numerical tests have been performed under different combinations of local tip speed ratio, local solidity, local twist and airfoil aerodynamic data. Results show that the simple iterative methods have a good convergence ability which...... to the physical solution, especially for the locations near the blade tip and root where the failure rate of the iterative method is high. The stability and accuracy of aerodynamic calculations and optimizations are greatly reduced due to this problem. The intrinsic mechanisms leading to convergence problems...
Iotti, Robert
2015-04-01
ITER is an international experimental facility being built by seven Parties to demonstrate the long term potential of fusion energy. The ITER Joint Implementation Agreement (JIA) defines the structure and governance model of such cooperation. There are a number of necessary conditions for such international projects to be successful: a complete design, strong systems engineering working with an agreed set of requirements, an experienced organization with systems and plans in place to manage the project, a cost estimate backed by industry, and someone in charge. Unfortunately for ITER many of these conditions were not present. The paper discusses the priorities in the JIA which led to setting up the project with a Central Integrating Organization (IO) in Cadarache, France as the ITER HQ, and seven Domestic Agencies (DAs) located in the countries of the Parties, responsible for delivering 90%+ of the project hardware as Contributions-in-Kind and also financial contributions to the IO, as ``Contributions-in-Cash.'' Theoretically the Director General (DG) is responsible for everything. In practice the DG does not have the power to control the work of the DAs, and there is not an effective management structure enabling the IO and the DAs to arbitrate disputes, so the project is not really managed, but is a loose collaboration of competing interests. Any DA can effectively block a decision reached by the DG. Inefficiencies in completing design while setting up a competent organization from scratch contributed to the delays and cost increases during the initial few years. So did the fact that the original estimate was not developed from industry input. Unforeseen inflation and market demand on certain commodities/materials further exacerbated the cost increases. Since then, improvements are debatable. Does this mean that the governance model of ITER is a wrong model for international scientific cooperation? I do not believe so. Had the necessary conditions for success
-Stability Approach to Variational Iteration Method for Solving Integral Equations
Directory of Open Access Journals (Sweden)
Rhoades BE
2009-01-01
Full Text Available We consider -stability definition according to Y. Qing and B. E. Rhoades (2008 and we show that the variational iteration method for solving integral equations is -stable. Finally, we present some text examples to illustrate our result.
A modified iterative ensemble Kalman filter data assimilation method
Xu, Baoxiong; Bai, Yulong; Wang, Yizhao; Li, Zhe; Ma, Boyang
2017-08-01
High nonlinearity is a typical characteristic associated with data assimilation systems. Additionally, iterative ensemble based methods have attracted a large amount of research attention, which has been focused on dealing with nonlinearity problems. To solve the local convergence problem of the iterative ensemble Kalman filter, a modified iterative ensemble Kalman filter algorithm was put forward, which was based on a global convergence strategy from the perspective of a Gauss-Newton iteration. Through self-adaption, the step factor was adjusted to enable every iteration to approach expected values during the process of the data assimilation. A sensitivity experiment was carried out in a low dimensional Lorenz-63 chaotic system, as well as a Lorenz-96 model. The new method was tested via ensemble size, observation variance, and inflation factor changes, along with other aspects. Meanwhile, comparative research was conducted with both a traditional ensemble Kalman filter and an iterative ensemble Kalman filter. The results showed that the modified iterative ensemble Kalman filter algorithm was a data assimilation method that was able to effectively estimate a strongly nonlinear system state.
Novel Computational Iterative Methods with Optimal Order for Nonlinear Equations
Directory of Open Access Journals (Sweden)
F. Soleymani
2011-01-01
Full Text Available This paper contributes a very general class of two-point iterative methods without memory for solving nonlinear equations. The class of methods is developed using weight function approach. Per iteration, each method of the class includes two evaluations of the function and one of its first-order derivative. The analytical study of the main theorem is presented in detail to show the fourth order of convergence. Furthermore, it is discussed that many of the existing fourth-order methods without memory are members from this developed class. Finally, numerical examples are taken into account to manifest the accuracy of the derived methods.
Volokitin, V.; Liniov, A.; Meyerov, I.; Hartmann, M.; Ivanchenko, M.; Hänggi, P.; Denisov, S.
2017-11-01
Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dim H =N ≲300 , while the direct long-time numerical integration of the master equation becomes increasingly problematic for N ≳400 , especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η1,η2,...,ηn} , one could propagate a quantum trajectory (with ηi's as norm thresholds) in a numerically exact way. By using a scalable N -particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N =2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.
Volokitin, V; Liniov, A; Meyerov, I; Hartmann, M; Ivanchenko, M; Hänggi, P; Denisov, S
2017-11-01
Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dimH=N≲300, while the direct long-time numerical integration of the master equation becomes increasingly problematic for N≳400, especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η_{1},η_{2},...,η_{n}}, one could propagate a quantum trajectory (with η_{i}'s as norm thresholds) in a numerically exact way. By using a scalable N-particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N=2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.
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...
Ultrasound wave propagation through rough interfaces: Iterative methods
Berkhoff, Arthur P.; Thijssen, J.M.; van den Berg, P.M.
Two iterative methods for the calculation of acoustic transmission through a rough interface between two media are compared. The methods employ a continuous version of the conjugate gradient technique. One method is based on plane-wave expansions and the other on boundary integral equations and
Variational Iterative Methods for Nonsymmetric Systems of Linear Equations.
1981-08-01
AD-A1S 365 YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE F/G 12/I VARIATIONAL ITERATIVE METHODS FOR NONS YMMETRIC SYSTEMS OF LINEA --ETC(UlI AUG 81...systems of linear equations. Linear Algebra and Its Anolications 29:1-16, 1980. [3] Rati Chandra. Coniuzate Gradient Methods for Partial Differential...19] David M. Young and ang C. lea. Generalized conjugate gradient acceleration of nonsymetrizable iterative methods. Linear Algebra and 1Us Ajpniis s 34:159-194, 1980. " i l- • .
Natural Preconditioning and Iterative Methods for Saddle Point Systems
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.
Non-asymptotic fractional order differentiators via an algebraic parametric method
Liu, Dayan
2012-08-01
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.
Robertson, Scott
2014-11-01
Analog gravity experiments make feasible the realization of black hole space-times in a laboratory setting and the observational verification of Hawking radiation. Since such analog systems are typically dominated by dispersion, efficient techniques for calculating the predicted Hawking spectrum in the presence of strong dispersion are required. In the preceding paper, an integral method in Fourier space is proposed for stationary 1+1-dimensional backgrounds which are asymptotically symmetric. Here, this method is generalized to backgrounds which are different in the asymptotic regions to the left and right of the scattering region.
DEFF Research Database (Denmark)
Vahdatirad, Mohammadjavad; Bayat, Mehdi; Andersen, Lars Vabbersgaard
2015-01-01
The mechanical responses of an offshore monopile foundation mounted in over-consolidated clay are calculated by employing a stochastic approach where a nonlinear p–y curve is incorporated with a finite element scheme. The random field theory is applied to represent a spatial variation for undrained...... shear strength of clay. Normal and Sobol sampling are employed to provide the asymptotic sampling method to generate the probability distribution of the foundation stiffnesses. Monte Carlo simulation is used as a benchmark. Asymptotic sampling accompanied with Sobol quasi random sampling demonstrates...... an efficient method for estimating the probability distribution of stiffnesses for the offshore monopile foundation....
Direct Determination of Asymptotic Structural Postbuckling Behaviour by the finite element method
DEFF Research Database (Denmark)
Poulsen, Peter Noe; Damkilde, Lars
1998-01-01
Application of the finite element method to Koiter's asymptotic postbuckling theory often leads to numerical problems. Generally it is believed that these problems are due to locking of non-linear terms of different orders. A general method is given here that explains the reason for the numerical...... convergence of the postbuckling coefficients. (C) 1998 John Wiley & Sons, Ltd....
Multicore Performance of Block Algebraic Iterative Reconstruction Methods
DEFF Research Database (Denmark)
Sørensen, Hans Henrik B.; Hansen, Per Christian
2014-01-01
, and those that compute a result for each block in parallel and then combine these results before the next iteration. The goal of this work is to demonstrate which block methods are best suited for implementation on modern multicore computers. To compare the performance of the different block methods, we use...
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.
Modified Chebyshev-Picard Iteration Methods for Orbit Propagation
Bai, Xiaoli; Junkins, John L.
2011-10-01
Modified Chebyshev-Picard Iteration methods are presented for solving high precision, long-term orbit propagation problems. Fusing Chebyshev polynomials with the classical Picard iteration method, the proposed methods iteratively refine an orthogonal function approximation of the entire state trajectory, in contrast to traditional, step-wise, forward integration methods. Numerical results demonstrate that for orbit propagation problems, the presented methods are comparable to or superior to a state-of-the-art 12th order Runge-Kutta-Nystrom method in a serial processor as measured by both precision and efficiency. We have found revolutionary long solution arcs with more than eleven digit path approximations over one to three lower-case Earth orbit periods, multiple solution arcs can be patched continuously together to achieve very long-term propagation, leading to more than ten digit accuracy with built-in precise interpolation. Of revolutionary practical promise to much more efficiently solving high precision, long-term orbital trajectory propagation problems is the observation that the presented methods are well suited to massive parallelization because computation of force functions along each path iteration can be rigorously distributed over many parallel cores with negligible cross communication needed.
A New Iterative Method to Calculate [pi
Dion, Peter; Ho, Anthony
2012-01-01
For at least 2000 years people have been trying to calculate the value of [pi], the ratio of the circumference to the diameter of a circle. People know that [pi] is an irrational number; its decimal representation goes on forever. Early methods were geometric, involving the use of inscribed and circumscribed polygons of a circle. However, real…
Newton iterative methods for large scale nonlinear systems. Progress report, 1992--1993
Energy Technology Data Exchange (ETDEWEB)
Walker, H.F.; Turner, K.
1993-06-01
Objective is to develop robust, efficient Newton iterative methods for general large scale problems well suited for discretizations of partial differential equations, integral equations, and other continuous problems. A concomitant objective is to develop improved iterative linear algebra methods. We first outline research on Newton iterative methods and then review work on iterative linear algebra methods. (DLC)
Chen, Chunhang; 陳, 春航
1995-01-01
The smoothing parameters in the Holt-Winters seasonal forecasting method are often estimated by minimizing the mean square error of one-step forecasts using the sample. In this note we show that such an estimator holds asymptotic normality for some stochastic processes.
A hyperpower iterative method for computing the generalized Drazin ...
Indian Academy of Sciences (India)
Home; Journals; Sadhana; Volume 42; Issue 5. A hyperpower iterative method for computing the generalized Drazin inverse of Banach algebra element. SHWETABH SRIVASTAVA DHARMENDRA K GUPTA PREDRAG STANIMIROVIC SUKHJIT SINGH FALGUNI ROY. Volume 42 Issue 5 May 2017 pp 625-630 ...
A cyclic iterative method for solving multiple sets split feasibility ...
African Journals Online (AJOL)
(An iterative regularization method for the solution of the split feasibility problem in Banach spaces, Inverse Problems 24 (2008), 055008) and many important recent results in this direction. Mathematics Subject Classification (2010): 49J53, 65K10, 49M37, 90C25. Keywords: Bregman projection, strong convergence, metric ...
Fleming, H. E.
1977-01-01
Linear numerical inversion methods applied to atmospheric remote sounding generally can be categorized in two ways: (1) iterative, and (2) inverse matrix methods. However, these two categories are not unrelated; a duality exists between them. In other words, given an iterative scheme, a corresponding inverse matrix method exists, and conversely. This duality concept is developed for the more familiar linear methods. The iterative duals are compared with the classical linear iterative approaches and their differences analyzed. The importance of the initial profile in all methods is stressed. Calculations using simulated data are made to compare accuracies and to examine the dependence of the solution on the initial profile.
Directory of Open Access Journals (Sweden)
H. Ullah
2015-01-01
Full Text Available The two-dimensional nonlinear wave equations are considered. Solution to the problem is approximated by using optimal homotopy asymptotic method (OHAM. The residual and convergence of the proposed method to nonlinear wave equation are presented through graphs. The resultant analytic series solution of the two-dimensional nonlinear wave equation shows the effectiveness of the proposed method. The comparison of results has been made with the existing results available in the literature.
Directory of Open Access Journals (Sweden)
Jafar Biazar
2015-01-01
Full Text Available We combine the Adomian decomposition method (ADM and Adomian’s asymptotic decomposition method (AADM for solving Riccati equations. We investigate the approximate global solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from Adomian’s asymptotic decomposition method for Riccati equations and in such cases when we do not find any region of overlap between the obtained approximate solutions by the two proposed methods, we connect the two approximations by the Padé approximant of the near-field approximation. We illustrate the efficiency of the technique for several specific examples of the Riccati equation for which the exact solution is known in advance.
Gao, Hao
2015-01-01
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. Specifically, 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 convergenc...
Evaluation of Continuation Desire as an Iterative Game Development Method
DEFF Research Database (Denmark)
Schoenau-Fog, Henrik; Birke, Alexander; Reng, Lars
2012-01-01
When developing a game it is always valuable to use feedback from players in each iteration, in order to plan the design of the next iteration. However, it can be challenging to devise a simple approach to acquiring information about a player's engagement while playing. In this paper we will thus...... concerning a crowd game which is controlled by smartphones and is intended to be played by audiences in cinemas and at venues with large screens. The case study demonstrates how the approach can be used to help improve the desire to continue when developing a game.......When developing a game it is always valuable to use feedback from players in each iteration, in order to plan the design of the next iteration. However, it can be challenging to devise a simple approach to acquiring information about a player's engagement while playing. In this paper we will thus...... use an evaluation method which focuses on assessing the desire to continue playing as an indicator of player engagement. This feedback can then be applied to detect and prevent any design decisions that would jeopardise a game's level of player engagement. The process is exemplified by a case study...
Iterative methods for stationary convection-dominated transport problems
Energy Technology Data Exchange (ETDEWEB)
Bova, S.W.; Carey, G.F. [Univ. of Texas, Austin, TX (United States)
1994-12-31
It is well known that many iterative methods fail when applied to nonlinear systems of convection-dominated transport equations. Most successful methods for obtaining steady-state solutions to such systems rely on time-stepping through an artificial transient, combined with careful construction of artificial dissipation operators. These operators provide control over spurious oscillations which pollute the steady state solutions, and, in the nonlinear case, may become amplified and lead to instability. In the present study, we investigate Taylor Galerkin and SUPG-type methods and compare results for steady-state solutions to the Euler equations of gas dynamics. In particular, we consider the efficiency of different iterative strategies and present results for representative two-dimensional calculations.
Quadratic maps without asymptotic measure
Hofbauer, Franz; Keller, Gerhard
1990-02-01
An interval map is said to have an asymptotic measure if the time averages of the iterates of Lebesgue measure converge weakly. We construct quadratic maps which have no asymptotic measure. We also find examples of quadratic maps which have an asymptotic measure with very unexpected properties, e.g. a map with the point mass on an unstable fix point as asymptotic measure. The key to our construction is a new characterization of kneading sequences.
An Assessment of Iterative Reconstruction Methods for Sparse Ultrasound Imaging.
Valente, Solivan A; Zibetti, Marcelo V W; Pipa, Daniel R; Maia, Joaquim M; Schneider, Fabio K
2017-03-08
Ultrasonic image reconstruction using inverse problems has recently appeared as an alternative to enhance ultrasound imaging over beamforming methods. This approach depends on the accuracy of the acquisition model used to represent transducers, reflectivity, and medium physics. Iterative methods, well known in general sparse signal reconstruction, are also suited for imaging. In this paper, a discrete acquisition model is assessed by solving a linear system of equations by an ℓ 1 -regularized least-squares minimization, where the solution sparsity may be adjusted as desired. The paper surveys 11 variants of four well-known algorithms for sparse reconstruction, and assesses their optimization parameters with the goal of finding the best approach for iterative ultrasound imaging. The strategy for the model evaluation consists of using two distinct datasets. We first generate data from a synthetic phantom that mimics real targets inside a professional ultrasound phantom device. This dataset is contaminated with Gaussian noise with an estimated SNR, and all methods are assessed by their resulting images and performances. The model and methods are then assessed with real data collected by a research ultrasound platform when scanning the same phantom device, and results are compared with beamforming. A distinct real dataset is finally used to further validate the proposed modeling. Although high computational effort is required by iterative methods, results show that the discrete model may lead to images closer to ground-truth than traditional beamforming. However, computing capabilities of current platforms need to evolve before frame rates currently delivered by ultrasound equipments are achievable.
An iterative method for selecting degenerate multiplex PCR primers.
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.
Iterative methods for photoacoustic tomography in attenuating acoustic media
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.
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.
Properties and Iterative Methods for the Q-Lasso
Directory of Open Access Journals (Sweden)
Maryam A. Alghamdi
2013-01-01
are taken to recover a signal/image via the lasso. Solutions of the Q-lasso depend on a tuning parameter γ. In this paper, we obtain basic properties of the solutions as a function of γ. Because of ill posedness, we also apply l1-l2 regularization to the Q-lasso. In addition, we discuss iterative methods for solving the Q-lasso which include the proximal-gradient algorithm and the projection-gradient algorithm.
Variation Iteration Method for The Approximate Solution of Nonlinear ...
African Journals Online (AJOL)
Tonistar
Nigerian Journal of Basic and Applied Science (June, 2016, 24(1): 70-75. DOI: http://dx.doi.org/10.4314/njbas.v24i1.11. ISSN 0794-5698. Variation Iteration Method for The ... rocket motor, acoustic, number theory, heat conduction, shock waves, etc. (Burger, 1948). Hence, obtaining the exact resolution of this equation for a ...
An efficient iterative method for solving Zakharov-Kuznetsov Equation
Saravi, Masoud; Nikkar, Ali
2013-11-01
In this paper, we apply new modified of Variational Iteration Method (VIM-II) which is a kind of analytical approximate method then, use it to solve Zakharov-Kuznetsov (ZK) equation that governs the behavior of the weakly nonlinear ion-acoustic waves in plasma. Two cases of this equation are considered and the results are compared with those that obtained by Adomian Decomposition Method (ADM) and Variational Homotopy Perturbation Method (VHPM). The results illustrate that proposed technique yields a very rapid convergence of the solution as well as low computational effort.
Computation of electron energy loss spectra by an iterative method
Energy Technology Data Exchange (ETDEWEB)
Koval, Peter [Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, E-20018 San Sebastián (Spain); Centro de Física de Materiales CFM-MPC, Centro Mixto CSIC-UPV/EHU, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián (Spain); Ljungberg, Mathias Per [Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, E-20018 San Sebastián (Spain); Foerster, Dietrich [LOMA, Université de Bordeaux 1, 351 Cours de la Liberation, 33405 Talence (France); Sánchez-Portal, Daniel [Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, E-20018 San Sebastián (Spain); Centro de Física de Materiales CFM-MPC, Centro Mixto CSIC-UPV/EHU, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián (Spain)
2015-07-01
A method is presented to compute the dielectric function for extended systems using linear response time-dependent density functional theory. Localized basis functions with finite support are used to expand both eigenstates and response functions. The electron-energy loss function is directly obtained by an iterative Krylov-subspace method. We apply our method to graphene and silicon and compare it to plane-wave based approaches. Finally, we compute electron-energy loss spectrum of C{sub 60} crystal to demonstrate the merits of the method for molecular crystals, where it will be most competitive.
Optimal homotopy asymptotic method for solving Volterra integral equation of first kind
Directory of Open Access Journals (Sweden)
N. Khan
2014-09-01
Full Text Available In this paper, authors demonstrate the efficiency of optimal homotopy asymptotic method (OHAM. This is done by solving nonlinear Volterra integral equation of first kind. OHAM is applied to Volterra integral equations which involves exponential, trigonometric function as their kernels. It is observed that solution obtained by OHAM is more accurate than existing techniques, which proves its validity and stability for solving Volterra integral equation of first kind.
Optimal homotopy asymptotic method for solving Volterra integral equation of first kind
Khan, N; Hashmi, M.S.; Iqbal, S.; Mahmood, T
2014-01-01
In this paper, authors demonstrate the efficiency of optimal homotopy asymptotic method (OHAM). This is done by solving nonlinear Volterra integral equation of first kind. OHAM is applied to Volterra integral equations which involves exponential, trigonometric function as their kernels. It is observed that solution obtained by OHAM is more accurate than existing techniques, which proves its validity and stability for solving Volterra integral equation of first kind.
Simon, Andrew E.; Kishk, Ahmed A.
2005-12-01
Geometry description in the finite difference time domain method is a tedious task if the geometry contains fine details, such as the case of corrugated objects. Such fine details constrain the cell size. The corrugated object can be modeled using the asymptotic corrugation boundary condition (ACBC) with a correction due to the width-over-period ratio. The ACBC forces certain field distributions inside the corrugation and allows for the removal of the corrugation teeth to have a homogeneous region with enforced field behavior that represents the actual corrugations. The ACBC approach is found to be accurate when the number of corrugations per wavelength is large (typically around 10 corrugations per wavelength). Computed results using ACBC are in good agreement with detailed simulations, which demonstrates the validity of the asymptotic approximations. Last, a major improvement in the computation time is achieved when using the ACBC to model structures that have a large number of corrugations per wavelength.
Sharma, J. N.; Sharma, P. K.; Rana, S. K.
2011-01-01
In this paper the asymptotic method has been applied to investigate propagation of generalized thermoelastic waves in an infinite homogenous isotropic plate. The governing equations for the extensional, transversal and flexural motions are derived from the system of three-dimensional dynamical equations of linear theories of generalized thermoelasticity. The asymptotic operator plate model for extensional and flexural free vibrations in a homogenous thermoelastic plate leads to sixth and fifth degree polynomial secular equations, respectively. These secular equations govern frequency and phase velocity of various possible modes of wave propagation at all wavelengths. The velocity dispersion equations for extensional and flexural wave motion are deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate. The approximation for long and short waves along with expression for group velocity has also been obtained. The Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations and its equivalence established with that of asymptotic method. The numeric values for phase velocity, group velocity and attenuation coefficients has also been obtained using MATHCAD software and are shown graphically for extensional and flexural waves in generalized theories of thermoelastic plate for solid helium material.
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.
An iterative method for airway segmentation using multiscale leakage detection
Nadeem, Syed Ahmed; Jin, Dakai; Hoffman, Eric A.; Saha, Punam K.
2017-02-01
There are growing applications of quantitative computed tomography for assessment of pulmonary diseases by characterizing lung parenchyma as well as the bronchial tree. Many large multi-center studies incorporating lung imaging as a study component are interested in phenotypes relating airway branching patterns, wall-thickness, and other morphological measures. To our knowledge, there are no fully automated airway tree segmentation methods, free of the need for user review. Even when there are failures in a small fraction of segmentation results, the airway tree masks must be manually reviewed for all results which is laborious considering that several thousands of image data sets are evaluated in large studies. In this paper, we present a CT-based novel airway tree segmentation algorithm using iterative multi-scale leakage detection, freezing, and active seed detection. The method is fully automated requiring no manual inputs or post-segmentation editing. It uses simple intensity based connectivity and a new leakage detection algorithm to iteratively grow an airway tree starting from an initial seed inside the trachea. It begins with a conservative threshold and then, iteratively shifts toward generous values. The method was applied on chest CT scans of ten non-smoking subjects at total lung capacity and ten at functional residual capacity. Airway segmentation results were compared to an expert's manually edited segmentations. Branch level accuracy of the new segmentation method was examined along five standardized segmental airway paths (RB1, RB4, RB10, LB1, LB10) and two generations beyond these branches. The method successfully detected all branches up to two generations beyond these segmental bronchi with no visual leakages.
AIR: fused Analytical and Iterative Reconstruction method for computed tomography
Yang, Liu; Qi, Sharon X; Gao, Hao
2013-01-01
Purpose: CT image reconstruction techniques have two major categories: analytical reconstruction (AR) method and iterative reconstruction (IR) method. AR reconstructs images through analytical formulas, such as filtered backprojection (FBP) in 2D and Feldkamp-Davis-Kress (FDK) method in 3D, which can be either mathematically exact or approximate. On the other hand, IR is often based on the discrete forward model of X-ray transform and formulated as a minimization problem with some appropriate image regularization method, so that the reconstructed image corresponds to the minimizer of the optimization problem. This work is to investigate the fused analytical and iterative reconstruction (AIR) method. Methods: Based on IR with L1-type image regularization, AIR is formulated with a AR-specific preconditioner in the data fidelity term, which results in the minimal change of the solution algorithm that replaces the adjoint X-ray transform by the filtered X-ray transform. As a proof-of-concept 2D example of AIR, FB...
Direct determination of asymptotic structural postbuckling behaviour by the finite element method
DEFF Research Database (Denmark)
Poulsen, Peter Noe; Damkilde, Lars
1997-01-01
Application of the Finite Element Method to Koiter's asymptotic postbuckling theory often leads to numerical problems. Generally it is believed that these problems are due to locking of nonlinear terms of different orders. A general method is given here that explains the reason for the numerical...... problems and eliminates these problems. The reason for the numerical problems is that the postbuckling stresses are inaccurately determined. By including a local stress contribution the postbuckling stresses are calculated correctly. The present method gives smooth postbuckling stresses and shows a quick...
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.
Asymptotic iteration method for the modified Pöschl–Teller potential ...
Indian Academy of Sciences (India)
2017-01-04
Jan 4, 2017 ... The increase in the radial quantum number nr causes a decrease in the energy value, and the wave functions of the radial and the angular parts are expressed in ... function and vibrational mean energy function are expressed in terms of error function. Keywords. Dirac equation spin symmetry; modified ...
Asymptotic iteration method for the modified Pöschl–Teller potential ...
Indian Academy of Sciences (India)
The increase in the radial quantum number n r causes a decrease in the energy value, and the wave functions of the radial and the angular parts are expressed in ... properties such as vibrational partition function, vibrational specific heat function and vibrational mean energy function are expressed in terms of error function.
Dhage Iteration Method for Generalized Quadratic Functional Integral Equations
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Bapurao C. Dhage
2015-01-01
Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.
Optimal homotopy asymptotic method for solving fractional relaxation-oscillation equation
Directory of Open Access Journals (Sweden)
Mohammad Hamarsheh
2015-11-01
Full Text Available In this paper, an approximate analytical solution of linear fractional relaxation-oscillation equations in which the fractional derivatives are given in the Caputo sense, is obtained by the optimal homotopy asymptotic method (OHAM. The studied OHAM is based on minimizing the residual error. The results given by OHAM are compared with the exact solutions and the solutions obtained by generalized Taylor matrix method. The reliability and efficiency of the proposed approach are demonstrated in three examples with the aid of the symbolic algebra program Maple.
Energy Technology Data Exchange (ETDEWEB)
Griebel, M. [Technische Universitaet Muenchen (Germany)
1994-12-31
In recent years, it has turned out that many modern iterative algorithms (multigrid schemes, multilevel preconditioners, domain decomposition methods etc.) for solving problems resulting from the discretization of PDEs can be interpreted as additive (Jacobi-like) or multiplicative (Gauss-Seidel-like) subspace correction methods. The key to their analysis is the study of certain metric properties of the underlying splitting of the discretization space V into a sum of subspaces V{sub j}, j = 1{hor_ellipsis}, J resp. of the variational problem on V into auxiliary problems on these subspaces. Here, the author proposes a modified approach to the abstract convergence theory of these additive and multiplicative Schwarz iterative methods, that makes the relation to traditional iteration methods more explicit. To this end he introduces the enlarged Hilbert space V = V{sub 0} x {hor_ellipsis} x V{sub j} which is nothing else but the usual construction of the Cartesian product of the Hilbert spaces V{sub j} and use it now in the discretization process. This results in an enlarged, semidefinite linear system to be solved instead of the usual definite system. Then, modern multilevel methods as well as domain decomposition methods simplify to just traditional (block-) iteration methods. Now, the convergence analysis can be carried out directly for these traditional iterations on the enlarged system, making convergence proofs of multilevel and domain decomposition methods more clear, or, at least, more classical. The terms that enter the convergence proofs are exactly the ones of the classical iterative methods. It remains to estimate them properly. The convergence proof itself follow basically line by line the old proofs of the respective traditional iterative methods. Additionally, new multilevel/domain decomposition methods are constructed straightforwardly by now applying just other old and well known traditional iterative methods to the enlarged system.
The workshop on iterative methods for large scale nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Walker, H.F. [Utah State Univ., Logan, UT (United States). Dept. of Mathematics and Statistics; Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States). Utah Supercomputing Inst.
1995-12-01
The aim of the workshop was to bring together researchers working on large scale applications with numerical specialists of various kinds. Applications that were addressed included reactive flows (combustion and other chemically reacting flows, tokamak modeling), porous media flows, cardiac modeling, chemical vapor deposition, image restoration, macromolecular modeling, and population dynamics. Numerical areas included Newton iterative (truncated Newton) methods, Krylov subspace methods, domain decomposition and other preconditioning methods, large scale optimization and optimal control, and parallel implementations and software. This report offers a brief summary of workshop activities and information about the participants. Interested readers are encouraged to look into an online proceedings available at http://www.usi.utah.edu/logan.proceedings. In this, the material offered here is augmented with hypertext abstracts that include links to locations such as speakers` home pages, PostScript copies of talks and papers, cross-references to related talks, and other information about topics addresses at the workshop.
Relativistic stars in Starobinsky gravity with the matched asymptotic expansions method
Arapoǧlu, Savaş; ćıkıntoǧlu, Sercan; Ekşi, K. Yavuz
2017-10-01
We study the structure of relativistic stars in R +α R2 theory using the method of matched asymptotic expansion to handle the higher order derivatives in field equations arising from the higher order curvature term. We find solutions, parametrized by α , for uniform density stars. We obtain the mass-radius relations and study the dependence of maximum mass on α . We find that Mmax is almost linearly proportional to α . For each α the maximum mass configuration has the biggest compactness parameter (η =G M /R c2), and we argue that the general relativistic stellar configuration corresponding to α =0 is the least compact among these.
Directory of Open Access Journals (Sweden)
A.N. Safiullina
2016-06-01
Full Text Available The problem of estimating the parameters m and p of the binomial distribution for a sample having the fixed volume n with the help of the method of moments is considered in this paper. Using the delta method, the joint asymptotic normality of the estimates is established and the parameters of the limit distribution are calculated. The moment estimates of the parameters m and p do not have averages and variance. An explanation is offered for the asymptotic normality parameters in terms of characteristics of the accuracy properties of the estimates. On the basis of the data of statistical modelling, the accuracy properties of the estimates by the delta-method and their modifications which do not have initial defects of the estimates (the values of the estimates of p are below zero and those of m are smaller than the greatest value in the sample are explored. An example of estimating the parameters m and p according to the observations of the number of responses in the experiment with nervous synapse (m is the number of vesicles with acetylcholine in the vicinity of the synapse, p is the probability of acetylcholine release by each vesicle is provided.
A variable-order laminated plate theory based on the variational-asymptotical method
Lee, Bok W.; Sutyrin, Vladislav G.; Hodges, Dewey H.
1993-01-01
The variational-asymptotical method is a mathematical technique by which the three-dimensional analysis of laminated plate deformation can be split into a linear, one-dimensional, through-the-thickness analysis and a nonlinear, two-dimensional, plate analysis. The elastic constants used in the plate analysis are obtained from the through-the-thickness analysis, along with approximate, closed-form three-dimensional distributions of displacement, strain, and stress. In this paper, a theory based on this technique is developed which is capable of approximating three-dimensional elasticity to any accuracy desired. The asymptotical method allows for the approximation of the through-the-thickness behavior in terms of the eigenfunctions of a certain Sturm-Liouville problem associated with the thickness coordinate. These eigenfunctions contain all the necessary information about the nonhomogeneities along the thickness coordinate of the plate and thus possess the appropriate discontinuities in the derivatives of displacement. The theory is presented in this paper along with numerical results for the eigenfunctions of various laminated plates.
An alternative approach to differential-difference equations using the variational iteration method
Energy Technology Data Exchange (ETDEWEB)
Faraz, Naeem; Khan, Yasir [Donghua Univ., Shanghai (China). Modern Textile Inst.; Austin, Francis [Hong Kong Polytechnic Univ., Kowloon (China). Dept. of Applied Mathematics
2010-12-15
Although a variational iteration algorithm was proposed by Yildirim (Math. Prob. Eng. 2008 (2008), Article ID 869614) that successfully solves differential-difference equations, the method involves some repeated and unnecessary iterations in each step. An alternative iteration algorithm (variational iteration algorithm-II) is constructed in this paper that overcomes this shortcoming and promises to provide a universal mathematical tool for many differential-difference equations. (orig.)
Convergence Theorem for Finite Family of Total Asymptotically Nonexpansive Mappings
Directory of Open Access Journals (Sweden)
E.U. Ofoedu
2015-11-01
Full Text Available In this paper we introduce an explicit iteration process and prove strong convergence of the scheme in a real Hilbert space $H$ to the common fixed point of finite family of total asymptotically nonexpansive mappings which is nearest to the point $u \\in H$. Our results improve previously known ones obtained for the class of asymptotically nonexpansive mappings. As application, iterative method for: approximation of solution of variational Inequality problem, finite family of continuous pseudocontractive mappings, approximation of solutions of classical equilibrium problems and approximation of solutions of convex minimization problems are proposed. Our theorems unify and complement many recently announced results.
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.
Numerical analysis for 2D waveguide by applying Raleigh Quotient Iteration Method
Adnan, Farasatul; Kabir, Ariful; Khan, A. F. M. Khodadad
2015-05-01
Rayleigh Quotient Iteration is an optimal shifted inverse iteration method that converges in less iteration than the other standard methods. Finite Element Method (FEM) is used to solve for the eigenvalues of a 2D rectangular waveguide using first order triangular elements. The FEM requires a large matrix equation to be solved and thus various techniques are sought to reduce the computation time. By using the Raleigh Quotient Iteration Method, we reduce computation time which saves memory. Our calculation gives good results compared to other standard techniques such as QR method, QZ method etc.
Xu, Zhiqiang
2017-02-16
Attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.
An Asymptotic-Preserving Method for a Relaxation of the Navier-Stokes-Korteweg Equations
Chertock, Alina; Neusser, Jochen
2015-01-01
The Navier-Stokes-Korteweg (NSK) equations are a classical diffuse-interface model for compressible two-phase flow. As direct numerical simulations based on the NSK system are quite expensive and in some cases even impossible, we consider a relaxation of the NSK system, for which robust numerical methods can be designed. However, time steps for explicit numerical schemes depend on the relaxation parameter and therefore numerical simulations in the relaxation limit are very inefficient. To overcome this restriction, we propose an implicit-explicit asymptotic-preserving finite volume method. We prove that the new scheme provides a consistent discretization of the NSK system in the relaxation limit and demonstrate that it is capable of accurately and efficiently computing numerical solutions of problems with realistic density ratios and small interfacial widths.
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Farrukh Mukhamedov
2012-01-01
Full Text Available We unify all known iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptotically I-nonexpansive mappings. Note that such a scheme contains a particular case of the method introduced by (C. E. Chidume and E. U. Ofoedu, 2009. We construct examples of total asymptotically nonexpansive mappings which are not asymptotically nonexpansive. Note that no such kind of examples were known in the literature. We prove the strong convergence theorems for such iterative process to a common fixed point of the finite family of total asymptotically I-nonexpansive and total asymptotically nonexpansive mappings, defined on a nonempty closed-convex subset of uniformly convex Banach spaces. Moreover, our results extend and unify all known results.
Dilts, James
2016-01-01
For each set of (freely chosen) seed data, the conformal method reduces the Einstein constraint equations to a system of elliptic equations, the conformal constraint equations. We prove an admissibility criterion, based on a (conformal) prescribed scalar curvature problem, which provides a necessary condition on the seed data for the conformal constraint equations to (possibly) admit a solution. We then consider sets of asymptotically Euclidean (AE) seed data for which solutions of the conformal constraint equations exist, and examine the blowup properties of these solutions as the seed data sets approach sets for which no solutions exist. We also prove that there are AE seed data sets which include a Yamabe nonpositive metric and lead to solutions of the conformal constraints. These data sets allow the mean curvature function to have zeroes.
International Conference on Boundary and Interior Layers : Computational and Asymptotic Methods
Kopteva, Natalia; O'Riordan, Eugene; Stynes, Martin
2009-01-01
These Proceedings contain a selection of the lectures given at the conference BAIL 2008: Boundary and Interior Layers – Computational and Asymptotic Methods, which was held from 28th July to 1st August 2008 at the University of Limerick, Ireland. The ?rst three BAIL conferences (1980, 1982, 1984) were organised by Professor John Miller in Trinity College Dublin, Ireland. The next seven were held in Novosibirsk (1986), Shanghai (1988), Colorado (1992), Beijing (1994), Perth (2002),Toulouse(2004),and Got ¨ tingen(2006).With BAIL 2008the series returned to Ireland. BAIL 2010 is planned for Zaragoza. The BAIL conferences strive to bring together mathematicians and engineers whose research involves layer phenomena,as these two groups often pursue largely independent paths. BAIL 2008, at which both communities were well represented, succeeded in this regard. The lectures given were evenly divided between app- cations and theory, exposing all conference participants to a broad spectrum of research into problems e...
Asymptotics and Borel summability
Costin, Ovidiu
2008-01-01
Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.To give a sense of how new methods are us
Directory of Open Access Journals (Sweden)
C. Ünlü
2013-01-01
Full Text Available A modification of the variational iteration method (VIM for solving systems of nonlinear fractional-order differential equations is proposed. The fractional derivatives are described in the Caputo sense. The solutions of fractional differential equations (FDE obtained using the traditional variational iteration method give good approximations in the neighborhood of the initial position. The main advantage of the present method is that it can accelerate the convergence of the iterative approximate solutions relative to the approximate solutions obtained using the traditional variational iteration method. Illustrative examples are presented to show the validity of this modification.
Iterative Reconstruction Methods for Hybrid Inverse Problems in Impedance Tomography
DEFF Research Database (Denmark)
Hoffmann, Kristoffer; Knudsen, Kim
2014-01-01
impedance imaging, magnetic resonance electrical impedance tomography, and ultrasound modulated electrical impedance tomography, and the unified approach to the reconstruction problem encompasses several algorithms suggested in the literature. The four proposed algorithms are implemented numerically in two......For a general formulation of hybrid inverse problems in impedance tomography the Picard and Newton iterative schemes are adapted and four iterative reconstruction algorithms are developed. The general problem formulation includes several existing hybrid imaging modalities such as current density...
Dynamic RCS Simulation of a Missile Target Group Based on the High-frequency Asymptotic Method
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Zhao Tao
2014-04-01
Full Text Available To simulate dynamic Radar Cross Section (RCS of missile target group, an efficient RCS prediction approach is proposed based on the high-frequency asymptotic theory. The minimal energy trajectory and coordinate transformation is used to get trajectories of the missile, decoys and roll booster, and establish the dynamic scene for the separate procedure of the target group, and the dynamic RCS including specular reflection, edge diffraction and multi-reflection from the target group are obtained by Physical Optics (PO, Equivalent Edge Currents (EEC and Shooting-and-Bouncing Ray (SBR methods. Compared with the dynamic RCS result with the common interpolation method, the proposed method is consistent with the common method when the targets in the scene are far away from each other and each target is not sheltered by others in the incident direction. When the target group is densely distributed and the shelter effect can not be neglected, the interpolation method is extremely difficult to realize, whereas the proposed method is successful.
Iterative methods for symmetric ill-conditioned Toeplitz matrices
Energy Technology Data Exchange (ETDEWEB)
Huckle, T. [Institut fuer Informatik, Muenchen (Germany)
1996-12-31
We consider ill-conditioned symmetric positive definite, Toeplitz systems T{sub n}x = b. If we want to solve such a system iteratively with the conjugate gradient method, we can use band-Toeplitz-preconditioners or Sine-Transform-peconditioners M = S{sub n}{Lambda}S{sub n}, S{sub n} the Sine-Transform-matrix and {Lambda} a diagonal matrix. A Toeplitz matrix T{sub n} = (t{sub i-j)}{sub i}{sup n},{sub j=1} is often related to an underlying function f defined by the coefficients t{sub j}, j = -{infinity},..,-1,0, 1,.., {infinity}. There are four cases, for which we want to determine a preconditioner M: - T{sub n} is related to an underlying function which is given explicitly; - T{sub n} is related to an underlying function that is given by its Fourier coefficients; - T{sub n} is related to an underlying function that is unknown; - T{sub n} is not related to an underlying function. Especially for the first three cases we show how positive definite and effective preconditioners based on the Sine-Transform can be defined for general nonnegative underlying function f. To define M, we evaluate or estimate the values of f at certain positions, and build a Sine-transform matrix with these values as eigenvalues. Then, the spectrum of the preconditioned system is bounded from above and away from zero.
Solution of Cubic Equations by Iteration Methods on a Pocket Calculator
Bamdad, Farzad
2004-01-01
A method to provide students a vision of how they can write iteration programs on an inexpensive programmable pocket calculator, without requiring a PC or a graphing calculator is developed. Two iteration methods are used, successive-approximations and bisection methods.
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.
A Comparative Approach to the Solution of the Zabolotskaya-Khokhlov Equation by Iteration Methods
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Saeed Ahmed
2016-01-01
Full Text Available We employed different iteration methods like Homotopy Analysis Method (HAM, Adomian Decomposition Method (ADM, and Variational Iteration Method (VIM to find the approximate solution to the Zabolotskaya-Khokhlov (ZK equation. Iteration methods are used to solve linear and nonlinear PDEs whose classical methods are either very complex or too limited to apply. A comparison study has been made to see which of these methods converges to the approximate solution rapidly. The result revealed that, amongst these methods, ADM is more effective and simpler tool in its nature which does not require any transformation or linearization.
Iterative methods for plasma sheath calculations: Application to spherical probe
Parker, L. W.; Sullivan, E. C.
1973-01-01
The computer cost of a Poisson-Vlasov iteration procedure for the numerical solution of a steady-state collisionless plasma-sheath problem depends on: (1) the nature of the chosen iterative algorithm, (2) the position of the outer boundary of the grid, and (3) the nature of the boundary condition applied to simulate a condition at infinity (as in three-dimensional probe or satellite-wake problems). Two iterative algorithms, in conjunction with three types of boundary conditions, are analyzed theoretically and applied to the computation of current-voltage characteristics of a spherical electrostatic probe. The first algorithm was commonly used by physicists, and its computer costs depend primarily on the boundary conditions and are only slightly affected by the mesh interval. The second algorithm is not commonly used, and its costs depend primarily on the mesh interval and slightly on the boundary conditions.
A New General Iterative Method for a Finite Family of Nonexpansive Mappings in Hilbert Spaces
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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.
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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.
Comparison of advanced iterative reconstruction methods for SPECT/CT
Energy Technology Data Exchange (ETDEWEB)
Knoll, Peter; Koechle, Gunnar; Mirzaei, Siroos [Wilhelminenspital, Vienna (Austria). Dept. of Nuclear Medicine and PET Center; Kotalova, Daniela; Samal, Martin [Charles Univ. Prague, Prague (Czech Republic); Kuzelka, Ivan; Zadrazil, Ladislav [Hospital Havlickuv Brod (Czech Republic); Minear, Greg [Landesklinikum St. Poelten (Austria). Dept. of Internal Medicine II; Bergmann, Helmar [Medical Univ. of Vienna (Austria). Center for Medical Physics and Biomedical Engineering
2012-07-01
Aim: Corrective image reconstruction methods which produce reconstructed images with improved spatial resolution and decreased noise level became recently commercially available. In this work, we tested the performance of three new software packages with reconstruction schemes recommended by the manufacturers using physical phantoms simulating realistic clinical settings. Methods: A specially designed resolution phantom containing three {sup 99m}Tc lines sources and the NEMA NU-2 image quality phantom were acquired on three different SPECT/CT systems (General Electrics Infinia, Philips BrightView and Siemens Symbia T6). Measurement of both phantoms was done with the trunk filled with a {sup 99m}Tc-water solution. The projection data were reconstructed using the GE's Evolution for Bone {sup registered}, Philips Astonish {sup registered} and Siemens Flash3D {sup registered} software. The reconstruction parameters employed (number of iterations and subsets, the choice of post-filtering) followed theses recommendations of each vendor. These results were compared with reference reconstructions using the ordered subset expectation maximization (OSEM) reconstruction scheme. Results: The best results (smallest value for resolution, highest percent contrast values) for all three packages were found for the scatter corrected data without applying any post-filtering. The advanced reconstruction methods improve the full width at half maximum (FWHM) of the line sources from 11.4 to 9.5 mm (GE), from 9.1 to 6.4 mm (Philips), and from 12.1 to 8.9 mm (Siemens) if no additional post filter was applied. The total image quality control index measured for a concentration ratio of 8:1 improves for GE from 147 to 189, from 179. to 325 for Philips and from 217 to 320 for Siemens using the reference method for comparison. The same trends can be observed for the 4:1 concentration ratio. The use of a post-filter reduces the background variability approximately by a factor of two, but
Numerical Analysis of Asymptotic Stability of Equilibrium Points
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A. A. Vorkel
2017-01-01
Full Text Available The aim of this study is to numerically analyze an asymptotic stability of the equilibrium points of autonomous systems of ordinary differential equations on the basis of the asymptotic stability criterion given in the article and the functional localization method of invariant compact sets. The article formulates the necessary and sufficient conditions for an asymptotic stability in terms of invariant compact sets and positively invariant sets and describes a functional localization method. Presents appropriate localization theorems for invariant compact sets of dynamical systems.To investigate the asymptotic stability is proposed an algorithm for a numerical iteration procedure to construct the localizing bounds for invariant compact sets contained in a given initial set. Application of the asymptotic stability criterion is based on the results of this procedure. The author of the article verifies the conditions of the appropriate theorem and confirms the use of this criterion.The examples of two- and three-dimensional systems of differential equations demonstrate a principle of the iteration procedure. The article also gives an example of the system with a limit cycle and it shows that the developed numerical algorithm and the functional localization method of invariant compact sets can be used to analyze stability of the limit cycles.Thanks to the method described in the article, when analyzing an asymptotic stability of equilibrium points, finding a Lyapunov function and calculating eigenvalues of a matrix of linear approximation are non-essential. Thus, it is possible to avoid labour-intensive work with complex analytical structures.The numerical iteration procedure can be used in systems of different dimensions and makes the presented algorithm of asymptotic stability analysis universal.
On the Convergence for an Iterative Method for Quasivariational Inclusions
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Wu Changqun
2010-01-01
Full Text Available We introduce an iterative algorithm for finding a common element of the set of solutions of quasivariational inclusion problems and of the set of fixed points of strict pseudocontractions in the framework Hilbert spaces. The results presented in this paper improve and extend the corresponding results announced by many others.
A New Newton-Like Iterative Method for Roots of Analytic Functions
Otolorin, Olayiwola
2005-01-01
A new Newton-like iterative formula for the solution of non-linear equations is proposed. To derive the formula, the convergence criteria of the one-parameter iteration formula, and also the quasilinearization in the derivation of Newton's formula are reviewed. The result is a new formula which eliminates the limitations of other methods. There is…
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Liaqat Ali
2016-09-01
Full Text Available In this research work a new version of Optimal Homotopy Asymptotic Method is applied to solve nonlinear boundary value problems (BVPs in finite and infinite intervals. It comprises of initial guess, auxiliary functions (containing unknown convergence controlling parameters and a homotopy. The said method is applied to solve nonlinear Riccati equations and nonlinear BVP of order two for thin film flow of a third grade fluid on a moving belt. It is also used to solve nonlinear BVP of order three achieved by Mostafa et al. for Hydro-magnetic boundary layer and micro-polar fluid flow over a stretching surface embedded in a non-Darcian porous medium with radiation. The obtained results are compared with the existing results of Runge-Kutta (RK-4 and Optimal Homotopy Asymptotic Method (OHAM-1. The outcomes achieved by this method are in excellent concurrence with the exact solution and hence it is proved that this method is easy and effective.
On Two Iterative Methods for Mixed Monotone Variational Inequalities
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Xiwen Lu
2010-01-01
Full Text Available A mixed monotone variational inequality (MMVI problem in a Hilbert space H is formulated to find a point u∗∈H such that 〈Tu∗,v−u∗〉+φ(v−φ(u∗≥0 for all v∈H, where T is a monotone operator and φ is a proper, convex, and lower semicontinuous function on H. Iterative algorithms are usually applied to find a solution of an MMVI problem. We show that the iterative algorithm introduced in the work of Wang et al., (2001 has in general weak convergence in an infinite-dimensional space, and the algorithm introduced in the paper of Noor (2001 fails in general to converge to a solution.
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Yong-Ju Yang
2013-01-01
Full Text Available The local fractional variational iteration method for local fractional Laplace equation is investigated in this paper. The operators are described in the sense of local fractional operators. The obtained results reveal that the method is very effective.
A non-iterative method for constraining masses in particle decays
Bingül, Ahmet
2012-11-01
To overcome the mass constraint problem of particle decays, a non-iterative method is developed as an alternative to relatively complicated and slow iterative methods. The new method can be applied to any two-body decay or a many-body decay which can be reduced to a two-body decay having well known daughter masses. By using a toy detector simulation and ALEPH full simulation data, the performance of the new method is compared with the traditional iterative chi-square method for several decay types. No significant difference is obtained between the two methods in terms of improvement in momentum resolution. However, the non-iterative method is found to be much faster than the chi-square method.
Drawing dynamical and parameters planes of iterative families and methods.
Chicharro, Francisco I; Cordero, Alicia; Torregrosa, Juan R
2013-01-01
The complex dynamical analysis of the parametric fourth-order Kim's iterative family is made on quadratic polynomials, showing the MATLAB codes generated to draw the fractal images necessary to complete the study. The parameter spaces associated with the free critical points have been analyzed, showing the stable (and unstable) regions where the selection of the parameter will provide us the excellent schemes (or dreadful ones).
A stochastic iteration method for the solution of finite dimensional ...
African Journals Online (AJOL)
Let A be a real n x n matrix, let b a real column n-vector and φ: Rn → R such that Ax + δφ(x) ∋b where δφ is the sub gradient of φ. A computable stochastic iterative scheme is suggested; which is a modification of Robbins-Monroe procedure and studied in the context of the above concrete problem. This scheme is shown to ...
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/.
Iterative interferometry-based method for picking microseismic events
Iqbal, Naveed; Al-Shuhail, Abdullatif A.; Kaka, SanLinn I.; Liu, Entao; Raj, Anupama Govinda; McClellan, James H.
2017-05-01
Continuous microseismic monitoring of hydraulic fracturing is commonly used in many engineering, environmental, mining, and petroleum applications. Microseismic signals recorded at the surface, suffer from excessive noise that complicates first-break picking and subsequent data processing and analysis. This study presents a new first-break picking algorithm that employs concepts from seismic interferometry and time-frequency (TF) analysis. The algorithm first uses a TF plot to manually pick a reference first-break and then iterates the steps of cross-correlation, alignment, and stacking to enhance the signal-to-noise ratio of the relative first breaks. The reference first-break is subsequently used to calculate final first breaks from the relative ones. Testing on synthetic and real data sets at high levels of additive noise shows that the algorithm enhances the first-break picking considerably. Furthermore, results show that only two iterations are needed to converge to the true first breaks. Indeed, iterating more can have detrimental effects on the algorithm due to increasing correlation of random noise.
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R. Yulita Molliq
2012-01-01
Full Text Available In this study, fractional Rosenau-Hynam equations is considered. We implement relatively new analytical techniques, the variational iteration method and the homotopy perturbation method, for solving this equation. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for fractional Rosenau-Hynam equations. In these schemes, the solution takes the form of a convergent series with easily computable components. The present methods perform extremely well in terms of efficiency and simplicity.
Energy Technology Data Exchange (ETDEWEB)
Dranishnikov, A N [Steklov Mathematical Institute, Russian Academy of Sciences (Russian Federation)
2000-12-31
In this paper we study the similarity between local topology and its global analogue, so-called asymptotic topology. In the asymptotic case, the notions of dimension, cohomological dimension, and absolute extensor are introduced and some basic facts about them are proved. The Higson corona functor establishing a connection between macro- and micro-topology is considered. A relationship between problems of general asymptotic topology and the Novikov conjecture on higher signatures is discussed. Some new results concerning the Novikov conjecture and other related conjectures are presented.
Pseudoinverse preconditioners and iterative methods for large dense linear least-squares problems
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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.
Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces
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Juguo Su
2012-01-01
Full Text Available The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.
Application of the perturbation iteration method to boundary layer type problems.
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.
Novel method for rail wear inspection based on the sparse iterative closest point method
Yi, Bing; Yang, Yue; Yi, Qian; Dai, Wanlin; Li, Xiongbing
2017-12-01
As trains become progressively faster, it is becoming imperative to automatically and precisely inspect the rail profile of high-speed railways to ensure their safety and reliability. To realize this, a new method based on the sparse iterative closest point method is proposed in this study. Moreover, the noncontact method is mainly used for convenience and practicality. First, a line laser-based measurement system is constructed, and the position of the line laser is calculated to ensure that both the top and sides of the rail are in range of the line laser. Then, the measured data of the rail profile are separated into a baseline part and worn part. The baseline is involved in registering the measured data and reference profile by the sparse iterative closest point method. The worn part is then transformed by the same matrix of the baseline part. Finally, the Hausdorff distance is introduced to measure the distance between the wear model and reference model. The experimental results demonstrate the effectiveness and efficiency of the proposed method.
Worst-case Analysis of Strategy Iteration and the Simplex Method
DEFF Research Database (Denmark)
Hansen, Thomas Dueholm
programming is an exceedingly important problem with numerous applications. The simplex method was introduced by Dantzig in 1947, and has since then been studied extensively. It can be shown that MDPs can be formulated as linear programs, thus, giving rise to the connection. Strategy iteration and simplex......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...... an adversary. 2TBSGs form an intriguing class of games whose status in many ways resembles that of linear programming 40 years ago. They can be solved efficiently with strategy iteration algorithms, resembling the simplex method for linear programming, but no polynomial time algorithm is known. Linear...
A novel method of Newton iteration-based interval analysis for multidisciplinary systems
Wang, Lei; Xiong, Chuang; Wang, RuiXing; Wang, XiaoJun; Wu, Di
2017-09-01
A Newton iteration-based interval uncertainty analysis method (NI-IUAM) is proposed to analyze the propagating effect of interval uncertainty in multidisciplinary systems. NI-IUAM decomposes one multidisciplinary system into single disciplines and utilizes a Newton iteration equation to obtain the upper and lower bounds of coupled state variables at each iterative step. NI-IUAM only needs to determine the bounds of uncertain parameters and does not require specific distribution formats. In this way, NI-IUAM may greatly reduce the necessity for raw data. In addition, NI-IUAM can accelerate the convergence process as a result of the super-linear convergence of Newton iteration. The applicability of the proposed method is discussed, in particular that solutions obtained in each discipline must be compatible in multidisciplinary systems. The validity and efficiency of NI-IUAM is demonstrated by both numerical and engineering examples.
Numerical Solutions of Fractional Fokker-Planck Equations Using Iterative Laplace Transform Method
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Limei Yan
2013-01-01
Full Text Available A relatively new iterative Laplace transform method, which combines two methods; the iterative method and the Laplace transform method, is applied to obtain the numerical solutions of fractional Fokker-Planck equations. The method gives numerical solutions in the form of convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results show that the approach is easy to implement and straightforward when applied to space-time fractional Fokker-Planck equations. The method provides a promising tool for solving space-time fractional partial differential equations.
Three-step iterative methods with eighth-order convergence for solving nonlinear equations
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Mashallah Matinfar
2013-01-01
Full Text Available A family of eighth-order iterative methods for solution of nonlinear equations is presented. We propose an optimal three-step method with eight-order convergence for finding the simple roots of nonlinear equations by Hermite interpolation method. Per iteration of this method requires two evaluations of the function and two evaluations of its first derivative, which implies that the efficiency index of the developed methods is 1.682. Some numerical examples illustrate that the algorithms are more efficient and performs better than the other methods.
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.
The asymptotic convergence factor for a polygon under a perturbation
Energy Technology Data Exchange (ETDEWEB)
Li, X. [Georgia Southern Univ., Statesboro, GA (United States)
1994-12-31
Let Ax = b be a large system of linear equations, where A {element_of} C{sup NxN}, nonsingular and b {element_of} C{sup N}. A few iterative methods for solving have recently been presented in the case where A is nonsymmetric. Many of their algorithms consist of two phases: Phase I: estimate the extreme eigenvalues of A; Phase II: construct and apply an iterative method based on the estimates. For convenience, it is rewritten as an equivalent fixed-point form, x = Tx + c. Let {Omega} be a compact set excluding 1 in the complex plane, and let its complement in the extended complex plane be simply connected. The asymptotic convergence factor (ACF) for {Omega}, denoted by {kappa}({Omega}), measures the rate of convergence for the asymptotically optimal semiiterative methods for solving, where {sigma}(T) {contained_in} {Omega}.
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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.
Parallel Iterative Solution Methods for Linear Systems arising from Discretized PDE's
Vorst, H.A. van der
1995-01-01
In these notes we will present an overview of a number of related iterative methods for the solution of linear systems of equations. These methods are so-called Krylov projection type methods and the include popular methods as Conjugate Gradients, Bi-Conjugate Gradients, CGST Bi-CGSTAB, QMR, LSQR
An efficient iterative method for solving the Fokker-Planck equation
AL-Jawary, M. A.
In the present paper, the new iterative method proposed by Daftardar-Gejji and Jafari (NIM or DJM) (2006) is used to solve the linear and nonlinear Fokker-Planck equations and some similar equations. In this iterative method the solution is obtained in the series form that converge to the exact solution with easily computed components. The results demonstrate that the method has many merits such as being derivative-free, overcome the difficulty arising in calculating Adomian polynomials to handle the nonlinear terms in Adomian decomposition method (ADM). It does not require to calculate Lagrange multiplier as in variational iteration method (VIM) and for solving a nonlinear case, the terms of the sequence become complex after several iterations. Thus, analytical evaluation of terms becomes very difficult or impossible in VIM. No needs to construct a homotopy and solve the corresponding algebraic equations as in homotopy perturbation method (HPM). In this work, the applications of the DJM for 1D, 2D, 3D linear and nonlinear Fokker-Planck equations are given and the results demonstrate that the presented method is very effective and reliable and does not require any restrictive assumptions for nonlinear terms and provide the analytic solutions. A symbolic manipulator Mathematica® 10.0 was used to evaluate terms in the iterative process.
A comparison of iterative methods for a model coupled system of elliptic equations
Energy Technology Data Exchange (ETDEWEB)
Donato, J.M.
1993-08-01
Many interesting areas of current industry work deal with non-linear coupled systems of partial differential equations. We examine iterative methods for the solution of a model two-dimensional coupled system based on a linearized form of the two carrier drift-diffusion equations from semiconductor modeling. Discretizing this model system yields a large non-symmetric indefinite sparse matrix. To solve the model system various point and block methods, including the hybrid iterative method Alternate Block Factorization (ABF), are applied. We also employ GMRES with various preconditioners, including block and point incomplete LU (ILU) factorizations. The performance of these methods is compared. It is seen that the preferred ordering of the grid variables and the choice of iterative method are dependent upon the magnitudes of the coupling parameters. For this model, ABF is the most robust of the non-accelerated iterative methods. Among the preconditioners employed with GMRES, the blocked ``by grid point`` version of both the ILU and MILU preconditioners are the most robust and the most time efficient over the wide range of parameter values tested. This information may aid in the choice of iterative methods and preconditioners for solving more complicated, yet analogous, coupled systems.
A Comparison of Iterative 2D-3D Pose Estimation Methods for Real-Time Applications
DEFF Research Database (Denmark)
Grest, Daniel; Krüger, Volker; Petersen, Thomas
2009-01-01
This work compares iterative 2D-3D Pose Estimation methods for use in real-time applications. The compared methods are available for public as C++ code. One method is part of the openCV library, namely POSIT. Because POSIT is not applicable for planar 3Dpoint congurations, we include the planar P...
An Iterative Method for the Matrix Principal n-th Root
Lakić, Slobodan
1995-01-01
In this paper we give an iterative method to compute the principal n-th root and the principal inverse n-th root of a given matrix. As we shall show this method is locally convergent. This method is analyzed and its numerical stability is investigated.
An incremental-iterative method for modeling damage evolution in voxel-based microstructure models
Zhu, Qi-Zhi; Yvonnet, Julien
2015-02-01
Numerical methods motivated by rapid advances in image processing techniques have been intensively developed during recent years and increasingly applied to simulate heterogeneous materials with complex microstructure. The present work aims at elaborating an incremental-iterative numerical method for voxel-based modeling of damage evolution in quasi-brittle microstructures. The iterative scheme based on the Lippmann-Schwinger equation in the real space domain (Yvonnet, in Int J Numer Methods Eng 92:178-205, 2012) is first cast into an incremental form so as to implement nonlinear material models efficiently. In the proposed scheme, local strain increments at material grid points are computed iteratively by a mapping operation through a transformation array, while local stresses are determined using a constitutive model that accounts for material degradation by damage. For validation, benchmark studies and numerical simulations using microtomographic data of concrete are performed. For each test, numerical predictions by the incremental-iterative scheme and the finite element method, respectively, are presented and compared for both global responses and local damage distributions. It is emphasized that the proposed incremental-iterative formulation can be straightforwardly applied in the framework of other Lippmann-Schwinger equation-based schemes, like the fast Fourier transform method.
Picard Iteration, Chebyshev Polynomials and Chebyshev-Picard Methods: Application in Astrodynamics
Junkins, John L.; Bani Younes, Ahmad; Woollands, Robyn M.; Bai, Xiaoli
2013-12-01
This paper extends previous work on parallel-structured Modified Chebyshev Picard Iteration (MCPI) Methods. The MCPI approach iteratively refines path approximation of the state trajectory for smooth nonlinear dynamical systems and this paper shows that the approach is especially suitable for initial value problems of astrodynamics. Using Chebyshev polynomials, as the orthogonal approximation basis, it is straightforward to distribute the computation of force functions needed in MCPI to generate the polynomial coefficients (approximating the path iterations) to different processors. Combining Chebyshev polynomials with Picard iteration, MCPI methods iteratively refines path estimates over large time intervals chosen to be within the domain of convergence of Picard iteration. The developed vector-matrix form makes MCPI methods computationally efficient and a more systematic approach is given, leading to a modest correction to results in the published dissertation by Bai. The power of MCPI methods for solving IVPs is clearly illustrated using a simple nonlinear differential equation with a known analytical solution. Compared with the most common integration scheme, the standard Runge-Kutta 4-5 method as implemented in MATLAB, MCPI methods generate solutions with better accuracy as well as orders of magnitude speedups, on a serial machine. MCPI performance is also compared to state of the art integrators such as the Runge-Kutta Nystrom 12(10) methods applied to the relevant orbit mechanics problems. The MCPI method is shown to be well-suited to solving these problems in serial processors with over an order of magnitude speedup relative to known methods. Furthermore, the approach is parallel-structured so that it is suited for parallel implementation and further speedups. When used in conjunction with the recently developed local gravity approximations in conjunction with parallel computation, we anticipate MCPI will enable revolutionary speedups while ensuring
Ramnath, Rudrapatna V
2012-01-01
This book addresses the task of computation from the standpoint of asymptotic analysis and multiple scales that may be inherent in the system dynamics being studied. This is in contrast to the usual methods of numerical analysis and computation. The technical literature is replete with numerical methods such as Runge-Kutta approach and its variations, finite element methods, and so on. However, not much attention has been given to asymptotic methods for computation, although such approaches have been widely applied with great success in the analysis of dynamic systems. The presence of differen
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
Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation
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Dang Quang A.
2012-01-01
Full Text Available Solving boundary value problems (BVPs for the fourth-order differential equations by the reduction of them to BVPs for the second-order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by ourselves in recent works, we construct iterative method for the second BVP for biharmonic-type equation, which describes the deflection of a plate resting on a biparametric elastic foundation. The convergence rate of the method is established. The optimal value of the iterative parameter is found. Several numerical examples confirm the efficiency of the proposed method.
Iterative method of baffle design for modified Ritchey-Chretien telescope.
Senthil Kumar, M; Narayanamurthy, C S; Kiran Kumar, A S
2013-02-20
We developed a baffle design method based on a combination of the results of optical design software and analytical relations formulated herein. The method finds the exact solution for baffle parameters of a modified Ritchey-Chretien telescope by iteratively solving the analytical relations using the actual ray coordinates of the telescope computed with the aid of optical design software. The baffle system so designed not only blocks the direct rays of stray light reaching the image plane but also provides minimum obscuration to imaging light. Based on the iterative method, we proposed a baffle design approach for a rectangular-image-format telescope.
A Splitting-based Iterative Method for Sparse Reconstruction
Directory of Open Access Journals (Sweden)
Liquan Kang
2016-02-01
Full Text Available In this paper, we study a ℓ1-norm regularized minimization method for sparse solution recovery in compressed sensing and X-ray CT image reconstruction. In the proposed method, an alternating minimization algorithm is employed to solve the involved ℓ1-norm regularized minimization problem. Under some suitable conditions, the proposed algorithm is shown to be globally convergent. Numerical results indicate that the presented method is effective and promising.
On iterative methods for the incompressible Stokes problem
Rehman, M. ur; Geenen, T.; Vuik, C.; Segal, G.; MacLachlan, S.P.
2011-01-01
In this paper, we discuss various techniques for solving the system of linear equations that arise from the discretization of the incompressible Stokes equations by the finite-element method. The proposed solution methods, based on a suitable approximation of the Schur-complement matrix, are shown
Directory of Open Access Journals (Sweden)
Baojian Hong
2014-01-01
Full Text Available Based on He’s variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS. The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of the GFNLS are investigated. Furthermore, the approximate iterative series and numerical results show that the modified fractional variational iteration method is powerful, reliable, and effective when compared with some classic traditional methods such as homotopy analysis method, homotopy perturbation method, adomian decomposition method, and variational iteration method in searching for approximate solutions of the Schrödinger equations.
Hong, Baojian; Lu, Dianchen
2014-01-01
Based on He's variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of the GFNLS are investigated. Furthermore, the approximate iterative series and numerical results show that the modified fractional variational iteration method is powerful, reliable, and effective when compared with some classic traditional methods such as homotopy analysis method, homotopy perturbation method, adomian decomposition method, and variational iteration method in searching for approximate solutions of the Schrödinger equations.
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Hai Bi
2012-01-01
Full Text Available This paper discusses efficient numerical methods for the Steklov eigenvalue problem and establishes a new multiscale discretization scheme and an adaptive algorithm based on the Rayleigh quotient iterative method. The efficiency of these schemes is analyzed theoretically, and the constants appeared in the error estimates are also analyzed elaborately. Finally, numerical experiments are provided to support the theory.
A new Sumudu transform iterative method for time-fractional Cauchy reaction-diffusion equation.
Wang, Kangle; Liu, Sanyang
2016-01-01
In this paper, a new Sumudu transform iterative method is established and successfully applied to find the approximate analytical solutions for time-fractional Cauchy reaction-diffusion equations. The approach is easy to implement and understand. The numerical results show that the proposed method is very simple and efficient.
An iterative method for the canard explosion in general planar systems
DEFF Research Database (Denmark)
Brøns, Morten
2012-01-01
are also observed in systems where no such parameter is present. Here we show how the iterative method of Roussel and Fraser, devised to construct regular slow manifolds, can be used to determine a canard point in a general planar system of nonlinear ODEs. We demonstrate the method on the van der Pol...
Templates for the solution of linear systems: building blocks for iterative methods
Barrett, R.; Berry, M.; Chan, T.; Demmel, J.; Donato, J.; Dongarra, J.; Eijkhout, V.; Pozo, R.; Romine, C.; Vorst, H.A. van der
1994-01-01
We have divided this book into five main chapters. Chapter 1 gives the motivation for this book and the use of templates. Chapter 2 describes stationary and nonstationary iterative methods. In this chapter we present both historical development and state-of-the-art methods for solving some of the
Directory of Open Access Journals (Sweden)
Qiang Wu
2013-01-01
Full Text Available Bioluminescence tomography (BLT has a great potential to provide a powerful tool for tumor detection, monitoring tumor therapy progress, and drug development; developing new reconstruction algorithms will advance the technique to practical applications. In the paper, we propose a BLT reconstruction algorithm by combining SP3 equations and Bregman iteration method to improve the quality of reconstructed sources. The numerical results for homogeneous and heterogeneous phantoms are very encouraging and give significant improvement over the algorithms without the use of SP3 equations and Bregman iteration method.
Mechanical Analogy-based Iterative Method for Solving a System of Linear Equations
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Yu. V. Berchun
2015-01-01
Full Text Available The paper reviews prerequisites to creating a variety of the iterative methods to solve a system of linear equations (SLE. It considers the splitting methods, variation-type methods, projection-type methods, and the methods of relaxation.A new iterative method based on mechanical analogy (the movement without resistance of a material point, that is connected by ideal elastically-linear constraints with unending guides defined by equations of solved SLE. The mechanical system has the unique position of stable equilibrium, the coordinates of which correspond to the solution of linear algebraic equation. The model of the mechanical system is a system of ordinary differential equations of the second order, integration of which allows you to define the point trajectory. In contrast to the classical methods of relaxation the proposed method does not ensure a trajectory passage through the equilibrium position. Thus the convergence of the method is achieved through the iterative stop of a material point at the moment it passes through the next (from the beginning of the given iteration minimum of potential energy. After that the next iteration (with changed initial coordinates starts.A resource-intensive process of numerical integration of differential equations in order to obtain a precise law of motion (at each iteration is replaced by defining its approximation. The coefficients of the approximating polynomial of the fourth order are calculated from the initial conditions, including higher-order derivatives. The resulting approximation enables you to evaluate the kinetic energy of a material point to calculate approximately the moment of time to reach the maximum kinetic energy (and minimum of the potential one, i.e. the end of the iteration.The software implementation is done. The problems with symmetric positive definite matrix, generated as a result of using finite element method, allowed us to examine a convergence rate of the proposed method
Directory of Open Access Journals (Sweden)
Cristinel Mortici
2015-01-01
Full Text Available In this survey we present our recent results on analysis of gamma function and related functions. The results obtained are in the theory of asymptotic analysis, approximation of gamma and polygamma functions, or in the theory of completely monotonic functions. The motivation of this first part is the work of C. Mortici [Product Approximations via Asymptotic Integration Amer. Math. Monthly 117 (2010 434-441] where a simple strategy for constructing asymptotic series is presented. The classical asymptotic series associated to Stirling, Wallis, Glaisher-Kinkelin are rediscovered. In the second section we discuss some new inequalities related to Landau constants and we establish some asymptotic formulas.
An iterative method to invert the LTSn matrix
Energy Technology Data Exchange (ETDEWEB)
Cardona, A.V.; Vilhena, M.T. de [UFRGS, Porto Alegre (Brazil)
1996-12-31
Recently Vilhena and Barichello proposed the LTSn method to solve, analytically, the Discrete Ordinates Problem (Sn problem) in transport theory. The main feature of this method consist in the application of the Laplace transform to the set of Sn equations and solve the resulting algebraic system for the transport flux. Barichello solve the linear system containing the parameter s applying the definition of matrix invertion exploiting the structure of the LTSn matrix. In this work, it is proposed a new scheme to invert the LTSn matrix, decomposing it in blocks and recursively inverting this blocks.
Wang, Jinguo; Zhao, Zhiqin; Song, Jian; Chen, Guoping; Nie, Zaiping; Liu, Qing-Huo
2015-05-01
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. 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. 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. 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.
Frozen Jacobian Multistep Iterative Method for Solving Nonlinear IVPs and BVPs
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Fayyaz Ahmad
2017-01-01
Full Text Available In this paper, we present and illustrate a frozen Jacobian multistep iterative method to solve systems of nonlinear equations associated with initial value problems (IVPs and boundary value problems (BVPs. We have used Jacobi-Gauss-Lobatto collocation (J-GL-C methods to discretize the IVPs and BVPs. Frozen Jacobian multistep iterative methods are computationally very efficient. They require only one inversion of the Jacobian in the form of LU-factorization. The LU factors can then be used repeatedly in the multistep part to solve other linear systems. The convergence order of the proposed iterative method is 5m-11, where m is the number of steps. The validity, accuracy, and efficiency of our proposed frozen Jacobian multistep iterative method is illustrated by solving fifteen IVPs and BVPs. It has been observed that, in all the test problems, with one exception in this paper, a single application of the proposed method is enough to obtain highly accurate numerical solutions. In addition, we present a comprehensive comparison of J-GL-C methods on a collection of test problems.
Parvathi, S. P.; Ramanan, R. V.
2017-04-01
In a direct interplanetary transfer, the spacecraft moves from a parking orbit of the departure planet to a parking orbit of the arrival planet. The transfer trajectory must be designed such that the specified arrival parking orbit conditions are achieved. For a fixed departure epoch and flight duration, there are four distinct transfer trajectory design options in a direct transfer. The conventional patched conic method, the most widely used analytical trajectory design method, does not identify these design options. An iterative patched conic method that identifies these distinct design options is developed and presented in this paper. This method involves two iterative processes: (i) iteration on the hyperbolic orbit characteristics using an analytical tuning strategy to achieve the hyperbolic excess velocity vector at the patch point, (ii) iteration on the patch points at the sphere of influence. The performance of the proposed method is compared with the conventional and V-infinity tuned patched conic methods. A design analysis tool, based on the proposed method, is developed and tested in various orbiter mission scenarios.
Convergence of GAOR Iterative Method with Strictly Diagonally Dominant Matrices
Directory of Open Access Journals (Sweden)
Guangbin Wang
2011-01-01
Full Text Available We discuss the convergence of GAOR method for linear systems with strictly diagonally dominant matrices. Moreover, we show that our results are better than ones of Darvishi and Hessari (2006, Tian et al. (2008 by using three numerical examples.
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.
Boosting iterative stochastic ensemble method for nonlinear calibration of subsurface flow models
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.
Parallel iterative solvers and preconditioners using approximate hierarchical methods
Energy Technology Data Exchange (ETDEWEB)
Grama, A.; Kumar, V.; Sameh, A. [Univ. of Minnesota, Minneapolis, MN (United States)
1996-12-31
In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.
Method and apparatus for iterative lysis and extraction of algae
Chew, Geoffrey; Boggs, Tabitha; Dykes, Jr., H. Waite H.; Doherty, Stephen J.
2015-12-01
A method and system for processing algae involves the use of an ionic liquid-containing clarified cell lysate to lyse algae cells. The resulting crude cell lysate may be clarified and subsequently used to lyse algae cells. The process may be repeated a number of times before a clarified lysate is separated into lipid and aqueous phases for further processing and/or purification of desired products.
A two-step iterative method for evolving nonlinear acoustic systems to a steady-state
Watson, Willie R.; Myers, Michael K.
1990-01-01
A new approach for evolving two-dimensional nonlinear acoustic systems with flow to a steady state is presented. The approach is a two-step iterative method which is tested on a benchmark acoustic problem for which an exact analytical solution is available. Results are also calculated for a nonlinear acoustic problem for which an exact analytical solution is not known. Results indicate that the two-step method represents a powerful, efficient, and stable method for evolving two-dimensional acoustic systems to a steady state, and that the method is applicable to any number of spatial dimensions and to other hyperbolic systems. It is noted that for the benchmark problem only a single iteration on the method is required when the transient and steady-state field are of the same order of magnitude; however, four iterations are required when the steady-state field is several orders of magnitude smaller than the transient field. This method requires six iterations before achieving a steady state for the nonlinear test problem.
A fast method to emulate an iterative POCS image reconstruction algorithm.
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.
A three-step least-squares iterative method for tilt phase-shift interferometry.
Liu, Qian; Wang, Yang; Ji, Fang; He, Jianguo
2013-12-02
An iterative method based on least-squares fittings is proposed to retrieve wavefront phase from tilt phase-shift interferograms. In each iteration cycle, proposed method calculates wavefront phase and tilt phase shifts in x- and y-directions in three individual least-squares fitting steps. In tilt phase shifts extracting steps, phase shifts of interferograms columns or rows are calculated with least-squares method, and then tilt phase shifts of interferograms in x- or y-direction are determined by linear regressions. At least three interferograms of three by three pixels are required with proposed method. The performance of proposed method is demonstrated by simulations and experiments. Tilt gradients and translational phase shifts could be extracted with high accuracy and large wavefront tilts could be well handled with proposed method. The method could be applied to temporal phase-shift interferometers with uncalibrated transducers or that in vibrating environment.
A New Three-step Iterative Method for Solving Nonlinear Equations
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M. Matin Far
2012-03-01
Full Text Available In this paper, a new three-step iterative method for finding a simple root of the nonlinear equation of f(x = 0 will be introduced. This method is based on the two-step method of [C. Chun, Y. Ham, Some fourth-order modifications of Newton’s method, Appl. Math. Comput. 197 (2008 654-658]. The new method requires three evaluations of the function and two of its first-derivative. We will prove that the order of convergence of the new method and its efficiency index will respectively be 8, and 1.5157. Some numerical experiments are given to illustrate the performance of the three-step iterative method.
Kew, Lee Ming; Ali, Norhashidah Hj. Mohd
2015-08-01
In this paper, new group iterative numerical schemes based on the centred and rotated (skewed) seven-point finite difference discretisations are proposed for the solution of a three dimensional second order hyperbolic telegraph equation, subject to specific initial and Dirichlet boundary conditions. Both schemes are shown to be of second order accuracies and unconditionally stable. The scheme derived from the rotated grid stencil results in a reduced linear system with lower computational complexity compared to the scheme derived from the centred approximation formula. A comparative study with other common point iterative methods based on the seven-point centred difference approximation together with their computational complexity analyses is also presented.
Monte Carlo methods in PageRank computation: When one iteration is sufficient
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
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
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 Impact factor: 1.241, year: 2016 https://link.springer.com/article/10.1007%2Fs11075-016-0136-5
Applications of normal S-iterative method to a nonlinear integral equation.
Gürsoy, Faik
2014-01-01
It has been shown that a normal S-iterative method converges to the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. Furthermore, a data dependence result for the solution of this integral equation has been proven.
New iterative method for fractional gas dynamics and coupled Burger's equations.
Al-Luhaibi, Mohamed S
2015-01-01
This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger's equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.
New Iterative Method for Fractional Gas Dynamics and Coupled Burger's Equations
Al-luhaibi, Mohamed S.
2015-01-01
This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger’s equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.
Nikazad, Touraj; Abbasi, Mokhtar
2017-04-01
In this paper, we introduce a subclass of strictly quasi-nonexpansive operators which consists of well-known operators as paracontracting operators (e.g., strictly nonexpansive operators, metric projections, Newton and gradient operators), subgradient projections, a useful part of cutter operators, strictly relaxed cutter operators and locally strongly Féjer operators. The members of this subclass, which can be discontinuous, may be employed by fixed point iteration methods; in particular, iterative methods used in convex feasibility problems. The closedness of this subclass, with respect to composition and convex combination of operators, makes it useful and remarkable. Another advantage with members of this subclass is the possibility to adapt them to handle convex constraints. We give convergence result, under mild conditions, for a perturbation resilient iterative method which is based on an infinite pool of operators in this subclass. The perturbation resilient iterative methods are relevant and important for their possible use in the framework of the recently developed superiorization methodology for constrained minimization problems. To assess the convergence result, the class of operators and the assumed conditions, we illustrate some extensions of existence research works and some new results.
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 ...
A two-step iterative method and its acceleration for outer inverses
Indian Academy of Sciences (India)
A two-step iterative method and its accelerated version for approximating outer inverse A2 T,S of an arbitrary matrix A are proposed. A convergence theorem for its existence is established. The rigorous error bounds are derived. Numerical experiments involving singular square, rectangular, random matrices and a sparse ...
Iterative method of analysis of single queue, multi-server with limited ...
African Journals Online (AJOL)
In this paper, analysis of single queue, multi-server with limited system capacity under first come first served discipline was carried out using iterative method. The arrivals of customers and service times of customers are assumed poisson and exponential distributions respectively. This queuing model is an extension of ...
Song, Junqiang; Leng, Hongze; Lu, Fengshun
2014-01-01
We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. PMID:24511303
Variational Iteration Method for the Magnetohydrodynamic Flow over a Nonlinear Stretching Sheet
Directory of Open Access Journals (Sweden)
Lan Xu
2013-01-01
Full Text Available The variational iteration method (VIM is applied to solve the boundary layer problem of magnetohydrodynamic flow over a nonlinear stretching sheet. The combination of the VIM and the Padé approximants is shown to be a powerful method for solving two-point boundary value problems consisting of systems of nonlinear differential equations. And the comparison of the obtained results with other available results shows that the method is very effective and convenient for solving boundary layer problems.
Retrieval of spherical particle size distribution with an improved Tikhonov iteration method
Tang Hong
2012-01-01
The problem of retrieval for spherical particle size distribution in the independent mode is studied, and an improved Tikhonov iteration method is proposed. In this method, the particle size distribution is retrieved from the light extinction data through the Phillips-Twomey method firstly in the independent mode, and then the obtained inversion results of the particle size distribution is used as the initial distribution and the final retrieved particle size distribution is obtained. S...
Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management
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.
Discrete fourier transform (DFT) analysis for applications using iterative transform methods
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.
An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients
Hou, Thomas Y.; Hwang, Feng-Nan; Liu, Pengfei; Yao, Chien-Chou
2017-05-01
We propose an iteratively adaptive Multi-scale Finite Element Method (MsFEM) for elliptic PDEs with rough coefficients. The choice of the local boundary conditions for the multi-sale basis functions determines the accuracy of the MsFEM numerical solution, and one needs to incorporate the global information of the elliptic equation into the local boundary conditions of the multi-scale basis functions to recover the underlying fine-mesh solution of the equation. In our proposed iteratively adaptive method, we achieve this global-to-local information transfer through the combination of coarse-mesh solving using adaptive multi-scale basis functions and fine-mesh smoothing operations. In each iteration step, we first update the multi-scale basis functions based on the approximate numerical solutions of the previous iteration steps, and obtain the coarse-mesh approximate solution using a Galerkin projection. Then we apply several steps of smoothing operations to the coarse-mesh approximate solution on the underlying fine mesh to get the updated approximate numerical solution. The proposed algorithm can be viewed as a nonlinear two-level multi-grid method with the restriction and prolongation operators adapted to the approximate numerical solutions of the previous iteration steps. Convergence analysis of the proposed algorithm is carried out under the framework of two-level multi-grid method, and the harmonic coordinates are employed to establish the approximation property of the adaptive multi-scale basis functions. We demonstrate the efficiency of our proposed multi-scale methods through several numerical examples including a multi-scale coefficient problem, a high-contrast interface problem, and a convection-dominated diffusion problem.
Energy Technology Data Exchange (ETDEWEB)
Jin, Shi, E-mail: sjin@wisc.edu [Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (United States); Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240 (China); Lu, Hanqing, E-mail: hanqing@math.wisc.edu [Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (United States)
2017-04-01
In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (in the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.
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.
A Numerical Iterative Method for Solving Systems of First-Order Periodic Boundary Value Problems
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Mohammed AL-Smadi
2014-01-01
Full Text Available The objective of this paper is to present a numerical iterative method for solving systems of first-order ordinary differential equations subject to periodic boundary conditions. This iterative technique is based on the use of the reproducing kernel Hilbert space method in which every function satisfies the periodic boundary conditions. The present method is accurate, needs less effort to achieve the results, and is especially developed for nonlinear case. Furthermore, the present method enables us to approximate the solutions and their derivatives at every point of the range of integration. Indeed, three numerical examples are provided to illustrate the effectiveness of the present method. Results obtained show that the numerical scheme is very effective and convenient for solving systems of first-order ordinary differential equations with periodic boundary conditions.
FBP embedded iterative method to efficiently solve the low-dose CT
Ueda, Ryosuke; Yamazaki, Fukashi; Kudo, Hiroyuki
2017-03-01
Low-dose X-ray CT is the reconstruction under the less X-ray intensity. In exchange for the intensity reduction, the noise level increases relatively. It is known that the Statistical Iterative Reconstruction (SIR) method is effective in reducing the image degradation due to the noise. One of the SIR formulations is the penalized weighted least squares (PWLS). Since the PWLS requires a large computational cost, the acceleration method such as the Iterative FBP (IFBP) has been studied. However, IFBP cannot exactly minimize the PWLS cost function. This paper shows a new acceleration method for eﬃciently solving the PWLS problem. Based on the Alternating Projection Proximal (APP) method, our approach exactly solves the PWLS. The design of the FBP filter is also presented. The reconstruction of the chest X-ray image is carried out. It is shown that the proposed method can give the highly acceleration and the exact solution.
Stellar surface as low-rank modification in iterative methods for binary neutron stars
Lau, Stephen R.
2017-11-01
We present a new multidomain spectral method for the treatment of non-spherical stellar surfaces in iterative methods for binary neutron stars. A stellar surface changes throughout the course of an iterative solution, potentially stalling the convergence. Our method affords low-complexity updates of the relevant subdomain preconditioners, thereby avoiding such stalling. Unlike current collocation (or nodal) approaches for treating surfaces (which rely on coordinate transformations to ensure that stellar surfaces arise at subdomain boundaries), our approach requires no regridding or nontrivial Jacobians. For polytropes with an equation of state specified by an integer polytropic index, our method delivers exponential accuracy with increased truncation, although for "stiff" equations of state (e.g. fractional) it suffers from the same accuracy loss as current methods. We have presented an outline of our approach before, but here present details with numerical tests.
On asymptotics for difference equations
Rafei, M.
2012-01-01
In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the
Backtracking-Based Iterative Regularization Method for Image Compressive Sensing Recovery
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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.
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Rai Nath Kabindra Rajeev
2009-01-01
Full Text Available In this paper, the solution of the one dimensional moving boundary problem with periodic boundary conditions is obtained with the help of variational iterational method. By using initial and boundary values, the explicit solutions of the equations have been derived, which accelerate the rapid convergence of the series solution. The method performs extremely well in terms of efficiency and simplicity. The temperature distribution and the position of moving boundary are evaluated and numerical results are presented graphically.
Improvement of the image quality of random phase--free holography using an iterative method
Shimobaba, Tomoyoshi; Endo, Yutaka; Hirayama, Ryuji; Hiyama, Daisuke; Hasegawa, Satoki; Nagahama, Yuki; Sano, Marie; Oikawa, Minoru; Sugie, Takashige; Ito, Tomoyoshi
2015-01-01
Our proposed method of random phase-free holography using virtual convergence light can obtain large reconstructed images exceeding the size of the hologram, without the assistance of random phase. The reconstructed images have low-speckle noise in the amplitude and phase-only holograms (kinoforms); however, in low-resolution holograms, we obtain a degraded image quality compared to the original image. We propose an iterative random phase-free method with virtual convergence light to address this problem.
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 effo...... prey harvesting. The results are compared with the results obtained by Adomian decomposition method and reveal that VIM is very effective and convenient for solving nonlinear differential equations....
Evaluating user reputation in online rating systems via an iterative group-based ranking method
Gao, Jian; Zhou, Tao
2017-05-01
Reputation is a valuable asset in online social lives and it has drawn increased attention. Due to the existence of noisy ratings and spamming attacks, how to evaluate user reputation in online rating systems is especially significant. However, most of the previous ranking-based methods either follow a debatable assumption or have unsatisfied robustness. In this paper, we propose an iterative group-based ranking method by introducing an iterative reputation-allocation process into the original group-based ranking method. More specifically, the reputation of users is calculated based on the weighted sizes of the user rating groups after grouping all users by their rating similarities, and the high reputation users' ratings have larger weights in dominating the corresponding user rating groups. The reputation of users and the user rating group sizes are iteratively updated until they become stable. Results on two real data sets with artificial spammers suggest that the proposed method has better performance than the state-of-the-art methods and its robustness is considerably improved comparing with the original group-based ranking method. Our work highlights the positive role of considering users' grouping behaviors towards a better online user reputation evaluation.
Iterative Method to Solve a Data Completion Problem for Biharmonic Equation for Rectangular Domain
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Tajani Chakir
2017-07-01
Full Text Available In this work, we are interested in a class of problems of great importance in many areas of industry and engineering. It is the invese problem for the biharmonic equation. It consists to complete the missing data on the inaccessible part from the measured data on the accessible part of the boundary. To solve this ill-posed problem, we opted for the alternative iterative method developed by Kozlov, Mazya and Fomin which is a convergent method for the elliptical Cauchy problems in general. The numerical implementation of the iterative algorithm is based on the application of the boundary element method (BEM for a sequence of mixed well-posed direct problems. Numerical results are performed for a square domain showing the effectiveness of the algorithm by BEM to produce accurate and stable numerical results.
A two-step filtering-based iterative image reconstruction method for interior tomography.
Zhang, Hanming; Li, Lei; Yan, Bin; Wang, Linyuan; Cai, Ailong; Hu, Guoen
2016-10-06
The optimization-based method that utilizes the additional sparse prior of region-of-interest (ROI) image, such as total variation, has been the subject of considerable research in problems of interior tomography reconstruction. One challenge for optimization-based iterative ROI image reconstruction is to build the relationship between ROI image and truncated projection data. When the reconstruction support region is smaller than the original object, an unsuitable representation of data fidelity may lead to bright truncation artifacts in the boundary region of field of view. In this work, we aim to develop an iterative reconstruction method to suppress the truncation artifacts and improve the image quality for direct ROI image reconstruction. A novel reconstruction approach is proposed based on an optimization problem involving a two-step filtering-based data fidelity. Data filtering is achieved in two steps: the first takes the derivative of projection data; in the second step, Hilbert filtering is applied in the differentiated data. Numerical simulations and real data reconstructions have been conducted to validate the new reconstruction method. Both qualitative and quantitative results indicate that, as theoretically expected, the proposed method brings reasonable performance in suppressing truncation artifacts and preserving detailed features. The presented local reconstruction method based on the two-step filtering strategy provides a simple and efficient approach for the iterative reconstruction from truncated projections.
A Posteriori Error Estimation for Finite Element Methods and Iterative Linear Solvers
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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)
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Marwan Abukhaled
2013-01-01
Full Text Available The variational iteration method is applied to solve a class of nonlinear singular boundary value problems that arise in physiology. The process of the method, which produces solutions in terms of convergent series, is explained. The Lagrange multipliers needed to construct the correctional functional are found in terms of the exponential integral and Whittaker functions. The method easily overcomes the obstacle of singularities. Examples will be presented to test the method and compare it to other existing methods in order to confirm fast convergence and significant accuracy.
Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems
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Xiaofeng Wang
2016-02-01
Full Text Available In this work, two multi-step derivative-free iterative methods are presented for solving system of nonlinear equations. The new methods have high computational efficiency and low computational cost. The order of convergence of the new methods is proved by a development of an inverse first-order divided difference operator. The computational efficiency is compared with the existing methods. Numerical experiments support the theoretical results. Experimental results show that the new methods remarkably reduce the computing time in the process of high-precision computing.
Environmental dose rate assessment of ITER using the Monte Carlo method
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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.
Harmonics analysis of the ITER poloidal field converter based on a piecewise method
Xudong, WANG; Liuwei, XU; Peng, FU; Ji, LI; Yanan, WU
2017-12-01
Poloidal field (PF) converters provide controlled DC voltage and current to PF coils. The many harmonics generated by the PF converter flow into the power grid and seriously affect power systems and electric equipment. Due to the complexity of the system, the traditional integral operation in Fourier analysis is complicated and inaccurate. This paper presents a piecewise method to calculate the harmonics of the ITER PF converter. The relationship between the grid input current and the DC output current of the ITER PF converter is deduced. The grid current is decomposed into the sum of some simple functions. By calculating simple function harmonics based on the piecewise method, the harmonics of the PF converter under different operation modes are obtained. In order to examine the validity of the method, a simulation model is established based on Matlab/Simulink and a relevant experiment is implemented in the ITER PF integration test platform. Comparative results are given. The calculated results are found to be consistent with simulation and experiment. The piecewise method is proved correct and valid for calculating the system harmonics.
Study on registration method based on Gauss-Newton iteration algorithm for augmented reality system
Li, Yu; Liu, Yue; Wang, Yongtian
2004-03-01
Three key technologies influence the performance of current AR (Augmented Reality) system, namely image grabbing, accurate registration and binocular stereovision. This paper studies a vision-based AR system and its setup, presents an image grabbing solution using an IEEE 1394 interface, discusses the binocular stereovision technology and develops an effective Gauss-Newton iteration algorithm for registration. Experiment results show that the proposed method is computationally efficient and accurate.
New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations
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Mohamed S. Al-luhaibi
2015-01-01
Full Text Available This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger’s equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.
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Asma Ali Elbeleze
2014-01-01
Full Text Available We are concerned here with singular partial differential equations of fractional order (FSPDEs. The variational iteration method (VIM is applied to obtain approximate solutions of this type of equations. Convergence analysis of the VIM is discussed. This analysis is used to estimate the maximum absolute truncated error of the series solution. A comparison between the results of VIM solutions and exact solution is given. The fractional derivatives are described in Caputo sense.
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Fatima A. Alawad
2013-01-01
Full Text Available In this paper, the exact solutions of space-time fractional telegraph equations are given in terms of Mittage-Leffler functions via a combination of Laplace transform and variational iteration method. New techniques are used to overcome the difficulties arising in identifying the general Lagrange multiplier. As a special case, the obtained solutions reduce to the solutions of standard telegraph equations of the integer orders.
Ibiş, Birol; Bayram, Mustafa
2014-01-01
This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE) involving Jumarie's modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM). FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, more efficient, and more convenient for solving time FADEs.
Iterative computation of the optimal H(infinity) norm by using two-Riccati-equation method
Chang, B. C.; Li, X. P.; Yeh, H. H.; Banda, S. S.
1990-01-01
The two-Riccati-equation method solution to a standard H(infinity) control problem can be used to characterize all possible stabilizing optimal or suboptimal H(infinity) controllers if the optimal or suboptimal H(infinity) norm is available in the literature. An iterative algorithm for computing the optimal H(infinity) norm is proposed. The algorithm employs fixed-point, double secant and bisection to guarantee a super linear convergence.
Highly Nonlinear Temperature-Dependent Fin Analysis by Variational Iteration Method
DEFF Research Database (Denmark)
Fouladi, F.; Hosseinzadeh, E.; Barari, Amin
2010-01-01
In this research, the variational iteration method as an approximate analytical method is utilized to overcome some inherent limitations arising as uncontrollability to the nonzero endpoint boundary conditions and is used to solve some examples in the field of heat transfer. The available exact...... solutions for the linear equations and the numerical solutions for the nonlinear ones are good bases to demonstrate the accuracy and efficiency of the proposed method. With the help of the method one can simply analyze the thermal characteristics of a straight rectangular fin for all possible types of heat...
Fast iterative boundary element methods for high-frequency scattering problems in 3D elastodynamics
Chaillat, Stéphanie; Darbas, Marion; Le Louër, Frédérique
2017-07-01
The fast multipole method is an efficient technique to accelerate the solution of large scale 3D scattering problems with boundary integral equations. However, the fast multipole accelerated boundary element method (FM-BEM) is intrinsically based on an iterative solver. It has been shown that the number of iterations can significantly hinder the overall efficiency of the FM-BEM. The derivation of robust preconditioners for FM-BEM is now inevitable to increase the size of the problems that can be considered. The main constraint in the context of the FM-BEM is that the complete system is not assembled to reduce computational times and memory requirements. Analytic preconditioners offer a very interesting strategy by improving the spectral properties of the boundary integral equations ahead from the discretization. The main contribution of this paper is to combine an approximate adjoint Dirichlet to Neumann (DtN) map as an analytic preconditioner with a FM-BEM solver to treat Dirichlet exterior scattering problems in 3D elasticity. The approximations of the adjoint DtN map are derived using tools proposed in [40]. The resulting boundary integral equations are preconditioned Combined Field Integral Equations (CFIEs). We provide various numerical illustrations of the efficiency of the method for different smooth and non-smooth geometries. In particular, the number of iterations is shown to be completely independent of the number of degrees of freedom and of the frequency for convex obstacles.
Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory
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Lin, Lin; Shao, Sihong; E, Weinan
2012-11-06
We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Pt$_{2}$, Au$_{2}$, TlF, and Bi$_{2}$Se$_{3}$ indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements.
A New Iterative Scheme of Modified Mann Iteration in Banach Space
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Jinzuo Chen
2014-01-01
Full Text Available We introduce the modified iterations of Mann's type for nonexpansive mappings and asymptotically nonexpansive mappings to have the strong convergence in a uniformly convex Banach space. We study approximation of common fixed point of asymptotically nonexpansive mappings in Banach space by using a new iterative scheme. Applications to the accretive operators are also included.
Desmal, Abdulla
2014-07-01
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 algorithms minimize a cost function weighted between measurement-data misfit and a zeroth/first-norm penalty term and therefore promote "sharpness" in the solution. Consequently, when applied to domains with sharp variations, discontinuities, or sparse content, the proposed framework is more efficient and accurate than the "classical" BIM that minimizes a cost function with a second-norm penalty term. Indeed, numerical results demonstrate the superiority of the IST-BIM over the classical BIM when they are applied to sparse domains: Permittivity and conductivity profiles recovered using the IST-BIM are sharper and more accurate and converge faster. © 1963-2012 IEEE.
Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models
Elsheikh, Ahmed H.
2013-05-01
A novel multi-modal parameter estimation algorithm is introduced. Parameter estimation is an ill-posed inverse problem that might admit many different solutions. This is attributed to the limited amount of measured data used to constrain the inverse problem. The proposed multi-modal model calibration algorithm uses an iterative stochastic ensemble method (ISEM) for parameter estimation. ISEM employs an ensemble of directional derivatives within a Gauss-Newton iteration for nonlinear parameter estimation. ISEM is augmented with a clustering step based on k-means algorithm to form sub-ensembles. These sub-ensembles are used to explore different parts of the search space. Clusters are updated at regular intervals of the algorithm to allow merging of close clusters approaching the same local minima. Numerical testing demonstrates the potential of the proposed algorithm in dealing with multi-modal nonlinear parameter estimation for subsurface flow models. © 2013 Elsevier B.V.
Solution of the solidification problem by using the variational iteration method
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E. Hetmaniok
2009-10-01
Full Text Available The paper presents the approximated solution of the solidification problem, modelled with the aid of the one-phase Stefan problem with the boundary condition of the second kind, by using the variational iteration method. For solving this problem one needs to determine the distribution of temperature in the given domain and the position of the moving interface. The proposed method of solution consists of describing the considered problem with a system of differential equations in a domain with known boundary, and solving the received system with the aid of VIM method. The accuracy of the obtained approximated solution is verified by comparing it with the analytical solution.
a Method of Tomato Image Segmentation Based on Mutual Information and Threshold Iteration
Wu, Hongxia; Li, Mingxi
Threshold Segmentation is a kind of important image segmentation method and one of the important preconditioning steps of image detection and recognition, and it has very broad application during the research scopes of the computer vision. According to the internal relation between segment image and original image, a tomato image automatic optimization segmentation method (MI-OPT) which mutual information associate with optimum threshold iteration was presented. Simulation results show that this method has a better image segmentation effect on the tomato images of mature period and little background color difference or different color.
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Fairouz Zouyed
2015-01-01
Full Text Available This paper discusses the inverse problem of determining an unknown source in a second order differential equation from measured final data. This problem is ill-posed; that is, the solution (if it exists does not depend continuously on the data. In order to solve the considered problem, an iterative method is proposed. Using this method a regularized solution is constructed and an a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.
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Iryna Komashynska
2014-01-01
Full Text Available We present an efficient iterative method for solving a class of nonlinear second-order Fredholm integrodifferential equations associated with different boundary conditions. A simple algorithm is given to obtain the approximate solutions for this type of equations based on the reproducing kernel space method. The solution obtained by the method takes form of a convergent series with easily computable components. Furthermore, the error of the approximate solution is monotone decreasing with the increasing of nodal points. The reliability and efficiency of the proposed algorithm are demonstrated by some numerical experiments.
Failure analysis of laminated composites by using iterative three-dimensional finite element method
Hwang, W. C.; Sun, C. T.
1989-05-01
A failure analysis of laminated composites is accomplished by using an iterative three-dimensional finite element method. Based on Tsai-Wu failure theory, three different modes of failure are proposed: fiber breakage, matrix cracking, and delamination. The first ply failure load is then evaluated. As the applied load exceeds the first ply failure load, localized structural failure occurs and the global structural stiffness should change. The global stiffness matrix is modified by taking nonlinearity due to partial failures within a laminate into consideration. The first ply failure load is analyzed by using a iterative mixed field method in solving the linear part of the finite element equations. The progressive failure problem is solved numerically by using Newton-Raphson iterative schemes for the solution of nonlinear finite element equations. Numerical examples include angle-ply symmetric Thornel 300 graphite/934 resin epoxy laminates under uniaxial tension. First ply failure loads as well as the final failure loads are evaluated. Good correlation between analytical results and experimental data are observed. Numerical results also include the investigation of composite specimens with a centered hole, under uniaxial tension. Excellent correlation with the experimental data is observed.
Gillis, T.; Winckelmans, G.; Chatelain, P.
2017-10-01
We formulate the penalization problem inside a vortex particle-mesh method as a linear system. This system has to be solved at every wall boundary condition enforcement within a time step. Furthermore, because the underlying problem is a Poisson problem, the solution of this linear system is computationally expensive. For its solution, we here use a recycling iterative solver, rBiCGStab, in order to reduce the number of iterations and therefore decrease the computational cost of the penalization step. For the recycled subspace, we use the orthonormalized previous solutions as only the right hand side changes from the solution at one time to the next. This method is validated against benchmark results: the impulsively started cylinder, with validation at low Reynolds number (Re = 550) and computational savings assessments at moderate Reynolds number (Re = 9500); then on a flat plate benchmark (Re = 1000). By improving the convergence behavior, the approach greatly reduces the computational cost of iterative penalization, at a moderate cost in memory overhead.
Asymptotic Behavior of the Maximum Entropy Routing in Computer Networks
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Milan Tuba
2013-01-01
Full Text Available Maximum entropy method has been successfully used for underdetermined systems. Network design problem, with routing and topology subproblems, is an underdetermined system and a good candidate for maximum entropy method application. Wireless ad-hoc networks with rapidly changing topology and link quality, where the speed of recalculation is of crucial importance, have been recently successfully investigated by maximum entropy method application. In this paper we prove a theorem that establishes asymptotic properties of the maximum entropy routing solution. This result, besides being theoretically interesting, can be used to direct initial approximation for iterative optimization algorithms and to speed up their convergence.
Asymptotically Efficient Identification of Known-Sensor Hidden Markov Models
Mattila, Robert; Rojas, Cristian R.; Krishnamurthy, Vikram; Wahlberg, Bo
2017-12-01
We consider estimating the transition probability matrix of a finite-state finite-observation alphabet hidden Markov model with known observation probabilities. The main contribution is a two-step algorithm; a method of moments estimator (formulated as a convex optimization problem) followed by a single iteration of a Newton-Raphson maximum likelihood estimator. The two-fold contribution of this letter is, firstly, to theoretically show that the proposed estimator is consistent and asymptotically efficient, and secondly, to numerically show that the method is computationally less demanding than conventional methods - in particular for large data sets.
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S. Irandoust-pakchin
2011-03-01
Full Text Available In this paper, the modification of He's variational iteration method(MVIM is developed to solve fractional ordinary differentialequations and fractional partial differential equations. It is usedthe free choice of initial approximation to propose the reliablemodification of He's variational iteration method. Some of thefractional differential equations are examined to illustrate theeffectiveness and convenience of the method. The results show thatthe proposed method has accelerated convergence.
Polling models with renewal arrivals: a new method to derive heavy-traffic asymptotics
van der Mei, R.D.; Winands, E.M.M.
2008-01-01
We consider asymmetric cyclic polling systems with an arbitrary number of queues, general service-time distributions, zero switch-over times, gated service at each queue, and with general renewal arrival processes at each of the queues. For this classical model, we propose a new method to derive
Decision-directed iterative methods for PAPR reduction in optical wireless OFDM systems
Azim, Ali W.; Le Guennec, Yannis; Maury, Ghislaine
2017-04-01
In this paper, we propose two iterative decision-directed methods for peak-to-average power ratio (PAPR) reduction in optical-orthogonal frequency division multiplexing (O-OFDM) systems. The proposed methods are applicable to state-of-the-art intensity modulation-direct detection (IM-DD) O-OFDM techniques for optical wireless communication (OWC) systems, including both direct-current (DC) biased O-OFDM (DCO-OFDM), and asymmetrically clipped O-OFDM (ACO-OFDM). Conventional O-OFDM suffers from high power consumption due to high PAPR. The high PAPR of the O-OFDM signal can be counteracted by clipping the signal to a predefined threshold. However, because of clipping an inevitable distortion occurs due to the loss of useful information, thus, clipping mitigation methods are required. The proposed iterative decision-directed methods operate at the receiver, and recover the lost information by mitigating the clipping distortion. Simulation results acknowledge that the high PAPR of O-OFDM can be significantly reduced using clipping, and the proposed methods can successfully circumvent the clipping distortions. Furthermore, the proposed PAPR reduction methods exhibit a much lower computational complexity compared to standard PAPR reduction methods.
A POCS method for iterative deblending constrained by a blending mask
Zhou, Yatong
2017-03-01
A recently emerging seismic acquisition technology called simultaneous source shooting has attracted much attention from both academia and industry. The key topic in the newly developed technique is the removal of intense blending interferences caused by the simultaneous ignition of multiple airgun sources. In this paper, I propose a novel inversion strategy with multiple convex constraints to improve the deblending performance based on the projection onto convex sets (POCS) iterative framework. In the POCS iterative framework, as long as the multiple constraints are convex, the iterations are guaranteed to converge. In addition to the sparse constraint, I seek another important constraint from the untainted data. I create a blending mask in order to fully utilize the useful information hidden behind the noisy blended data. The blending mask is constructed by numerically blending a matrix with all its entries set to be one and then setting the non-one entries of the blended matrix zero. I use both synthetic and field data examples to demonstrate the successful performance of the proposed method.
Costabel, M.; Ervin, V. J.; Stephan, E. P.
1990-07-01
Previously Costabel and Stephan proved the convergence of the collocation method for boundary integral equations on polygonal domains for piecewise linear trial functions which are constant on subintervals next to corners. The convergence and associated error estimates were given in suitable Sobolev spaces with appropriately weighted norms. In this paper we present, for Laplace's equation, the implementation of their method and a slightly modified version. In the latter we use piecewise linear trial functions which are discontinuous at the corners. Of particular note is that the computed experimental convergence rates are in complete agreement with the predicted theoretical rates. In particular, our numerical results underline clearly how the order of convergence depends on the graded mesh.
Multipoint Iterative Methods for Finding All the Simple Zeros in an Interval
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T. Lotfi
2014-01-01
Full Text Available Two new families of multipoint without memory iterative methods with eighth- and sixteenth-orders are constructed using the symbolic software Mathematica. The key idea in constructing such methods is based on producing some generic suitable functions to reduce the functional evaluations and increase the order of convergence along the computational efficiency. Again by applying Mathematica, we design a hybrid algorithm to capture all the simple real solutions of nonlinear equations in an interval. The application of the new schemes in producing fractal pictures is also furnished.
Masmoudi, Nabil
2014-05-01
Traveltimes are conventionally evaluated by solving the zero-order approximation of the Wentzel, Kramers and Brillouin (WKB) expansion of the wave equation. This high frequency approximation is good enough for most imaging applications and provides us with a traveltime equation called the eikonal equation. The eikonal equation is a non-linear partial differential equation which can be solved by any of the familiar numerical methods. Among the most popular of these methods is the method of characteristics which yields the ray tracing equations and the finite difference approaches. In the first part of the Master Thesis, we use the ray tracing method to solve the eikonal equation to get P-waves traveltimes for orthorhombic models with arbitrary orientation of symmetry planes. We start with a ray tracing procedure specified in curvilinear coordinate system valid for anisotropy of arbitrary symmetry. The coordinate system is constructed so that the coordinate lines are perpendicular to the symmetry planes of an orthorohombic medium. Advantages of this approach are the conservation of orthorhombic symmetry throughout the model and reduction of the number of parameters specifying the model. We combine this procedure with first-order ray tracing and dynamic ray tracing equations for P waves propagating in smooth, inhomogeneous, weakly anisotropic media. The first-order ray tracing and dynamic ray tracing equations are derived from the exact ones by replacing the exact P-wave eigenvalue of the Christoffel matrix by its first-order approximation. In the second part of the Master Thesis, we compute traveltimes using the fast marching method and we develop an approach to estimate the anisotropy parameters. The idea is to relate them analytically to traveltimes which is challenging in inhomogeneous media. Using perturbation theory, we develop traveltime approximations for transversely isotropic media with horizontal symmetry axis (HTI) as explicit functions of the
Robertson, Scott; Leonhardt, Ulf
2014-11-01
Hawking radiation has become experimentally testable thanks to the many analog systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion and give rise to a numerically soluble and stable ordinary differential equation only if the rest-frame dispersion relation Ω^{2}(k) is a polynomial of relatively low degree. Here we present a new method for the calculation of wave scattering in a one-dimensional medium of arbitrary dispersion. It views the wave equation as an integral equation in Fourier space, which can be solved using standard and efficient numerical techniques.
Zhu, W; Wang, Y; Yao, Y; Chang, J; Graber, H L; Barbour, R L
1997-04-01
We present an iterative total least-squares algorithm for computing images of the interior structure of highly scattering media by using the conjugate gradient method. For imaging the dense scattering media in optical tomography, a perturbation approach has been described previously [Y. Wang et al., Proc. SPIE 1641, 58 (1992); R. L. Barbour et al., in Medical Optical Tomography: Functional Imaging and Monitoring (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87-120], which solves a perturbation equation of the form W delta x = delta I. In order to solve this equation, least-squares or regularized least-squares solvers have been used in the past to determine best fits to the measurement data delta I while assuming that the operator matrix W is accurate. In practice, errors also occur in the operator matrix. Here we propose an iterative total least-squares (ITLS) method that minimizes the errors in both weights and detector readings. Theoretically, the total least-squares (TLS) solution is given by the singular vector of the matrix [W/ delta I] associated with the smallest singular value. The proposed ITLS method obtains this solution by using a conjugate gradient method that is particularly suitable for very large matrices. Simulation results have shown that the TLS method can yield a significantly more accurate result than the least-squares method.
Energy Technology Data Exchange (ETDEWEB)
Hagstrom, T. [Univ. of New Mexico, Albuquerque, NM (United States); Radhakrishnan, K. [Sverdrup Technology, Brook Park, OH (United States)
1994-12-31
The authors report on some iterative methods which they have tested for use in combustion simulations. In particular, they have developed a code to solve zero Mach number reacting flow equations with complex reaction and diffusion physics. These equations have the form of a nonlinear parabolic system coupled with constraints. In semi-discrete form, one obtains DAE`s of index two or three depending on the number of spatial dimensions. The authors have implemented a fourth order (fully implicit) BDF method in time, coupled with a suite of fourth order explicit and implicit spatial difference approximations. Most codes they know of for simulating reacting flows use a splitting strategy to march in time. This results in a sequence of nonlinear systems to solve, each of which has a simpler structure than the one they are faced with. The rapid and robust solution of the coupled system is the essential requirement for the success of their approach. They have implemented and analyzed nonlinear generalizations of conjugate gradient-like methods for nonsymmetric systems, including CGS and the quasi-Newton based method of Eirola and Nevanlinna. They develop a general framework for the nonlinearization of linear methods in terms of the acceleration of fixed-point iterations, where the latter is assumed to include the {open_quote}preconditioning{open_quote}. Their preconditioning is a single step of a split method, using lower order spatial difference approximations as well as simplified (Fickian) approximations of the diffusion physics.
Nonlinear vibrations of non-uniform beams by the MTS asymptotic expansion method
Clementi, F.; Demeio, L.; Mazzilli, C. E. N.; Lenci, S.
2015-09-01
The frequency response curves of a non-uniform beam undergoing nonlinear oscillations are determined analytically by the multiple time scale method, which provides approximate, but accurate results. The axial inertia in neglected, and so the equations of motion are statically condensed on the transversal displacement only. The nonlinearity due to the stretching of the axis of the beam is considered. The effects of variable cross-section, of variable material properties and of the distributed axial loading are taken into account in the formulation. They have been illustrated by means of two examples and are also compared with existing results. The main result of this work is that the effects of any type of non-uniformity can be detected by simple formulas.
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)
Information operator approach and iterative regularization methods for atmospheric remote sensing
Energy Technology Data Exchange (ETDEWEB)
Doicu, A. [German Aerospace Center, Remote Sensing Technology Institute, Oberpfaffenhofen (Germany)]. E-mail: adrian.doicu@dlr.de; Hilgers, S. [German Aerospace Center, Remote Sensing Technology Institute, Oberpfaffenhofen (Germany); Bargen, A. von [German Aerospace Center, Remote Sensing Technology Institute, Oberpfaffenhofen (Germany); Rozanov, A. [Institute of Environmental Physics, University of Bremen (Germany); Eichmann, K.-U. [Institute of Environmental Physics, University of Bremen (Germany); Savigny, C. von [Institute of Environmental Physics, University of Bremen (Germany); Burrows, J.P. [Institute of Environmental Physics, University of Bremen (Germany)
2007-01-15
In this study, we present the main features of the information operator approach for solving linear inverse problems arising in atmospheric remote sensing. This method is superior to the stochastic version of the Tikhonov regularization (or the optimal estimation method) due to its capability to filter out the noise-dominated components of the solution generated by an inappropriate choice of the regularization parameter. We extend this approach to iterative methods for nonlinear ill-posed problems and derive the truncated versions of the Gauss-Newton and Levenberg-Marquardt methods. Although the paper mostly focuses on discussing the mathematical details of the inverse method, retrieval results have been provided, which exemplify the performances of the methods. These results correspond to the NO{sub 2} retrieval from SCIAMACHY limb scatter measurements and have been obtained by using the retrieval processors developed at the German Aerospace Center Oberpfaffenhofen and Institute of Environmental Physics of the University of Bremen.
National Research Council Canada - National Science Library
Kordolaimi, Sofia D; Saradeas, Ioannis; Ploussi, Agapi; Pantos, Ioannis; Argentos, Stylianos; Efstathopoulos, Efstathios P
2014-01-01
The purpose of this study is to introduce an efficient method for the optimization of iterative reconstruction CT protocols based on phantom image analysis and the comparison of obtained results with actual patient data...
Raphael, Claire E; Kyriacou, Andreas; Jones, Siana; Pabari, Punam; Cole, Graham; Baruah, Resham; Hughes, Alun D; Francis, Darrel P
2013-09-20
AV delay optimisation of biventricular pacing devices (cardiac resynchronisation therapy, CRT) is performed in trials and recommended by current guidelines. The Doppler echocardiographic iterative method is the most commonly recommended. Yet whether it can be executed reliably has never been tested formally. 36 multinational specialists, familiar with using the echocardiographic iterative method of CRT optimisation, were shown 20-40 sets of transmitral Doppler traces at 6-8 AV settings and asked to select the optimal AV delay. Unknown to the specialists, some Doppler datasets appeared in duplicate, allowing assessment of both inter and intra-specialist interpretation. On the Kappa scale of agreement (1 = perfect agreement, 0 = chance alone), the agreement regarding optimal AV delay between specialists was poor (kappa=0.12 ± 0.08). More importantly, agreement of specialists with themselves (i.e. viewing identical sets of traces, twice) was also poor, with Kappa=0.23 ± 0.07 and mean absolute difference in optimum AV delay of 83 ms between first and second viewing of the same traces. Iterative AV optimisation is not executed reliably by experts, even in an artificially simplified context where biological variability and variation in image acquisition are eliminated by use of identical traces. This cannot be blamed on insufficient skills of some experts or discordant methods of selecting the optimum, because operators also showed poor agreement with themselves when assessing the same trace. Instead, guidelines should retract any recommendation for this algorithm. Guideline-development processes might usefully begin with a rudimentary check on proposed algorithms, to establish at least minimal credibility. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.
An iterative inverse method to estimate basal topography and initialize ice flow models
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W. J. J. van Pelt
2013-06-01
Full Text Available We evaluate an inverse approach to reconstruct distributed bedrock topography and simultaneously initialize an ice flow model. The inverse method involves an iterative procedure in which an ice dynamical model (PISM is run multiple times over a prescribed period, while being forced with space- and time-dependent climate input. After every iteration bed heights are adjusted using information of the remaining misfit between observed and modeled surface topography. The inverse method is first applied in synthetic experiments with a constant climate forcing to verify convergence and robustness of the approach in three dimensions. In a next step, the inverse approach is applied to Nordenskiöldbreen, Svalbard, forced with height- and time-dependent climate input since 1300 AD. An L-curve stopping criterion is used to prevent overfitting. Validation against radar data reveals a high correlation (up to R = 0.89 between modeled and observed thicknesses. Remaining uncertainties can mainly be ascribed to inaccurate model physics, in particular, uncertainty in the description of sliding. Results demonstrate the applicability of this inverse method to reconstruct the ice thickness distribution of glaciers and ice caps. In addition to reconstructing bedrock topography, the method provides a direct tool to initialize ice flow models for forecasting experiments.
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.
Directory of Open Access Journals (Sweden)
Stefan M. Stefanov
2014-01-01
Full Text Available We consider the data fitting problem, that is, the problem of approximating a function of several variables, given by tabulated data, and the corresponding problem for inconsistent (overdetermined systems of linear algebraic equations. Such problems, connected with measurement of physical quantities, arise, for example, in physics, engineering, and so forth. A traditional approach for solving these two problems is the discrete least squares data fitting method, which is based on discrete l2-norm. In this paper, an alternative approach is proposed: with each of these problems, we associate a nondifferentiable (nonsmooth unconstrained minimization problem with an objective function, based on discrete l1- and/or l∞-norm, respectively; that is, these two norms are used as proximity criteria. In other words, the problems under consideration are solved by minimizing the residual using these two norms. Respective subgradients are calculated, and a subgradient method is used for solving these two problems. The emphasis is on implementation of the proposed approach. Some computational results, obtained by an appropriate iterative method, are given at the end of the paper. These results are compared with the results, obtained by the iterative gradient method for the corresponding “differentiable” discrete least squares problems, that is, approximation problems based on discrete l2-norm.
An iterative stochastic ensemble method for parameter estimation of subsurface flow models
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.
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Brajesh Kumar Singh
2017-01-01
Full Text Available This paper deals with an alternative approximate analytic solution to time fractional partial differential equations (TFPDEs with proportional delay, obtained by using fractional variational iteration method, where the fractional derivative is taken in Caputo sense. The proposed series solutions are found to converge to exact solution rapidly. To confirm the efficiency and validity of FRDTM, the computation of three test problems of TFPDEs with proportional delay was presented. The scheme seems to be very reliable, effective, and efficient powerful technique for solving various types of physical models arising in science and engineering.
Directory of Open Access Journals (Sweden)
Ali Konuralp
2014-01-01
Full Text Available Application process of variational iteration method is presented in order to solve the Volterra functional integrodifferential equations which have multi terms and vanishing delays where the delay function θ(t vanishes inside the integral limits such that θ(t=qt for 0
A variation iteration method for isotropic velocity-dependent potentials: Scattering case
Energy Technology Data Exchange (ETDEWEB)
Eed, H. [Applied Science Private University, Basic Science Department, Amman (Jordan)
2014-12-01
We propose a new approximation scheme to obtain analytic expressions for the Schroedinger equation with isotropic velocity-dependent potential to determine the scattering phase shift. In order to test the validity of our approach, we applied it to an exactly solvable model for nucleon-nucleon scattering. The results of the variation iteration method (VIM) formalism compare quite well with those of the exactly solvable model. The developed formalism can be applied in problems concerning pion-nucleon, nucleon-nucleon, and electron-atom scattering. (orig.)
A fast iterative method for Chandrasekhar's -functions for general laws of scattering
Kawabata, Kiyoshi
2015-08-01
This work shows that notable acceleration of the speed of calculating Chandrasekhar's -functions for general laws of scattering with an iterative method can be realized by supplying a starting approximation produced by the following procedure: (i) in the cases of azimuth-angle independent Fourier components, values of the isotropic scattering -function given by an accurate yet simple-to-apply formula, in particular, the one by Kawabata and Limaye (Astrophys. Space Sci. 332:365, 2011), and (ii) for azimuth-angle dependent Fourier components, an already obtained solution of the next lower order term.
Entezami, Alireza; Shariatmadar, Hashem; Sarmadi, Hassan
2017-07-01
A new sensitivity-based damage detection method is proposed to identify and estimate the location and severity of structural damage using incomplete noisy modal data. For these purposes, an improved sensitivity function of modal strain energy (MSE) based on Lagrange optimization problem is derived to adapt the initial sensitivity formulation of MSE to damage detection problem with the aid of new mathematical approaches. In the presence of incomplete noisy modal data, the sensitivity matrix is sparse, rectangular, and ill-conditioned, which leads to an ill-posed damage equation. To overcome this issue, a new regularization method named as Regularized Least Squares Minimal Residual (RLSMR) is proposed to solve the ill-posed damage equation. This method relies on Krylov subspace and exploits bidiagonalization and iterative algorithms to solve linear mathematical systems. For the majority of Krylov subspace methods, conventional direct methods for the determination of an optimal regularization parameter may not be proper. To cope with this limitation, a hybrid technique is introduced that depends on the residual of RLSMR method, the number of iterations, and the bidiagonalization algorithm. The accuracy and performance of the improved and proposed methods are numerically examined by a planner truss by incorporating incomplete noisy modal parameters and finite element modeling errors. A comparative study on the initial and improved sensitivity functions is conduced to investigate damage detectability of these sensitivity formulations. Furthermore, the accuracy and robustness of RLSMR method in detecting damage are compared with the well-known Tikhonov regularization method. Results show that the improved sensitivity of MSE is an efficient tool for using in the damage detection problem due to a high sensitivity to damage and reliable damage detectability in comparison with the initial sensitivity function. Additionally, it is observed that the RLSMR method with the aid
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Ibrahim Karahan
2016-04-01
Full Text Available Let C be a nonempty closed convex subset of a real Hilbert space H. Let {T_{n}}:C›H be a sequence of nearly nonexpansive mappings such that F:=?_{i=1}^{?}F(T_{i}?Ø. Let V:C›H be a ?-Lipschitzian mapping and F:C›H be a L-Lipschitzian and ?-strongly monotone operator. This paper deals with a modified iterative projection method for approximating a solution of the hierarchical fixed point problem. It is shown that under certain approximate assumptions on the operators and parameters, the modified iterative sequence {x_{n}} converges strongly to x^{*}?F which is also the unique solution of the following variational inequality: ?0, ?x?F. As a special case, this projection method can be used to find the minimum norm solution of above variational inequality; namely, the unique solution x^{*} to the quadratic minimization problem: x^{*}=argmin_{x?F}?x?². The results here improve and extend some recent corresponding results of other authors.
An iterative finite-element collocation method for parabolic problems using domain decomposition
Energy Technology Data Exchange (ETDEWEB)
Curran, M.C.
1992-11-01
Advection-dominated flows occur widely in the transport of groundwater contaminants, the movements of fluids in enhanced oil recovery projects, and many other contexts. In numerical models of such flows, adaptive local grid refinement is a conceptually attractive approach for resolving the sharp fronts or layers that tend to characterize the solutions. However, this approach can be difficult to implement in practice. A domain decomposition method developed by Bramble, Ewing, Pasciak, and Schatz, known as the BEPS method, overcomes many of the difficulties. We demonstrate the applicability of the iterative BEPS ideas to finite-element collocation on trial spaces of piecewise Hermite bicubics. The resulting scheme allows one to refine selected parts of a spatial grid without destroying algebraic efficiencies associated with the original coarse grid. We apply the method to two dimensional time-dependent advection-diffusion problems.
An iterative finite-element collocation method for parabolic problems using domain decomposition
Energy Technology Data Exchange (ETDEWEB)
Curran, M.C.
1992-01-01
Advection-dominated flows occur widely in the transport of groundwater contaminants, the movements of fluids in enhanced oil recovery projects, and many other contexts. In numerical models of such flows, adaptive local grid refinement is a conceptually attractive approach for resolving the sharp fronts or layers that tend to characterize the solutions. However, this approach can be difficult to implement in practice. A domain decomposition method developed by Bramble, Ewing, Pasciak, and Schatz, known as the BEPS method, overcomes many of the difficulties. We demonstrate the applicability of the iterative BEPS ideas to finite-element collocation on trial spaces of piecewise Hermite bicubics. The resulting scheme allows one to refine selected parts of a spatial grid without destroying algebraic efficiencies associated with the original coarse grid. We apply the method to two dimensional time-dependent advection-diffusion problems.
A linearly approximated iterative Gaussian decomposition method for waveform LiDAR processing
Mountrakis, Giorgos; Li, Yuguang
2017-07-01
Full-waveform LiDAR (FWL) decomposition results often act as the basis for key LiDAR-derived products, for example canopy height, biomass and carbon pool estimation, leaf area index calculation and under canopy detection. To date, the prevailing method for FWL product creation is the Gaussian Decomposition (GD) based on a non-linear Levenberg-Marquardt (LM) optimization for Gaussian node parameter estimation. GD follows a ;greedy; approach that may leave weak nodes undetected, merge multiple nodes into one or separate a noisy single node into multiple ones. In this manuscript, we propose an alternative decomposition method called Linearly Approximated Iterative Gaussian Decomposition (LAIGD method). The novelty of the LAIGD method is that it follows a multi-step ;slow-and-steady; iterative structure, where new Gaussian nodes are quickly discovered and adjusted using a linear fitting technique before they are forwarded for a non-linear optimization. Two experiments were conducted, one using real full-waveform data from NASA's land, vegetation, and ice sensor (LVIS) and another using synthetic data containing different number of nodes and degrees of overlap to assess performance in variable signal complexity. LVIS data revealed considerable improvements in RMSE (44.8% lower), RSE (56.3% lower) and rRMSE (74.3% lower) values compared to the benchmark GD method. These results were further confirmed with the synthetic data. Furthermore, the proposed multi-step method reduces execution times in half, an important consideration as there are plans for global coverage with the upcoming Global Ecosystem Dynamics Investigation LiDAR sensor on the International Space Station.
Miao, Linling; Young, Charles D.; Sing, Charles E.
2017-07-01
Brownian Dynamics (BD) simulations are a standard tool for understanding the dynamics of polymers in and out of equilibrium. Quantitative comparison can be made to rheological measurements of dilute polymer solutions, as well as direct visual observations of fluorescently labeled DNA. The primary computational challenge with BD is the expensive calculation of hydrodynamic interactions (HI), which are necessary to capture physically realistic dynamics. The full HI calculation, performed via a Cholesky decomposition every time step, scales with the length of the polymer as O(N3). This limits the calculation to a few hundred simulated particles. A number of approximations in the literature can lower this scaling to O(N2 - N2.25), and explicit solvent methods scale as O(N); however both incur a significant constant per-time step computational cost. Despite this progress, there remains a need for new or alternative methods of calculating hydrodynamic interactions; large polymer chains or semidilute polymer solutions remain computationally expensive. In this paper, we introduce an alternative method for calculating approximate hydrodynamic interactions. Our method relies on an iterative scheme to establish self-consistency between a hydrodynamic matrix that is averaged over simulation and the hydrodynamic matrix used to run the simulation. Comparison to standard BD simulation and polymer theory results demonstrates that this method quantitatively captures both equilibrium and steady-state dynamics after only a few iterations. The use of an averaged hydrodynamic matrix allows the computationally expensive Brownian noise calculation to be performed infrequently, so that it is no longer the bottleneck of the simulation calculations. We also investigate limitations of this conformational averaging approach in ring polymers.
Guthrie, Kate M; Rosen, Rochelle K; Vargas, Sara E; Guillen, Melissa; Steger, Arielle L; Getz, Melissa L; Smith, Kelley A; Ramirez, Jaime J; Kojic, Erna M
2017-10-01
The development of HIV-preventive topical vaginal microbicides has been challenged by a lack of sufficient adherence in later stage clinical trials to confidently evaluate effectiveness. This dilemma has highlighted the need to integrate translational research earlier in the drug development process, essentially applying behavioral science to facilitate the advances of basic science with respect to the uptake and use of biomedical prevention technologies. In the last several years, there has been an increasing recognition that the user experience, specifically the sensory experience, as well as the role of meaning-making elicited by those sensations, may play a more substantive role than previously thought. Importantly, the role of the user-their sensory perceptions, their judgements of those experiences, and their willingness to use a product-is critical in product uptake and consistent use post-marketing, ultimately realizing gains in global public health. Specifically, a successful prevention product requires an efficacious drug, an efficient drug delivery system, and an effective user. We present an integrated iterative drug development and user experience evaluation method to illustrate how user-centered formulation design can be iterated from the early stages of preclinical development to leverage the user experience. Integrating the user and their product experiences into the formulation design process may help optimize both the efficiency of drug delivery and the effectiveness of the user.
A guidance law for UAV autonomous aerial refueling based on the iterative computation method
Directory of Open Access Journals (Sweden)
Luo Delin
2014-08-01
Full Text Available The rendezvous and formation problem is a significant part for the unmanned aerial vehicle (UAV autonomous aerial refueling (AAR technique. It can be divided into two major phases: the long-range guidance phase and the formation phase. In this paper, an iterative computation guidance law (ICGL is proposed to compute a series of state variables to get the solution of a control variable for a UAV conducting rendezvous with a tanker in AAR. The proposed method can make the control variable converge to zero when the tanker and the UAV receiver come to a formation flight eventually. For the long-range guidance phase, the ICGL divides it into two sub-phases: the correction sub-phase and the guidance sub-phase. The two sub-phases share the same iterative process. As for the formation phase, a velocity coordinate system is created by which control accelerations are designed to make the speed of the UAV consistent with that of the tanker. The simulation results demonstrate that the proposed ICGL is effective and robust against wind disturbance.
Ultra-high speed digital micro-mirror device based ptychographic iterative engine method.
Sun, Aihui; He, Xiaoliang; Kong, Yan; Cui, Haoyang; Song, Xiaojun; Xue, Liang; Wang, Shouyu; Liu, Cheng
2017-07-01
To reduce the long data acquisition time of the common mechanical scanning based Ptychographic Iterative Engine (PIE) technique, the digital micro-mirror device (DMD) is used to form the fast scanning illumination on the sample. Since the transverse mechanical scanning in the common PIE is replaced by the on/off switching of the micro-mirrors, the data acquisition time can be reduced from more than 15 minutes to less than 20 seconds for recording 12 × 10 diffraction patterns to cover the same field of 147.08 mm(2). Furthermore, since the precision of DMD fabricated with the optical lithography is always higher than 10 nm (1 μm for the mechanical translation stage), the time consuming position-error-correction procedure is not required in the iterative reconstruction. These two improvements fundamentally speed up both the data acquisition and the reconstruction procedures in PIE, and relax its requirements on the stability of the imaging system, therefore remarkably improve its applicability for many practices. It is demonstrated experimentally with both USAF resolution target and biological sample that, the spatial resolution of 5.52 μm and the field of view of 147.08 mm(2) can be reached with the DMD based PIE method. In a word, by using the DMD to replace the translation stage, we can effectively overcome the main shortcomings of common PIE related to the mechanical scanning, while keeping its advantages on both the high resolution and large field of view.
Iterative observer based method for source localization problem for Poisson equation in 3D
Majeed, Muhammad Usman
2017-07-10
A state-observer based method is developed to solve point source localization problem for Poisson equation in a 3D rectangular prism with available boundary data. The technique requires a weighted sum of solutions of multiple boundary data estimation problems for Laplace equation over the 3D domain. The solution of each of these boundary estimation problems involves writing down the mathematical problem in state-space-like representation using one of the space variables as time-like. First, system observability result for 3D boundary estimation problem is recalled in an infinite dimensional setting. Then, based on the observability result, the boundary estimation problem is decomposed into a set of independent 2D sub-problems. These 2D problems are then solved using an iterative observer to obtain the solution. Theoretical results are provided. The method is implemented numerically using finite difference discretization schemes. Numerical illustrations along with simulation results are provided.
Comparison of Iterative Methods for Computing the Pressure Field in a Dynamic Network Model
DEFF Research Database (Denmark)
Mogensen, Kristian; Stenby, Erling Halfdan; Banerjee, Srilekha
1999-01-01
In dynamic network models, the pressure map (the pressure in the pores) must be evaluated at each time step. This calculation involves the solution of a large number of nonlinear algebraic systems of equations and accounts for more than 80 of the total CPU-time. Each nonlinear system requires...... at least the partial solution of a sequence of linear systems. We present a comparative study of iterative methods for solving these systems, where we apply both standard routines from the public domain package ITPACK 2C and our own routines tailored to the network problem. The conjugate gradient method......, preconditioned by symmetric successive overrelaxation, was found to be consistently faster and more robust than the other solvers tested. In particular, it was found to be much superior to the successive overrelaxation technique currently used by many researchers....
Single image super-resolution via an iterative reproducing kernel Hilbert space method.
Deng, Liang-Jian; Guo, Weihong; Huang, Ting-Zhu
2016-11-01
Image super-resolution, a process to enhance image resolution, has important applications in satellite imaging, high definition television, medical imaging, etc. Many existing approaches use multiple low-resolution images to recover one high-resolution image. In this paper, we present an iterative scheme to solve single image super-resolution problems. It recovers a high quality high-resolution image from solely one low-resolution image without using a training data set. We solve the problem from image intensity function estimation perspective and assume the image contains smooth and edge components. We model the smooth components of an image using a thin-plate reproducing kernel Hilbert space (RKHS) and the edges using approximated Heaviside functions. The proposed method is applied to image patches, aiming to reduce computation and storage. Visual and quantitative comparisons with some competitive approaches show the effectiveness of the proposed method.
A non-iterative method for computing the infimum in H(infinity)-optimization
Chen, Ben M.; Saberi, Ali; Ly, Uy-Loi
1992-01-01
This paper presents a simple and non-iterative procedure for the computation of the exact value of the infimum in the singular H(infinity)-optimization problem, and is an extension of our earlier work. The problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. Our method is applicable to a class of singular H(infinity)-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the j-omega axis and also satisfy certain geometric conditions. The computation of the infimum in our method involves solving two well-defined Riccati and two Liapunov equations.
DEFF Research Database (Denmark)
Nielsen, Allan Aasbjerg
2007-01-01
(IR) MAD method in a series of iterations places increasing focus on “difficult” observations, here observations whose change status over time is uncertain. The MAD method is based on the established technique of canonical correlation analysis: for the multivariate data acquired at two points in time...... and covering the same geographical region, we calculate the canonical variates and subtract them from each other. These orthogonal differences contain maximum information on joint change in all variables (spectral bands). The change detected in this fashion is invariant to separate linear (affine......) transformations in the originally measured variables at the two points in time such as 1) changes in gain and offset in the measuring device used to acquire the data; 2) data normalization or calibration schemes that are linear (affine) in the gray values of the original variables; or 3) orthogonal or other...
Directory of Open Access Journals (Sweden)
Kim Jong
2011-01-01
Full Text Available Abstract We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-ϕ-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. 2000 Mathematics subject classification: 47H05, 47H09, 47H10, 47J25
Accuracy improvement of a hybrid robot for ITER application using POE modeling method
Energy Technology Data Exchange (ETDEWEB)
Wang, Yongbo, E-mail: yongbo.wang@hotmail.com [Laboratory of Intelligent Machines, Lappeenranta University of Technology, FIN-53851 Lappeenranta (Finland); Wu, Huapeng; Handroos, Heikki [Laboratory of Intelligent Machines, Lappeenranta University of Technology, FIN-53851 Lappeenranta (Finland)
2013-10-15
Highlights: ► The product of exponential (POE) formula for error modeling of hybrid robot. ► Differential Evolution (DE) algorithm for parameter identification. ► Simulation results are given to verify the effectiveness of the method. -- Abstract: This paper focuses on the kinematic calibration of a 10 degree-of-freedom (DOF) redundant serial–parallel hybrid robot to improve its accuracy. The robot was designed to perform the assembling and repairing tasks of the vacuum vessel (VV) of the international thermonuclear experimental reactor (ITER). By employing the product of exponentials (POEs) formula, we extended the POE-based calibration method from serial robot to redundant serial–parallel hybrid robot. The proposed method combines the forward and inverse kinematics together to formulate a hybrid calibration method for serial–parallel hybrid robot. Because of the high nonlinear characteristics of the error model and too many error parameters need to be identified, the traditional iterative linear least-square algorithms cannot be used to identify the parameter errors. This paper employs a global optimization algorithm, Differential Evolution (DE), to identify parameter errors by solving the inverse kinematics of the hybrid robot. Furthermore, after the parameter errors were identified, the DE algorithm was adopted to numerically solve the forward kinematics of the hybrid robot to demonstrate the accuracy improvement of the end-effector. Numerical simulations were carried out by generating random parameter errors at the allowed tolerance limit and generating a number of configuration poses in the robot workspace. Simulation of the real experimental conditions shows that the accuracy of the end-effector can be improved to the same precision level of the given external measurement device.
Clinical correlative evaluation of an iterative method for reconstruction of brain SPECT images
Energy Technology Data Exchange (ETDEWEB)
Nobili, Flavio E-mail: fnobili@smartino.ge.it; Vitali, Paolo; Calvini, Piero; Bollati, Francesca; Girtler, Nicola; Delmonte, Marta; Mariani, Giuliano; Rodriguez, Guido
2001-08-01
Background: Brain SPECT and PET investigations have showed discrepancies in Alzheimer's disease (AD) when considering data deriving from deeply located structures, such as the mesial temporal lobe. These discrepancies could be due to a variety of factors, including substantial differences in gamma-cameras and underlying technology. Mesial temporal structures are deeply located within the brain and the commonly used Filtered Back-Projection (FBP) technique does not fully take into account either the physical parameters of gamma-cameras or geometry of collimators. In order to overcome these limitations, alternative reconstruction methods have been proposed, such as the iterative method of the Conjugate Gradients with modified matrix (CG). However, the clinical applications of these methods have so far been only anecdotal. The present study was planned to compare perfusional SPECT data as derived from the conventional FBP method and from the iterative CG method, which takes into account the geometrical and physical characteristics of the gamma-camera, by a correlative approach with neuropsychology. Methods: Correlations were compared between perfusion of the hippocampal region, as achieved by both the FBP and the CG reconstruction methods, and a short-memory test (Selective Reminding Test, SRT), specifically addressing one of its function. A brain-dedicated camera (CERASPECT) was used for SPECT studies with {sup 99m}Tc-hexamethylpropylene-amine-oxime in 23 consecutive patients (mean age: 74.2{+-}6.5) with mild (Mini-Mental Status Examination score {>=}15, mean 20.3{+-}3), probable AD. Counts from a hippocampal region in each hemisphere were referred to the average thalamic counts. Results: Hippocampal perfusion significantly correlated with the MMSE score with similar statistical significance (p<0.01) between the two reconstruction methods. Correlation between hippocampal perfusion and the SRT score was better with the CG method (r=0.50 for both hemispheres, p<0
Asymptotically Safe Dark Matter
DEFF Research Database (Denmark)
Sannino, Francesco; Shoemaker, Ian M.
2015-01-01
We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....
Wang, Xianghong; Liu, Xinyu; Wang, Nanshuo; Yu, Xiaojun; Bo, En; Chen, Si; Liu, Linbo
2017-02-01
Optical coherence tomography (OCT) provides high resolution and cross-sectional images of biological tissue and is widely used for diagnosis of ocular diseases. However, OCT images suffer from speckle noise, which typically considered as multiplicative noise in nature, reducing the image resolution and contrast. In this study, we propose a two-step iteration (TSI) method to suppress those noises. We first utilize augmented Lagrange method to recover a low-rank OCT image and remove additive Gaussian noise, and then employ the simple and efficient split Bregman method to solve the Total-Variation Denoising model. We validated such proposed method using images of swine, rabbit and human retina. Results demonstrate that our TSI method outperforms the other popular methods in achieving higher peak signal-to-noise ratio (PSNR) and structure similarity (SSIM) while preserving important structural details, such as tiny capillaries and thin layers in retinal OCT images. In addition, the results of our TSI method show clearer boundaries and maintains high image contrast, which facilitates better image interpretations and analyses.
Energy Technology Data Exchange (ETDEWEB)
Clemens, M.; Weiland, T. [Technische Hochschule Darmstadt (Germany)
1996-12-31
In the field of computational electrodynamics the discretization of Maxwell`s equations using the Finite Integration Theory (FIT) yields very large, sparse, complex symmetric linear systems of equations. For this class of complex non-Hermitian systems a number of conjugate gradient-type algorithms is considered. The complex version of the biconjugate gradient (BiCG) method by Jacobs can be extended to a whole class of methods for complex-symmetric algorithms SCBiCG(T, n), which only require one matrix vector multiplication per iteration step. In this class the well-known conjugate orthogonal conjugate gradient (COCG) method for complex-symmetric systems corresponds to the case n = 0. The case n = 1 yields the BiCGCR method which corresponds to the conjugate residual algorithm for the real-valued case. These methods in combination with a minimal residual smoothing process are applied separately to practical 3D electro-quasistatical and eddy-current problems in electrodynamics. The practical performance of the SCBiCG methods is compared with other methods such as QMR and TFQMR.
Applications of a direct/iterative design method to complex transonic configurations
Smith, Leigh Ann; Campbell, Richard L.
1992-01-01
The current study explores the use of an automated direct/iterative design method for the reduction of drag in transport configurations, including configurations with engine nacelles. The method requires the user to choose a proper target-pressure distribution and then develops a corresponding airfoil section. The method can be applied to two-dimensional airfoil sections or to three-dimensional wings. The three cases that are presented show successful application of the method for reducing drag from various sources. The first two cases demonstrate the use of the method to reduce induced drag by designing to an elliptic span-load distribution and to reduce wave drag by decreasing the shock strength for a given lift. In the second case, a body-mounted nacelle is added and the method is successfully used to eliminate increases in wing drag associated with the nacelle addition by designing to an arbitrary pressure distribution as a result of the redesigning of a wing in combination with a given underwing nacelle to clean-wing, target-pressure distributions. These cases illustrate several possible uses of the method for reducing different types of drag. The magnitude of the obtainable drag reduction varies with the constraints of the problem and the configuration to be modified.
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
Directory of Open Access Journals (Sweden)
shadan sadigh behzadi
2012-03-01
Full Text Available In this present paper, we solve a two-dimensional nonlinear Volterra-Fredholm integro-differential equation by using the following powerful, efficient but simple methods: (i Modified Adomian decomposition method (MADM, (ii Variational iteration method (VIM, (iii Homotopy analysis method (HAM and (iv Modified homotopy perturbation method (MHPM. The uniqueness of the solution and the convergence of the proposed methods are proved in detail. Numerical examples are studied to demonstrate the accuracy of the presented methods.
High-order noise analysis for low dose iterative image reconstruction methods: ASIR, IRIS, and MBAI
Do, Synho; Singh, Sarabjeet; Kalra, Mannudeep K.; Karl, W. Clem; Brady, Thomas J.; Pien, Homer
2011-03-01
Iterative reconstruction techniques (IRTs) has been shown to suppress noise significantly in low dose CT imaging. However, medical doctors hesitate to accept this new technology because visual impression of IRT images are different from full-dose filtered back-projection (FBP) images. Most common noise measurements such as the mean and standard deviation of homogeneous region in the image that do not provide sufficient characterization of noise statistics when probability density function becomes non-Gaussian. In this study, we measure L-moments of intensity values of images acquired at 10% of normal dose and reconstructed by IRT methods of two state-of-art clinical scanners (i.e., GE HDCT and Siemens DSCT flash) by keeping dosage level identical to each other. The high- and low-dose scans (i.e., 10% of high dose) were acquired from each scanner and L-moments of noise patches were calculated for the comparison.
Iterative method to compute the Fermat points and Fermat distances of multiquarks
Energy Technology Data Exchange (ETDEWEB)
Bicudo, P. [CFTP, Departamento de Fisica, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa (Portugal)], E-mail: bicudo@ist.utl.pt; Cardoso, M. [CFTP, Departamento de Fisica, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa (Portugal)
2009-04-13
The multiquark confining potential is proportional to the total distance of the fundamental strings linking the quarks and antiquarks. We address the computation of the total string distance and of the Fermat points where the different strings meet. For a meson the distance is trivially the quark-antiquark distance. For a baryon the problem was solved geometrically from the onset by Fermat and by Torricelli, it can be determined just with a rule and a compass, and we briefly review it. However we also show that for tetraquarks, pentaquarks, hexaquarks, etc., the geometrical solution is much more complicated. Here we provide an iterative method, converging fast to the correct Fermat points and the total distances, relevant for the multiquark potentials.
New-Sum: A Novel Online ABFT Scheme For General Iterative Methods
Energy Technology Data Exchange (ETDEWEB)
Tao, Dingwen; Song, Shuaiwen; Krishnamoorthy, Sriram; Wu, Panruo; Liang, Xin; Zhang, Eddy; Kerbyson, Darren J.; Chen, Zizhong
2016-05-31
Emerging high-performance computing platforms, with large component counts and lower power margins, are anticipated to be more susceptible to soft errors in both logic circuits and memory subsystems. We present an online algorithm-based fault tolerance (ABFT) approach to efficiently detect and recover soft errors for general iterative methods. We design a novel checksum-based encoding scheme for matrix-vector multiplication that is resilient to both arithmetic and memory errors. Our design decouples the checksum updating process from the actual computation, and allows adaptive checksum overhead control. Building on this new encoding mechanism, we propose two online ABFT designs that can effectively recover from errors when combined with a checkpoint/rollback scheme.
Green`s function of Maxwell`s equations and corresponding implications for iterative methods
Energy Technology Data Exchange (ETDEWEB)
Singer, B.S. [Macquarie Univ., Sydney (Australia); Fainberg, E.B. [Inst. of Physics of the Earth, Moscow (Russian Federation)
1996-12-31
Energy conservation law imposes constraints on the norm and direction of the Hilbert space vector representing a solution of Maxwell`s equations. In this paper, we derive these constrains and discuss the corresponding implications for the Green`s function of Maxwell`s equations in a dissipative medium. It is shown that Maxwell`s equations can be reduced to an integral equation with a contracting kernel. The equation can be solved using simple iterations. Software based on this algorithm have successfully been applied to a wide range of problems dealing with high contrast models. The matrix corresponding to the integral equation has a well defined spectrum. The equation can be symmetrized and solved using different approaches, for instance one of the conjugate gradient methods.
Liu, Hui; Li, Yingzi; Zhang, Yingxu; Chen, Yifu; Song, Zihang; Wang, Zhenyu; Zhang, Suoxin; Qian, Jianqiang
2018-01-01
Proportional-integral-derivative (PID) parameters play a vital role in the imaging process of an atomic force microscope (AFM). Traditional parameter tuning methods require a lot of manpower and it is difficult to set PID parameters in unattended working environments. In this manuscript, an intelligent tuning method of PID parameters based on iterative learning control is proposed to self-adjust PID parameters of the AFM according to the sample topography. This method gets enough information about the output signals of PID controller and tracking error, which will be used to calculate the proper PID parameters, by repeated line scanning until convergence before normal scanning to learn the topography. Subsequently, the appropriate PID parameters are obtained by fitting method and then applied to the normal scanning process. The feasibility of the method is demonstrated by the convergence analysis. Simulations and experimental results indicate that the proposed method can intelligently tune PID parameters of the AFM for imaging different topographies and thus achieve good tracking performance. Copyright © 2017 Elsevier Ltd. All rights reserved.
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.
Yang, J.; Lee, H.; Yoo, H.; Huh, S.
2009-12-01
When magnetotelluric (MT) data are obtained in the vicinity of the coast, the surrounding seas make it difficult to interpret subsurface structures, in particular for the deep parts of the subsurface. We apply an iterative method to remove the sea effects. The iterative method was originally developed to remove the distortion due to topographic changes from MT data recorded on the seafloor. The iterative sea-effect correction method is performed in two steps. One is to correct the sea effect, and the other is the inversion of the sea-effect corrected responses. The two steps are alternatively carried out, until a criterion for either the inversion or the sea-effect correction is satisfied. Since the 3D surrounding sea bathymetry is only incorporated into forward modeling for the sea-effect correction, it can be more robust than the method that incorporates the 3D sea bathymetry into a model space for inversion. The synthetic examples show that the sea-effect correction method yields an inverted model comparable to the true model. By applying the sea-effect correction method to real field data acquired in Jeju Island, Korea, we also demonstrate that the sea-effect correction method effectively removes the sea effects from the 1-D and 2-D real field data, which contributes to enhance the inversion results. From these results, we can conclude that the iterative sea-effect correction method can be promising to recover the true response of the subsurface more precisely. (a) Observed (uncorrected) (b) sea-effect corrected sounding curves of XY- and YX-mode with those of determinant average (DET) at the site JSL12. (c) 1-D resistivity models obtained by Occam inversion of determinant average (DET) at each iteration stage for the site JSL12. (d) RMS misfit between Z and Zo at each iteration stage. Note that the inverted model at the initial stage (0th) was obtained without sea effect correction.
Hand-Eye LRF-Based Iterative Plane Detection Method for Autonomous Robotic Welding
Directory of Open Access Journals (Sweden)
Sungmin Lee
2015-12-01
Full Text Available This paper proposes a hand-eye LRF-based (laser range finder welding plane-detection method for autonomous robotic welding in the field of shipbuilding. The hand-eye LRF system consists of a 6 DOF manipulator and an LRF attached to the wrist of the manipulator. The welding plane is detected by the LRF with only the wrist's rotation to minimize a mechanical error caused by the manipulator's motion. A position on the plane is determined as an average position of the detected points on the plane, and a normal vector to the plane is determined by applying PCA (principal component analysis to the detected points. In this case, the accuracy of the detected plane is analysed by simulations with respect to the wrist's angle interval and the plane angle. As a result of the analysis, an iterative plane-detection method with the manipulator's alignment motion is proposed to improve the performance of plane detection. For verifying the feasibility and effectiveness of the proposed plane-detection method, experiments are carried out with a prototype of the hand-eye LRF-based system, which consists of a 1 DOF wrist's joint, an LRF system and a rotatable plane. In addition, the experimental results of the PCA-based plane detection method are compared with those of the two representative plane-detection methods, based on RANSAC (RANdom SAmple Consensus and the 3D Hough transform in both accuracy and computation time's points of view.
Fuzzy based method for project planning of the infrastructure design for the diagnostic in ITER
Energy Technology Data Exchange (ETDEWEB)
Piros, Attila, E-mail: attila.piros@gt3.bme.hu [Department of Machine and Product Design, Budapest University of Technology and Economics, Budapest (Hungary); Veres, Gábor [Department of Plasma Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest (Hungary)
2013-10-15
The long-term design projects need special preparation before the start of the execution. This preparation usually includes the drawing of the network diagram for the whole procedure. This diagram includes the time estimation of the individual subtasks and gives us information about the predicted dates of the milestones. The calculated critical path in this network characterizes a specific design project concerning to its duration very well. Several methods are available to support this step of preparation. This paper describes a new method to map the structure of the design process and clarify the milestones and predict the dates of these milestones. The method is based on the PERT (Project Evaluation and Review Technique) network but as a novelty it applies fuzzy logic to find out the concerning times in this graph. With the application of the fuzzy logic the handling of the different kinds of design uncertainties becomes feasible. Many kinds of design uncertainties exist from the possible electric blackout up to the illness of an engineer. In many cases these uncertainties are related with human errors and described with linguistic expressions. The fuzzy logic enables to transform these ambiguous expressions into numeric values for further mathematical evaluation. The method is introduced in the planning of the design project of the infrastructure for the diagnostic systems of ITER. The method not only helps the project in the planning phase, but it will be a powerful tool in mathematical modeling and monitoring of the project execution.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zhenyue [Zhejiang Univ., Hangzhou (People' s Republic of China); Zha, Hongyuan [Pennsylvania State Univ., University Park, PA (United States); Simon, Horst [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2006-07-31
In this paper, we developed numerical algorithms for computing sparse low-rank approximations of matrices, and we also provided a detailed error analysis of the proposed algorithms together with some numerical experiments. The low-rank approximations are constructed in a certain factored form with the degree of sparsity of the factors controlled by some user-specified parameters. In this paper, we cast the sparse low-rank approximation problem in the framework of penalized optimization problems. We discuss various approximation schemes for the penalized optimization problem which are more amenable to numerical computations. We also include some analysis to show the relations between the original optimization problem and the reduced one. We then develop a globally convergent discrete Newton-like iterative method for solving the approximate penalized optimization problems. We also compare the reconstruction errors of the sparse low-rank approximations computed by our new methods with those obtained using the methods in the earlier paper and several other existing methods for computing sparse low-rank approximations. Numerical examples show that the penalized methods are more robust and produce approximations with factors which have fewer columns and are sparser.
Tian, Ye; Erb, Kay Condie; Adluru, Ganesh; Likhite, Devavrat; Pedgaonkar, Apoorva; Blatt, Michael; Kamesh Iyer, Srikant; Roberts, John; DiBella, Edward
2017-08-01
To evaluate the use of three different pre-reconstruction interpolation methods to convert non-Cartesian k-space data to Cartesian samples such that iterative reconstructions can be performed more simply and more rapidly. Phantom as well as cardiac perfusion radial datasets were reconstructed by four different methods. Three of the methods used pre-reconstruction interpolation once followed by a fast Fourier transform (FFT) at each iteration. The methods were: bilinear interpolation of nearest-neighbor points (BINN), 3-point interpolation, and a multi-coil interpolator called GRAPPA Operator Gridding (GROG). The fourth method performed a full non-Uniform FFT (NUFFT) at each iteration. An iterative reconstruction with spatiotemporal total variation constraints was used with each method. Differences in the images were quantified and compared. The GROG multicoil interpolation, the 3-point interpolation, and the NUFFT-at-each-iteration approaches produced high quality images compared to BINN, with the GROG-derived images having the fewest streaks among the three preinterpolation approaches. However, all reconstruction methods produced approximately equal results when applied to perfusion quantitation tasks. Pre-reconstruction interpolation gave approximately an 83% reduction in reconstruction time. Image quality suffers little from using a pre-reconstruction interpolation approach compared to the more accurate NUFFT-based approach. GROG-based pre-reconstruction interpolation appears to offer the best compromise by using multicoil information to perform the interpolation to Cartesian sample points prior to image reconstruction. Speed gains depend on the implementation and relatively standard optimizations on a MATLAB platform result in preinterpolation speedups of ~ 6 compared to using NUFFT at every iteration, reducing the reconstruction time from around 42 min to 7 min. © 2017 American Association of Physicists in Medicine.
Amano, Ken-ich
2013-01-01
We propose iterative methods for obtaining solvation structures on a solid plate which use force distributions measured by surface force apparatus (SFA) and atomic force microscopy (AFM) as input data. Two model systems are considered here. In the model system for SFA, the same two solid plates are immersed in a solvent, and a probe tip and a solid plate are immersed in a solvent in the model system for AFM. Advantages of the iterative methods are as follows: The iterative method for SFA can obtain the solvation structure, for example, in a Lennard-Jones liquid; The iterative method for AFM can obtain the solvation structure without an input datum of solvation structure around the probe tip.
Topographic mapping on large-scale tidal flats with an iterative approach on the waterline method
Kang, Yanyan; Ding, Xianrong; Xu, Fan; Zhang, Changkuan; Ge, Xiaoping
2017-05-01
Tidal flats, which are both a natural ecosystem and a type of landscape, are of significant importance to ecosystem function and land resource potential. Morphologic monitoring of tidal flats has become increasingly important with respect to achieving sustainable development targets. Remote sensing is an established technique for the measurement of topography over tidal flats; of the available methods, the waterline method is particularly effective for constructing a digital elevation model (DEM) of intertidal areas. However, application of the waterline method is more limited in large-scale, shifting tidal flats areas, where the tides are not synchronized and the waterline is not a quasi-contour line. For this study, a topographical map of the intertidal regions within the Radial Sand Ridges (RSR) along the Jiangsu Coast, China, was generated using an iterative approach on the waterline method. A series of 21 multi-temporal satellite images (18 HJ-1A/B CCD and three Landsat TM/OLI) of the RSR area collected at different water levels within a five month period (31 December 2013-28 May 2014) was used to extract waterlines based on feature extraction techniques and artificial further modification. These 'remotely-sensed waterlines' were combined with the corresponding water levels from the 'model waterlines' simulated by a hydrodynamic model with an initial generalized DEM of exposed tidal flats. Based on the 21 heighted 'remotely-sensed waterlines', a DEM was constructed using the ANUDEM interpolation method. Using this new DEM as the input data, it was re-entered into the hydrodynamic model, and a new round of water level assignment of waterlines was performed. A third and final output DEM was generated covering an area of approximately 1900 km2 of tidal flats in the RSR. The water level simulation accuracy of the hydrodynamic model was within 0.15 m based on five real-time tide stations, and the height accuracy (root mean square error) of the final DEM was 0.182 m
Ying, Jiangbo; Yap, Philip; Gandhi, Mihir; Liew, Tau Ming
2017-12-10
Dementia caregiving is often stressful and depression in family caregivers is not uncommon. As caregiver depression can have significant effects, there is a need for preventive efforts which are consistent with the extensive literature. We sought to consolidate the wide range of evidence (using a multi-method approach) into a simple framework that can guide the prevention of caregiver depression. Using multiple logistic regression, we derived the predictors of caregiver depression from an empirical dataset containing key information and depression scores (based on the Center-for-Epidemiological-Studies-Depression-Scale) of 394 family caregivers. We then chose an underpinning theory as the foundation of the framework, and conducted an umbrella systematic review to find possible links between the derived predictors and the theory. Last, we compared the iterated framework with known interventions for caregiver depression in recent literature to assess whether the framework could map meaningfully with the known interventions. Significant predictors of caregiver depression included primary caregiver (odds ratio, OR = 1.53), severe dementia (OR = 1.40), and behavioral problems (OR = 3.23), lower education (OR = 1.77), and spousal caregivers (OR = 1.98). The integrated framework derived focuses on four strategic areas: physical-care demands of persons with dementia (PWD), behavioral problems of PWD, caregiving competency, and loss and grief of caregivers. This framework is supported by known interventions for caregiver depression in recent literature. By consolidating a broad range of evidence, we iterated a framework to aid the understanding and prevention of caregiver depression in dementia. The framework offers an approach to prevention which is simple, systematic, and reflective of the extensive literature.
Energy Technology Data Exchange (ETDEWEB)
Zalach, J.; Franke, St. [INP Greifswald, Felix-Hausdorff-Str. 2, 17489 Greifswald (Germany)
2013-01-28
The Boltzmann plot method allows to calculate plasma temperatures and pressures if absolutely calibrated emission coefficients of spectral lines are available. However, xenon arcs are not very well suited to be analyzed this way, as there are only a limited number of lines with atomic data available. These lines have high excitation energies in a small interval between 9.8 and 11.5 eV. Uncertainties in the experimental method and in the atomic data further limit the accuracy of the evaluation procedure. This may result in implausible values of temperature and pressure with inadmissible uncertainty. To omit these shortcomings, an iterative scheme is proposed that is making use of additional information about the xenon fill pressure. This method is proved to be robust against noisy data and significantly reduces the uncertainties. Intentionally distorted synthetic data are used to illustrate the performance of the method, and measurements performed on a laboratory xenon high pressure discharge lamp are analyzed resulting in reasonable temperatures and pressures with significantly reduced uncertainties.
Nakamura, Gen; Wang, Haibing
2017-05-01
Consider the problem of reconstructing unknown Robin inclusions inside a heat conductor from boundary measurements. This problem arises from active thermography and is formulated as an inverse boundary value problem for the heat equation. In our previous works, we proposed a sampling-type method for reconstructing the boundary of the Robin inclusion and gave its rigorous mathematical justification. This method is non-iterative and based on the characterization of the solution to the so-called Neumann- to-Dirichlet map gap equation. In this paper, we give a further investigation of the reconstruction method from both the theoretical and numerical points of view. First, we clarify the solvability of the Neumann-to-Dirichlet map gap equation and establish a relation of its solution to the Green function associated with an initial-boundary value problem for the heat equation inside the Robin inclusion. This naturally provides a way of computing this Green function from the Neumann-to-Dirichlet map and explains what is the input for the linear sampling method. Assuming that the Neumann-to-Dirichlet map gap equation has a unique solution, we also show the convergence of our method for noisy measurements. Second, we give the numerical implementation of the reconstruction method for two-dimensional spatial domains. The measurements for our inverse problem are simulated by solving the forward problem via the boundary integral equation method. Numerical results are presented to illustrate the efficiency and stability of the proposed method. By using a finite sequence of transient input over a time interval, we propose a new sampling method over the time interval by single measurement which is most likely to be practical.
An Improved Iterative Fitting Method to Estimate Nocturnal Residual Layer Height
Directory of Open Access Journals (Sweden)
Wei Wang
2016-08-01
Full Text Available The planetary boundary layer (PBL is an atmospheric region near the Earth’s surface. It is significant for weather forecasting and for the study of air quality and climate. In this study, the top of nocturnal residual layers—which are what remain of the daytime mixing layer—are estimated by an elastic backscatter Lidar in Wuhan (30.5°N, 114.4°E, a city in Central China. The ideal profile fitting method is widely applied to determine the nocturnal residual layer height (RLH from Lidar data. However, the method is seriously affected by an optical thick layer. Thus, we propose an improved iterative fitting method to eliminate the optical thick layer effect on RLH detection using Lidar. Two typical case studies observed by elastic Lidar are presented to demonstrate the theory and advantage of the proposed method. Results of case analysis indicate that the improved method is more practical and precise than profile-fitting, gradient, and wavelet covariance transform method in terms of nocturnal RLH evaluation under low cloud conditions. Long-term observations of RLH performed with ideal profile fitting and improved methods were carried out in Wuhan from 28 May 2011 to 17 June 2016. Comparisons of Lidar-derived RLHs with the two types of methods verify that the improved solution is practical. Statistical analysis of a six-year Lidar signal was conducted to reveal the monthly average values of nocturnal RLH in Wuhan. A clear RLH monthly cycle with a maximum mean height of about 1.8 km above ground level was observed in August, and a minimum height of about 0.7 km was observed in January. The variation in monthly mean RLH displays an obvious quarterly dependence, which coincides with the annual variation in local surface temperature.
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.
A non-iterative immersed boundary method for spherical particles of arbitrary density ratio
Tschisgale, Silvio; Kempe, Tobias; Fröhlich, Jochen
2017-06-01
In this paper an immersed boundary method with semi-implicit fluid-solid coupling for mobile particles of arbitrary density ratio is developed. The new scheme does not require any iterations to balance fluid forces and particle forces at the interface. A new formulation of the particle equations of motion is proposed which not only accounts for the particle itself but also for a Lagrangian layer surrounding the particle surface. Furthermore, it is shown by analytical considerations that the six equations for the linear and angular velocity of the spherical particle decouple which allows their sequential solution. On this basis a new time integration scheme is obtained which is unconditionally stable for all fluid-solid density ratios and enables large time steps, with Courant numbers around unity. The new scheme is extensively validated for various test cases and its convergence is assessed. An appealing issue is that compared to existing immersed boundary methods the new scheme only alters coefficients in the particle equations and the order of the steps, making it easy to implement in present codes with explicit coupling. This substantially extends the field of application of such methods.
Comparison of combustion products by the iteration method and application of gasoline and biogas
Juntarakod, Paramust
2017-02-01
For a specific combustion problem involving calculations of several species at the equilibrium state, it is simpler to write a general computer program and calculate the combustion concentration. Original work describes, an adaptation of Newton-Raphson method was used for solving the highly linear system of equations describing the formation of equilibrium products in reacting of fuel-additive-air mixtures. This study also shows what possible of the results. In this paper, it presents the efficient numerical algorithms for solving the combustion problem, to be used linear equations based on the iteration method and high order of the Taylor series. The modified the Adomian decomposition method was applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of algorithms. Comparisons of results by the new Matlab routines and previous routines, the result data indicate that the new Matlab routines are reliable and application with gasoline and biogas with the variance of equivalence ratios, typical deviations from previous results are less than 0.1%.
Directory of Open Access Journals (Sweden)
Kravtsenyuk Olga V
2007-01-01
Full Text Available The possibility of improving the spatial resolution of diffuse optical tomograms reconstructed by the photon average trajectories (PAT method is substantiated. The PAT method recently presented by us is based on a concept of an average statistical trajectory for transfer of light energy, the photon average trajectory (PAT. The inverse problem of diffuse optical tomography is reduced to a solution of an integral equation with integration along a conditional PAT. As a result, the conventional algorithms of projection computed tomography can be used for fast reconstruction of diffuse optical images. The shortcoming of the PAT method is that it reconstructs the images blurred due to averaging over spatial distributions of photons which form the signal measured by the receiver. To improve the resolution, we apply a spatially variant blur model based on an interpolation of the spatially invariant point spread functions simulated for the different small subregions of the image domain. Two iterative algorithms for solving a system of linear algebraic equations, the conjugate gradient algorithm for least squares problem and the modified residual norm steepest descent algorithm, are used for deblurring. It is shown that a gain in spatial resolution can be obtained.
Iterative reconstruction method for light emitting sources based on the diffusion equation.
Slavine, Nikolai V; Lewis, Matthew A; Richer, Edmond; Antich, Peter P
2006-01-01
Bioluminescent imaging (BLI) of luciferase-expressing cells in live small animals is a powerful technique for investigating tumor growth, metastasis, and specific biological molecular events. Three-dimensional imaging would greatly enhance applications in biomedicine since light emitting cell populations could be unambiguously associated with specific organs or tissues. Any imaging approach must account for the main optical properties of biological tissue because light emission from a distribution of sources at depth is strongly attenuated due to optical absorption and scattering in tissue. Our image reconstruction method for interior sources is based on the deblurring expectation maximization method and takes into account both of these effects. To determine the boundary of the object we use the standard iterative algorithm-maximum likelihood reconstruction method with an external source of diffuse light. Depth-dependent corrections were included in the reconstruction procedure to obtain a quantitative measure of light intensity by using the diffusion equation for light transport in semi-infinite turbid media with extrapolated boundary conditions.
Directory of Open Access Journals (Sweden)
Vladimir V. Lyubimov
2007-01-01
Full Text Available The possibility of improving the spatial resolution of diffuse optical tomograms reconstructed by the photon average trajectories (PAT method is substantiated. The PAT method recently presented by us is based on a concept of an average statistical trajectory for transfer of light energy, the photon average trajectory (PAT. The inverse problem of diffuse optical tomography is reduced to a solution of an integral equation with integration along a conditional PAT. As a result, the conventional algorithms of projection computed tomography can be used for fast reconstruction of diffuse optical images. The shortcoming of the PAT method is that it reconstructs the images blurred due to averaging over spatial distributions of photons which form the signal measured by the receiver. To improve the resolution, we apply a spatially variant blur model based on an interpolation of the spatially invariant point spread functions simulated for the different small subregions of the image domain. Two iterative algorithms for solving a system of linear algebraic equations, the conjugate gradient algorithm for least squares problem and the modified residual norm steepest descent algorithm, are used for deblurring. It is shown that a 27% gain in spatial resolution can be obtained.
Simulation of neoclassical tearing mode stabilization via minimum seeking method on ITER
Energy Technology Data Exchange (ETDEWEB)
Park, M. H.; Kim, K.; Na, D. H.; Byun, C. S.; Na, Y. S. [Seoul National Univ., Seoul (Korea, Republic of); Kim, M. [FNC Technology Co. Ltd, Yongin (Korea, Republic of)
2016-10-15
Neoclassical tearing modes (NTMs) are well known resistive magnetohydrodynamic (MHD) instabilities. These instabilities are sustained by a helically perturbed bootstrap current. NTMs produce magnetic islands in tokamak plasmas that can degrade confinement and lead to plasma disruption. Because of this, the stabilization of NTMs is one of the key issues for tokamaks that achieve high fusion performance such as ITER. Compensating for the lack of bootstrap current by an Electron Cyclotron Current Drive (ECCD) has been proved experimentally as an effective method to stabilize NTMs. In order to stabilize NTMs, it is important to reduce misalignment. So that even ECCD can destabilize the NTMs when misalignment is large. Feedback control method that does not fully require delicate and accurate real-time measurements and calculations, such as equilibrium reconstruction and EC ray-tracing, has also been proposed. One of the feedback control methods is minimum seeking method. This control method minimizes the island width by tuning the misalignment, assuming that the magnetic island width is a function of the misalignment. As a robust and simple method of controlling NTM, minimum 'island width growth rate' seeking control is purposed and compared with performance of minimum ' island width' seeking control. At the integrated numerical system, simulations of the NTM suppression are performed with two types of minimum seeking controllers; one is a FDM based minimum seeking controller and the other is a sinusoidal perturbation based minimum seeking method. The full suppression is achieved both types of controller. The controllers adjust poloidal angle of EC beam and reduce misalignment to zero. The sinusoidal perturbation based minimum seeking control need to modify the adaptive gain.
Purcell, Michael James
Existing methods for focusing and imaging through strongly scattering materials are often limited by speed, the need for invasive feedback, and the shallow depth of penetration of photons into the material. These limitations have motivated the present research into the development of a new iterative phase optimization method for improving transmission of light through a sample of strongly scattering material. A new method, based on the detection of back-scattered light combined with active (phase-only) wavefront control was found to be partially successful, decreasing the power of backscattered incident light at 488 nm wavelength by approximately 35% in a 626 mum thick sample of Yttria (Y2O3) nanopowder (mean particle size 26 nm) in clear epoxy with transport mean free path length ˜116 mum. However, the observed transmitted power did not show simultaneous improvement. The conclusion was reached that scattering to the sides of the sample and polarization scrambling were responsible for the lack of improved transmission with this method. Some ideas for improvement are discussed in the thesis. This research subsequently led to the development of a lensless holographic imaging method based on a rotating diffuser for statistical averaging of the optical signal for overcoming speckle caused by reflection from a rough surface. This method made it possible to reduce background variations of intensity due to speckle and improve images reflected from rough, immobile surfaces with no direct path for photons between the object and camera. Improvements in the images obtained with this technique were evaluated quantitatively by comparing SSIM indices and were found to offer practical advances for transmissive and reflective geometries alike.
Goncharsky, Alexander V.; Romanov, Sergey Y.
2017-02-01
We develop efficient iterative methods for solving inverse problems of wave tomography in models incorporating both diffraction effects and attenuation. In the inverse problem the aim is to reconstruct the velocity structure and the function that characterizes the distribution of attenuation properties in the object studied. We prove mathematically and rigorously the differentiability of the residual functional in normed spaces, and derive the corresponding formula for the Fréchet derivative. The computation of the Fréchet derivative includes solving both the direct problem with the Neumann boundary condition and the reversed-time conjugate problem. We develop efficient methods for numerical computations where the approximate solution is found using the detector measurements of the wave field and its normal derivative. The wave field derivative values at detector locations are found by solving the exterior boundary value problem with the Dirichlet boundary conditions. We illustrate the efficiency of this approach by applying it to model problems. The algorithms developed are highly parallelizable and designed to be run on supercomputers. Among the most promising medical applications of our results is the development of ultrasonic tomographs for differential diagnosis of breast cancer.
Directory of Open Access Journals (Sweden)
Lihua Cai
Full Text Available Type 2 diabetes, which is a complex metabolic disease influenced by genetic and environment, has become a worldwide problem. Previous published results focused on genetic components through genome-wide association studies that just interpret this disease to some extent. Recently, two research groups published metagenome-wide association studies (MGWAS result that found meta-biomarkers related with type 2 diabetes. However, One key problem of analyzing genomic data is that how to deal with the ultra-high dimensionality of features. From a statistical viewpoint it is challenging to filter true factors in high dimensional data. Various methods and techniques have been proposed on this issue, which can only achieve limited prediction performance and poor interpretability. New statistical procedure with higher performance and clear interpretability is appealing in analyzing high dimensional data. To address this problem, we apply an excellent statistical variable selection procedure called iterative sure independence screening to gene profiles that obtained from metagenome sequencing, and 48/24 meta-markers were selected in Chinese/European cohorts as predictors with 0.97/0.99 accuracy in AUC (area under the curve, which showed a better performance than other model selection methods, respectively. These results demonstrate the power and utility of data mining technologies within the large-scale and ultra-high dimensional genomic-related dataset for diagnostic and predictive markers identifying.
Pak, Chan-gi; Lung, Shun-fat
2009-01-01
Modern airplane design is a multidisciplinary task which combines several disciplines such as structures, aerodynamics, flight controls, and sometimes heat transfer. Historically, analytical and experimental investigations concerning the interaction of the elastic airframe with aerodynamic and in retia loads have been conducted during the design phase to determine the existence of aeroelastic instabilities, so called flutter .With the advent and increased usage of flight control systems, there is also a likelihood of instabilities caused by the interaction of the flight control system and the aeroelastic response of the airplane, known as aeroservoelastic instabilities. An in -house code MPASES (Ref. 1), modified from PASES (Ref. 2), is a general purpose digital computer program for the analysis of the closed-loop stability problem. This program used subroutines given in the International Mathematical and Statistical Library (IMSL) (Ref. 3) to compute all of the real and/or complex conjugate pairs of eigenvalues of the Hessenberg matrix. For high fidelity configuration, these aeroelastic system matrices are large and compute all eigenvalues will be time consuming. A subspace iteration method (Ref. 4) for complex eigenvalues problems with nonsymmetric matrices has been formulated and incorporated into the modified program for aeroservoelastic stability (MPASES code). Subspace iteration method only solve for the lowest p eigenvalues and corresponding eigenvectors for aeroelastic and aeroservoelastic analysis. In general, the selection of p is ranging from 10 for wing flutter analysis to 50 for an entire aircraft flutter analysis. The application of this newly incorporated code is an experiment known as the Aerostructures Test Wing (ATW) which was designed by the National Aeronautic and Space Administration (NASA) Dryden Flight Research Center, Edwards, California to research aeroelastic instabilities. Specifically, this experiment was used to study an instability
Wang, G.L.; Chew, W.C.; Cui, T.J.; Aydiner, A.A.; Wright, D.L.; Smith, D.V.
2004-01-01
Three-dimensional (3D) subsurface imaging by using inversion of data obtained from the very early time electromagnetic system (VETEM) was discussed. The study was carried out by using the distorted Born iterative method to match the internal nonlinear property of the 3D inversion problem. The forward solver was based on the total-current formulation bi-conjugate gradient-fast Fourier transform (BCCG-FFT). It was found that the selection of regularization parameter follow a heuristic rule as used in the Levenberg-Marquardt algorithm so that the iteration is stable.
Woollands, Robyn M.; Read, Julie L.; Probe, Austin B.; Junkins, John L.
2017-07-01
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.
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.
Elsheikh, Ahmed H.
2013-06-01
We introduce a nonlinear orthogonal matching pursuit (NOMP) for sparse calibration of subsurface flow models. Sparse calibration is a challenging problem as the unknowns are both the non-zero components of the solution and their associated weights. NOMP is a greedy algorithm that discovers at each iteration the most correlated basis function with the residual from a large pool of basis functions. The discovered basis (aka support) is augmented across the nonlinear iterations. Once a set of basis functions are selected, the solution is obtained by applying Tikhonov regularization. The proposed algorithm relies on stochastically approximated gradient using an iterative stochastic ensemble method (ISEM). In the current study, the search space is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm. The proposed algorithm is the first ensemble based algorithm that tackels the sparse nonlinear parameter estimation problem. © 2013 Elsevier Ltd.
The iterative self-consistent reaction-field method: The refractive index of pure water
DEFF Research Database (Denmark)
Sylvester-Hvid, Kristian O.; Mikkelsen, K. V.; Ratner, M.A.
2011-01-01
We present different microscopic models for describing electromagnetic properties of condensed phases and the models involve iterative self-consistent procedures for calculating the properties. We report calculations of the frequency-dependent refractive index of pure water. We investigate...
De Lisle, Jerome; Seunarinesingh, Krishna; Mohammed, Rhoda; Lee-Piggott, Rinnelle
2017-01-01
In this study, methodology and theory were linked to explicate the nature of education practice within schools facing exceptionally challenging circumstances (SFECC) in Trinidad and Tobago. The research design was an iterative quan>QUAL-quan>qual multi-method research programme, consisting of 3 independent projects linked together by overall…
Nogry, S.; Jean-Daubias, S.; Guin, N.
2012-01-01
This article deals with evaluating an interactive learning environment (ILE) during the iterative-design process. Various aspects of the system must be assessed and a number of evaluation methods are available. In designing the ILE Ambre-add, several techniques were combined to test and refine the system. In particular, we point out the merits of…
DEFF Research Database (Denmark)
Miansari, Mo; Miansari, Me; Barari, Amin
2009-01-01
In this article, He’s variational iteration method (VIM), is implemented to solve the linear Helmholtz partial differential equation and some nonlinear fifth-order Korteweg-de Vries (FKdV) partial differential equations with specified initial conditions. The initial approximations can be freely...
Johnson, I. L., Jr.
1976-01-01
The Fletcher-Powell version of the Davidon variable metric unconstrained minimization technique is described. Equations that have been used successfully with the Davidon-Fletcher-Powell penalty function technique for solving constrained minimization problems and the advantages and disadvantages of using them are discussed. The experience gained in the behavior of the method while iterating is also related.
Energy Technology Data Exchange (ETDEWEB)
Mieville, Frederic A. [University Hospital Center and University of Lausanne, Institute of Radiation Physics, Lausanne (Switzerland); University Hospital Center and University of Lausanne, Institute of Radiation Physics - Medical Radiology, Lausanne (Switzerland); Gudinchet, Francois; Rizzo, Elena [University Hospital Center and University of Lausanne, Department of Radiology, Lausanne (Switzerland); Ou, Phalla; Brunelle, Francis [Necker Children' s Hospital, Department of Radiology, Paris (France); Bochud, Francois O.; Verdun, Francis R. [University Hospital Center and University of Lausanne, Institute of Radiation Physics, Lausanne (Switzerland)
2011-09-15
Radiation dose exposure is of particular concern in children due to the possible harmful effects of ionizing radiation. The adaptive statistical iterative reconstruction (ASIR) method is a promising new technique that reduces image noise and produces better overall image quality compared with routine-dose contrast-enhanced methods. To assess the benefits of ASIR on the diagnostic image quality in paediatric cardiac CT examinations. Four paediatric radiologists based at two major hospitals evaluated ten low-dose paediatric cardiac examinations (80 kVp, CTDI{sub vol} 4.8-7.9 mGy, DLP 37.1-178.9 mGy.cm). The average age of the cohort studied was 2.6 years (range 1 day to 7 years). Acquisitions were performed on a 64-MDCT scanner. All images were reconstructed at various ASIR percentages (0-100%). For each examination, radiologists scored 19 anatomical structures using the relative visual grading analysis method. To estimate the potential for dose reduction, acquisitions were also performed on a Catphan phantom and a paediatric phantom. The best image quality for all clinical images was obtained with 20% and 40% ASIR (p < 0.001) whereas with ASIR above 50%, image quality significantly decreased (p < 0.001). With 100% ASIR, a strong noise-free appearance of the structures reduced image conspicuity. A potential for dose reduction of about 36% is predicted for a 2- to 3-year-old child when using 40% ASIR rather than the standard filtered back-projection method. Reconstruction including 20% to 40% ASIR slightly improved the conspicuity of various paediatric cardiac structures in newborns and children with respect to conventional reconstruction (filtered back-projection) alone. (orig.)
Kassa, Semu Mitiku; Tsegay, Teklay Hailay
2017-08-01
Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.
Fake Review Detection From a Product Review Using Modified Method of Iterative Computation Framework
Directory of Open Access Journals (Sweden)
Wahyuni Eka Dyar
2016-01-01
Full Text Available The rapid growth of the Internet influenced many of our daily activities. One of the very rapid growth area is ecommerce. Generally e-commerce provide facility for customers to write reviews related with its service. The existence of these reviews can be used as a source of information. For examples, companies can use it to make design decisions of their products or services, while potential customers can use it to decide either to buy or to use a product. Unfortunately, the importance of the review is misused by certain parties who tried to create fake reviews, both aimed at raising the popularity or to discredit the product. This research aims to detect fake reviews for a product by using the text and rating property from a review. In short, the proposed system (ICF++ will measure the honesty value of a review, the trustiness value of the reviewers and the reliability value of a product. The honesty value of a review will be measured by utilizing the text mining and opinion mining techniques. The result from the experiment shows that the proposed system has a better accuracy compared with the result from iterative computation framework (ICF method.
e-Learning Application for Machine Maintenance Process using Iterative Method in XYZ Company
Nurunisa, Suaidah; Kurniawati, Amelia; Pramuditya Soesanto, Rayinda; Yunan Kurnia Septo Hediyanto, Umar
2016-02-01
XYZ Company is a company based on manufacturing part for airplane, one of the machine that is categorized as key facility in the company is Millac 5H6P. As a key facility, the machines should be assured to work well and in peak condition, therefore, maintenance process is needed periodically. From the data gathering, it is known that there are lack of competency from the maintenance staff to maintain different type of machine which is not assigned by the supervisor, this indicate that knowledge which possessed by maintenance staff are uneven. The purpose of this research is to create knowledge-based e-learning application as a realization from externalization process in knowledge transfer process to maintain the machine. The application feature are adjusted for maintenance purpose using e-learning framework for maintenance process, the content of the application support multimedia for learning purpose. QFD is used in this research to understand the needs from user. The application is built using moodle with iterative method for software development cycle and UML Diagram. The result from this research is e-learning application as sharing knowledge media for maintenance staff in the company. From the test, it is known that the application make maintenance staff easy to understand the competencies.
Miéville, Frédéric A.; Ayestaran, Paul; Argaud, Christophe; Rizzo, Elena; Ou, Phalla; Brunelle, Francis; Gudinchet, François; Bochud, François; Verdun, Francis R.
2010-04-01
Adaptive Statistical Iterative Reconstruction (ASIR) is a new imaging reconstruction technique recently introduced by General Electric (GE). This technique, when combined with a conventional filtered back-projection (FBP) approach, is able to improve the image noise reduction. To quantify the benefits provided on the image quality and the dose reduction by the ASIR method with respect to the pure FBP one, the standard deviation (SD), the modulation transfer function (MTF), the noise power spectrum (NPS), the image uniformity and the noise homogeneity were examined. Measurements were performed on a control quality phantom when varying the CT dose index (CTDIvol) and the reconstruction kernels. A 64-MDCT was employed and raw data were reconstructed with different percentages of ASIR on a CT console dedicated for ASIR reconstruction. Three radiologists also assessed a cardiac pediatric exam reconstructed with different ASIR percentages using the visual grading analysis (VGA) method. For the standard, soft and bone reconstruction kernels, the SD is reduced when the ASIR percentage increases up to 100% with a higher benefit for low CTDIvol. MTF medium frequencies were slightly enhanced and modifications of the NPS shape curve were observed. However for the pediatric cardiac CT exam, VGA scores indicate an upper limit of the ASIR benefit. 40% of ASIR was observed as the best trade-off between noise reduction and clinical realism of organ images. Using phantom results, 40% of ASIR corresponded to an estimated dose reduction of 30% under pediatric cardiac protocol conditions. In spite of this discrepancy between phantom and clinical results, the ASIR method is as an important option when considering the reduction of radiation dose, especially for pediatric patients.
A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems
Iglesias, Marco A.
2016-02-01
We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The general aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference to develop a derivative-free stable method easy to implement in applications where the PDE (forward) model is only accessible as a black box (e.g. with commercial software). The proposed regularizing ensemble Kalman method can be derived as an approximation of the regularizing Levenberg-Marquardt (LM) scheme (Hanke 1997 Inverse Problems 13 79-95) in which the derivative of the forward operator and its adjoint are replaced with empirical covariances from an ensemble of elements from the admissible space of solutions. The resulting ensemble method consists of an update formula that is applied to each ensemble member and that has a regularization parameter selected in a similar fashion to the one in the LM scheme. Moreover, an early termination of the scheme is proposed according to a discrepancy principle-type of criterion. The proposed method can be also viewed as a regularizing version of standard Kalman approaches which are often unstable unless ad hoc fixes, such as covariance localization, are implemented. The aim of this paper is to provide a detailed numerical investigation of the regularizing and convergence properties of the proposed regularizing ensemble Kalman scheme; the proof of these properties is an open problem. By means of numerical experiments, we investigate the conditions under which the proposed method inherits the regularizing properties of the LM scheme of (Hanke 1997 Inverse Problems 13 79-95) and is thus stable and suitable for its application in problems where the computation of the Fréchet derivative is not computationally feasible. More concretely, we study the effect of ensemble size, number of measurements, selection of initial ensemble and tunable parameters on the performance of the method
Furuichi, Mikito; Nishiura, Daisuke
2017-10-01
We developed dynamic load-balancing algorithms for Particle Simulation Methods (PSM) involving short-range interactions, such as Smoothed Particle Hydrodynamics (SPH), Moving Particle Semi-implicit method (MPS), and Discrete Element method (DEM). These are needed to handle billions of particles modeled in large distributed-memory computer systems. Our method utilizes flexible orthogonal domain decomposition, allowing the sub-domain boundaries in the column to be different for each row. The imbalances in the execution time between parallel logical processes are treated as a nonlinear residual. Load-balancing is achieved by minimizing the residual within the framework of an iterative nonlinear solver, combined with a multigrid technique in the local smoother. Our iterative method is suitable for adjusting the sub-domain frequently by monitoring the performance of each computational process because it is computationally cheaper in terms of communication and memory costs than non-iterative methods. Numerical tests demonstrated the ability of our approach to handle workload imbalances arising from a non-uniform particle distribution, differences in particle types, or heterogeneous computer architecture which was difficult with previously proposed methods. We analyzed the parallel efficiency and scalability of our method using Earth simulator and K-computer supercomputer systems.
Methodes iteratives paralleles: Applications en neutronique et en mecanique des fluides
Qaddouri, Abdessamad
Dans cette these, le calcul parallele est applique successivement a la neutronique et a la mecanique des fluides. Dans chacune de ces deux applications, des methodes iteratives sont utilisees pour resoudre le systeme d'equations algebriques resultant de la discretisation des equations du probleme physique. Dans le probleme de neutronique, le calcul des matrices des probabilites de collision (PC) ainsi qu'un schema iteratif multigroupe utilisant une methode inverse de puissance sont parallelises. Dans le probleme de mecanique des fluides, un code d'elements finis utilisant un algorithme iteratif du type GMRES preconditionne est parallelise. Cette these est presentee sous forme de six articles suivis d'une conclusion. Les cinq premiers articles traitent des applications en neutronique, articles qui representent l'evolution de notre travail dans ce domaine. Cette evolution passe par un calcul parallele des matrices des PC et un algorithme multigroupe parallele teste sur un probleme unidimensionnel (article 1), puis par deux algorithmes paralleles l'un mutiregion l'autre multigroupe, testes sur des problemes bidimensionnels (articles 2--3). Ces deux premieres etapes sont suivies par l'application de deux techniques d'acceleration, le rebalancement neutronique et la minimisation du residu aux deux algorithmes paralleles (article 4). Finalement, on a mis en oeuvre l'algorithme multigroupe et le calcul parallele des matrices des PC sur un code de production DRAGON ou les tests sont plus realistes et peuvent etre tridimensionnels (article 5). Le sixieme article (article 6), consacre a l'application a la mecanique des fluides, traite la parallelisation d'un code d'elements finis FES ou le partitionneur de graphe METIS et la librairie PSPARSLIB sont utilises.
Estimation of graphite dust production in ITER TBM using finite element method
Energy Technology Data Exchange (ETDEWEB)
Kang, Ji-Ho, E-mail: jhkang@kaeri.re.kr [Korea Atomic Energy Research Institute, 989-111, Daekeok-Daero, Yuseong-Gu, Daejeon 305-353 (Korea, Republic of); Kim, Eung Seon [Korea Atomic Energy Research Institute, 989-111, Daekeok-Daero, Yuseong-Gu, Daejeon 305-353 (Korea, Republic of); Ahn, Mu-Young; Lee, Youngmin; Park, Yi-Hyun; Cho, Seungyon [National Fusion Research Institute, 169-148, Gwahak-ro, Yuseong-gu, Daejeon (Korea, Republic of)
2015-12-15
Highlights: • Graphite dust production was estimated for the Korean Helium Cooled Ceramic Reflector. • Wear amount was calculated by Archard model using finite element analysis results. • Life time estimation of graphite dust production was done. - Abstract: In this study, an estimation method of graphite dust production in the pebble-bed type reflector region of the Korean Helium Cooled Ceramic Reflector (HCCR) Test Blanket Module (TBM) of the International Thermonuclear Experimental Reactor (ITER) project using Finite Element Method (FEM) was proposed and the total amount of dust production was calculated. A unit-cell model of uniformly arranged pebbles was defined with thermal and mechanical loadings. A commercial FEM program, Abaqus V6.10, was used to model and solve the stress field under multiple contact constraints between pebbles in the unit-cell. Resultant normal contact forces and slip distances on the contact points were applied into the Archard adhesive wear model to calculate the amount of graphite dust. The Finite Element (FE) analysis was repeated at 27 unit-cell locations chosen to form an interpolated dust density function for the entire region of the reflector. The dust production calculation was extended to the life time of the HCCR and the total graphite dust production was estimated to 0.279 g at the end of the life time with the maximum graphite dust density of 0.149 μg/mm{sup 3}. The dust explosion could be a safety issue with the calculated dust density level and it requires that an appropriate maintenance to remove sufficient amount of graphite dust regularly to prevent the possibility of dust explosion.
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Yi-Ju Chen
Full Text Available S-glutathionylation, the covalent attachment of a glutathione (GSH to the sulfur atom of cysteine, is a selective and reversible protein post-translational modification (PTM that regulates protein activity, localization, and stability. Despite its implication in the regulation of protein functions and cell signaling, the substrate specificity of cysteine S-glutathionylation remains unknown. Based on a total of 1783 experimentally identified S-glutathionylation sites from mouse macrophages, this work presents an informatics investigation on S-glutathionylation sites including structural factors such as the flanking amino acids composition and the accessible surface area (ASA. TwoSampleLogo presents that positively charged amino acids flanking the S-glutathionylated cysteine may influence the formation of S-glutathionylation in closed three-dimensional environment. A statistical method is further applied to iteratively detect the conserved substrate motifs with statistical significance. Support vector machine (SVM is then applied to generate predictive model considering the substrate motifs. According to five-fold cross-validation, the SVMs trained with substrate motifs could achieve an enhanced sensitivity, specificity, and accuracy, and provides a promising performance in an independent test set. The effectiveness of the proposed method is demonstrated by the correct identification of previously reported S-glutathionylation sites of mouse thioredoxin (TXN and human protein tyrosine phosphatase 1b (PTP1B. Finally, the constructed models are adopted to implement an effective web-based tool, named GSHSite (http://csb.cse.yzu.edu.tw/GSHSite/, for identifying uncharacterized GSH substrate sites on the protein sequences.
Sarwar, S.; Rashidi, M. M.
2016-07-01
This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.
Mabood, Fazle; Khan, Waqar A; Ismail, Ahmad Izani Md
2013-01-01
In this article, an approximate analytical solution of flow and heat transfer for a viscoelastic fluid in an axisymmetric channel with porous wall is presented. The solution is obtained through the use of a powerful method known as Optimal Homotopy Asymptotic Method (OHAM). We obtained the approximate analytical solution for dimensionless velocity and temperature for various parameters. The influence and effect of different parameters on dimensionless velocity, temperature, friction factor, and rate of heat transfer are presented graphically. We also compared our solution with those obtained by other methods and it is found that OHAM solution is better than the other methods considered. This shows that OHAM is reliable for use to solve strongly nonlinear problems in heat transfer phenomena.
Kordolaimi, Sofia D; Saradeas, Ioannis; Ploussi, Agapi; Pantos, Ioannis; Argentos, Stylianos; Efstathopoulos, Efstathios P
2014-10-01
The purpose of this study is to introduce an efficient method for the optimization of iterative reconstruction CT protocols based on phantom image analysis and the comparison of obtained results with actual patient data. We considered chest, abdomen, and pelvis CT examinations before the installation of an iterative reconstruction algorithm (iDose4) to define the exposure parameters used in clinical routine with filtered back projection (FBP). The body area of a CT phantom was subsequently scanned with various tube voltages and tube currents-exposure time products, and acquired data were reconstructed with FBP and different levels of iDose4. The contrast-to-noise ratio (CNR) for FBP with the original exposure parameters was calculated to define the minimum acceptable CNR value for each tube voltage. Then, an optimum tube current-exposure time products for each tube voltage and level of iterative reconstruction was estimated. We also compared findings derived by the phantom with real patient data by assessing dosimetric and image quality indexes from a patient cohort scanned with exposure parameters gradually adjusted during 1 year of adoption of iDose4. By use of the proposed phantom method, dose reduction up to 75% was achievable, whereas for an intermediate level of iteration (level 4), the dose reduction ranged between 50% and 60%, depending on the tube voltage. For comparison, with the gradual adjustment of exposure settings, the corresponding dose reduction for the same level of iteration was about 35%. The proposed method provides rapid and efficient optimization of CT protocols and could be used as the first step in the optimization process.
[Use of nonparametric methods in medicine. V. A probability test using iteration].
Gerylovová, A; Holcík, J
1990-10-01
The authors give an account of the so-called Wald-Wolfowitz test of iteration of two types of elements by means of which it is possible to test the probability of the pattern of two types of elements. To facilitate the application of the test five percent critical values are given for the number of iterations for left-sided, right-sided and bilateral alternative hypotheses. The authors present also tables of critical values for up and down iterations which are obtained when we replace the originally assessed sequence of observations by a sequence +1 and -1, depending on the sign of the consecutive differences. The application of the above tests is illustrated on examples.
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Birol İbiş
2014-12-01
Full Text Available The purpose of this paper was to obtain the analytical approximate solution of time-fractional Fornberg–Whitham, equation involving Jumarie’s modified Riemann–Liouville derivative by the fractional variational iteration method (FVIM. FVIM provides the solution in the form of a convergent series with easily calculable terms. The obtained approximate solutions are compared with the exact or existing numerical results in the literature to verify the applicability, efficiency and accuracy of the method.
Visser, Ruurd; Godart, J.; Wauben, D. J. L.; Langendijk, J. A.; van't Veld, A. A.; Korevaar, E. W.
2016-01-01
The objective of this study was to introduce a new iterative method to reconstruct multi leaf collimator (MLC) positions based on low resolution ionization detector array measurements and to evaluate its error detection performance. The iterative reconstruction method consists of a fluence model, a
Low dose dynamic CT myocardial perfusion imaging using a statistical iterative reconstruction method
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Tao, Yinghua [Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin 53705 (United States); Chen, Guang-Hong [Department of Medical Physics and Department of Radiology, University of Wisconsin-Madison, Madison, Wisconsin 53705 (United States); Hacker, Timothy A.; Raval, Amish N. [Department of Medicine, University of Wisconsin-Madison, Madison, Wisconsin 53792 (United States); Van Lysel, Michael S.; Speidel, Michael A., E-mail: speidel@wisc.edu [Department of Medical Physics and Department of Medicine, University of Wisconsin-Madison, Madison, Wisconsin 53705 (United States)
2014-07-15
Purpose: Dynamic CT myocardial perfusion imaging has the potential to provide both functional and anatomical information regarding coronary artery stenosis. However, radiation dose can be potentially high due to repeated scanning of the same region. The purpose of this study is to investigate the use of statistical iterative reconstruction to improve parametric maps of myocardial perfusion derived from a low tube current dynamic CT acquisition. Methods: Four pigs underwent high (500 mA) and low (25 mA) dose dynamic CT myocardial perfusion scans with and without coronary occlusion. To delineate the affected myocardial territory, an N-13 ammonia PET perfusion scan was performed for each animal in each occlusion state. Filtered backprojection (FBP) reconstruction was first applied to all CT data sets. Then, a statistical iterative reconstruction (SIR) method was applied to data sets acquired at low dose. Image voxel noise was matched between the low dose SIR and high dose FBP reconstructions. CT perfusion maps were compared among the low dose FBP, low dose SIR and high dose FBP reconstructions. Numerical simulations of a dynamic CT scan at high and low dose (20:1 ratio) were performed to quantitatively evaluate SIR and FBP performance in terms of flow map accuracy, precision, dose efficiency, and spatial resolution. Results: Forin vivo studies, the 500 mA FBP maps gave −88.4%, −96.0%, −76.7%, and −65.8% flow change in the occluded anterior region compared to the open-coronary scans (four animals). The percent changes in the 25 mA SIR maps were in good agreement, measuring −94.7%, −81.6%, −84.0%, and −72.2%. The 25 mA FBP maps gave unreliable flow measurements due to streaks caused by photon starvation (percent changes of +137.4%, +71.0%, −11.8%, and −3.5%). Agreement between 25 mA SIR and 500 mA FBP global flow was −9.7%, 8.8%, −3.1%, and 26.4%. The average variability of flow measurements in a nonoccluded region was 16.3%, 24.1%, and 937
Iterative Otsu's method for OCT improved delineation in the aorta wall
Alonso, Daniel; Real, Eusebio; Val-Bernal, José F.; Revuelta, José M.; Pontón, Alejandro; Calvo Díez, Marta; Mayorga, Marta; López-Higuera, José M.; Conde, Olga M.
2015-07-01
Degradation of human ascending thoracic aorta has been visualized with Optical Coherence Tomography (OCT). OCT images of the vessel wall exhibit structural degradation in the media layer of the artery, being this disorder the final trigger of the pathology. The degeneration in the vessel wall appears as low-reflectivity areas due to different optical properties of acidic polysaccharides and mucopolysaccharides in contrast with typical ordered structure of smooth muscle cells, elastin and collagen fibers. An OCT dimension indicator of wall degradation can be generated upon the spatial quantification of the extension of degraded areas in a similar way as conventional histopathology. This proposed OCT marker can offer in the future a real-time clinical perception of the vessel status to help cardiovascular surgeons in vessel repair interventions. However, the delineation of degraded areas on the B-scan image from OCT is sometimes difficult due to presence of speckle noise, variable signal to noise ratio (SNR) conditions on the measurement process, etc. Degraded areas can be delimited by basic thresholding techniques taking advantage of disorders evidences in B-scan images, but this delineation is not optimum in the aorta samples and requires complex additional processing stages. This work proposes an optimized delineation of degraded areas within the aorta wall, robust to noisy environments, based on the iterative application of Otsu's thresholding method. Results improve the delineation of wall anomalies compared with the simple application of the algorithm. Achievements could be also transferred to other clinical scenarios: carotid arteries, aorto-iliac or ilio-femoral sections, intracranial, etc.
On the generalized asymptotically nonspreading mappings in convex metric spaces
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Withun Phuengrattana
2017-04-01
Full Text Available In this article, we propose a new class of nonlinear mappings, namely, generalized asymptotically nonspreading mapping, and prove the existence of fixed points for such mapping in convex metric spaces. Furthermore, we also obtain the demiclosed principle and a delta-convergence theorem of Mann iteration for generalized asymptotically nonspreading mappings in CAT(0 spaces.
Iterative Learning Control with Forgetting Factor for Urban Road Network
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Tianyi Lan
2017-01-01
Full Text Available In order to improve the traffic condition, a novel iterative learning control (ILC algorithm with forgetting factor for urban road network is proposed by using the repeat characteristics of traffic flow in this paper. Rigorous analysis shows that the proposed ILC algorithm can guarantee the asymptotic convergence. Through iterative learning control of the traffic signals, the number of vehicles on each road in the network can gradually approach the desired level, thereby preventing oversaturation and traffic congestion. The introduced forgetting factor can effectively adjust the control input according to the states of the system and filter along the direction of the iteration. The results show that the forgetting factor has an important effect on the robustness of the system. The theoretical analysis and experimental simulations are given to verify the validity of the proposed method.
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Meister, H., E-mail: meister@ipp.mpg.de; Penzel, F.; Giannone, L.; Kannamueller, M.; Kling, A.; Koll, J.; Trautmann, T.
2011-10-15
In order to derive the local emission profile of the plasma radiation in a fusion device using the line-integrated measurements of the bolometer diagnostic, tomographic reconstruction methods have to be applied to the measurements from many lines-of-sight. A successful reconstruction needs to take the finite sizes of detectors and apertures and the resulting non-ideal measurements into account. In ITER a method for in situ measurement of the geometrical properties of the various components of the bolometer diagnostic after installation is required as the viewing cones have to pass through narrow gaps between components. The method proposed to be used for ITER uses the beam of a laser with high intensity to illuminate the bolometer assembly from many different angles {xi} and {theta}. A light-weight robot from Kuka Robotics is used to efficiently position the laser on many points covering the complete viewing cone of each line-of-sight and to direct the beam precisely into the entrance aperture of the bolometer. Measuring the response of the bolometer allows for the calculation of the transmission function t({xi}, {theta}), the angular etendue and finally the geometric function in reconstruction space, which is required for the tomography algorithms. Measuring the transmission function for a laboratory assembly demonstrates the viability of the proposed method. Results for a collimator-type camera from a prototype envisaged for ITER are presented. The implemented procedure is discussed in detail, in particular with respect to the automatisation applied which takes the achievable positioning and alignment accuracies of the robot into account. This discussion is extended towards the definition of requirements for a remote-handling tool for ITER.
Nonstandard asymptotic analysis
Berg, Imme
1987-01-01
This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the t...
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Jo, Yu Gwon; Oh, Yoo Min; Park, Hyang Kyu; Park, Kang Soon; Cho, Nam Zin [KAIST, Daejeon (Korea, Republic of)
2016-05-15
In this paper, two issues in the FSS iteration method, i.e., the waiting time for surface source data and the variance biases in local tallies are investigated for the domain decomposed, 3-D continuous-energy whole-core calculation. The fission sources are provided as usual, while the surface sources are provided by banking MC particles crossing local domain boundaries. The surface sources serve as boundary conditions for nonoverlapping local problems, so that each local problem can be solved independently. In this paper, two issues in the FSS iteration are investigated. One is quantifying the waiting time of processors to receive surface source data. By using nonblocking communication, 'time penalty' to wait for the arrival of the surface source data is reduced. The other important issue is underestimation of the sample variance of the tally because of additional inter-iteration correlations in surface sources. From the numerical results on a 3-D whole-core test problem, it is observed that the time penalty is negligible in the FSS iteration method and that the real variances of both pin powers and assembly powers are estimated by the HB method. For those purposes, three cases; Case 1 (1 local domain), Case 2 (4 local domains), Case 3 (16 local domains) are tested. For both Cases 2 and 3, the time penalties for waiting are negligible compared to the source-tracking times. However, for finer divisions of local domains, the loss of parallel efficiency caused by the different number of sources for local domains in symmetric locations becomes larger due to the stochastic errors in source distributions. For all test cases, the HB method very well estimates the real variances of local tallies. However, it is also noted that the real variances of local tallies estimated by the HB method show slightly smaller than the real variances obtained from 30 independent batch runs and the deviations become larger for finer divisions of local domains. The batch size used
Asymptotic Solutions of Serial Radial Fuel Shuffling
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Xue-Nong Chen
2015-12-01
Full Text Available In this paper, the mechanism of traveling wave reactors (TWRs is investigated from the mathematical physics point of view, in which a stationary fission wave is formed by radial fuel drifting. A two dimensional cylindrically symmetric core is considered and the fuel is assumed to drift radially according to a continuous fuel shuffling scheme. A one-group diffusion equation with burn-up dependent macroscopic coefficients is set up. The burn-up dependent macroscopic coefficients were assumed to be known as functions of neutron fluence. By introducing the effective multiplication factor keff, a nonlinear eigenvalue problem is formulated. The 1-D stationary cylindrical coordinate problem can be solved successively by analytical and numerical integrations for associated eigenvalues keff. Two representative 1-D examples are shown for inward and outward fuel drifting motions, respectively. The inward fuel drifting has a higher keff than the outward one. The 2-D eigenvalue problem has to be solved by a more complicated method, namely a pseudo time stepping iteration scheme. Its 2-D asymptotic solutions are obtained together with certain eigenvalues keff for several fuel inward drifting speeds. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor kinf and the normalized power are presented for two different drifting speeds.
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Junlin Shen
Full Text Available OBJECTIVES: To evaluate the clinical value of noise-based tube current reduction method with iterative reconstruction for obtaining consistent image quality with dose optimization in prospective electrocardiogram (ECG-triggered coronary CT angiography (CCTA. MATERIALS AND METHODS: We performed a prospective randomized study evaluating 338 patients undergoing CCTA with prospective ECG-triggering. Patients were randomly assigned to fixed tube current with filtered back projection (Group 1, n = 113, noise-based tube current with filtered back projection (Group 2, n = 109 or with iterative reconstruction (Group 3, n = 116. Tube voltage was fixed at 120 kV. Qualitative image quality was rated on a 5-point scale (1 = impaired, to 5 = excellent, with 3-5 defined as diagnostic. Image noise and signal intensity were measured; signal-to-noise ratio was calculated; radiation dose parameters were recorded. Statistical analyses included one-way analysis of variance, chi-square test, Kruskal-Wallis test and multivariable linear regression. RESULTS: Image noise was maintained at the target value of 35HU with small interquartile range for Group 2 (35.00-35.03HU and Group 3 (34.99-35.02HU, while from 28.73 to 37.87HU for Group 1. All images in the three groups were acceptable for diagnosis. A relative 20% and 51% reduction in effective dose for Group 2 (2.9 mSv and Group 3 (1.8 mSv were achieved compared with Group 1 (3.7 mSv. After adjustment for scan characteristics, iterative reconstruction was associated with 26% reduction in effective dose. CONCLUSION: Noise-based tube current reduction method with iterative reconstruction maintains image noise precisely at the desired level and achieves consistent image quality. Meanwhile, effective dose can be reduced by more than 50%.
El-Amin, Mohamed
2017-08-29
Purpose In this paper, we introduce modeling, numerical simulation, and convergence analysis of the problem nanoparticles transport carried by a two-phase flow in a porous medium. The model consists of equations of pressure, saturation, nanoparticles concentration, deposited nanoparticles concentration on the pore-walls, and entrapped nanoparticles concentration in pore-throats. Design/methodology/approach Nonlinear iterative IMPES-IMC (IMplicit Pressure Explicit Saturation–IMplicit Concentration) scheme is used to solve the problem under consideration. The governing equations are discretized using the cell-centered finite difference (CCFD) method. The pressure and saturation equations are coupled to calculate the pressure, then the saturation is updated explicitly. Therefore, the equations of nanoparticles concentration, the deposited nanoparticles concentration on the pore walls and the entrapped nanoparticles concentration in pore throats are computed implicitly. Then, the porosity and the permeability variations are updated. Findings We stated and proved three lemmas and one theorem for the convergence of the iterative method under the natural conditions and some continuity and boundedness assumptions. The theorem is proved by induction states that after a number of iterations the sequences of the dependent variables such as saturation and concentrations approach solutions on the next time step. Moreover, two numerical examples are introduced with convergence test in terms of Courant–Friedrichs–Lewy (CFL) condition and a relaxation factor. Dependent variables such as pressure, saturation, concentration, deposited concentrations, porosity and permeability are plotted as contours in graphs, while the error estimations are presented in table for different values of number of time steps, number of iterations and mesh size. Research limitations/implications The domain of the computations is relatively small however, it is straightforward to extend this method
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Joshua Kim
2013-01-01
Full Text Available Tetrahedron beam computed tomography (TBCT performs volumetric imaging using a stack of fan beams generated by a multiple pixel X-ray source. While the TBCT system was designed to overcome the scatter and detector issues faced by cone beam computed tomography (CBCT, it still suffers the same large cone angle artifacts as CBCT due to the use of approximate reconstruction algorithms. It has been shown that iterative reconstruction algorithms are better able to model irregular system geometries and that algebraic iterative algorithms in particular have been able to reduce cone artifacts appearing at large cone angles. In this paper, the SART algorithm is modified for the use with the different TBCT geometries and is tested using both simulated projection data and data acquired using the TBCT benchtop system. The modified SART reconstruction algorithms were able to mitigate the effects of using data generated at large cone angles and were also able to reconstruct CT images without the introduction of artifacts due to either the longitudinal or transverse truncation in the data sets. Algebraic iterative reconstruction can be especially useful for dual-source dual-detector TBCT, wherein the cone angle is the largest in the center of the field of view.
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Daniel Marcsa
2015-01-01
Full Text Available The analysis and design of electromechanical devices involve the solution of large sparse linear systems, and require therefore high performance algorithms. In this paper, the primal Domain Decomposition Method (DDM with parallel forward-backward and with parallel Preconditioned Conjugate Gradient (PCG solvers are introduced in two-dimensional parallel time-stepping finite element formulation to analyze rotating machine considering the electromagnetic field, external circuit and rotor movement. The proposed parallel direct and the iterative solver with two preconditioners are analyzed concerning its computational efficiency and number of iterations of the solver with different preconditioners. Simulation results of a rotating machine is also presented.
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Cedola, A.P., E-mail: ariel.cedola@ing.unlp.edu.a [Grupo de Estudio de Materiales y Dispositivos Electronicos (GEMyDE), Dpto. Electrotecnia, Facultad de Ingenieria, Universidad Nacional de La Plata, 48 y 116, C.C. 91, La Plata 1900, Buenos Aires (Argentina); Cappelletti, M.A. [Grupo de Estudio de Materiales y Dispositivos Electronicos (GEMyDE), Dpto. Electrotecnia, Facultad de Ingenieria, Universidad Nacional de La Plata, 48 y 116, C.C. 91, La Plata 1900, Buenos Aires (Argentina); Casas, G. [Grupo de Estudio de Materiales y Dispositivos Electronicos (GEMyDE), Dpto. Electrotecnia, Facultad de Ingenieria, Universidad Nacional de La Plata, 48 y 116, C.C. 91, La Plata 1900, Buenos Aires (Argentina); Universidad Nacional de Quilmes, Roque Saenz Pena 352, Bernal 1876, Buenos Aires (Argentina); Peltzer y Blanca, E.L. [Grupo de Estudio de Materiales y Dispositivos Electronicos (GEMyDE), Dpto. Electrotecnia, Facultad de Ingenieria, Universidad Nacional de La Plata, 48 y 116, C.C. 91, La Plata 1900, Buenos Aires (Argentina); Instituto de Fisica de Liquidos y Sistemas Biologicos (IFLYSIB), CONICET - UNLP - CIC, La Plata 1900, Buenos Aires (Argentina)
2011-02-11
An iterative method based on numerical simulations was developed to enhance the proton radiation tolerance and the responsivity of Si PIN photodiodes. The method allows to calculate the optimal values of the intrinsic layer thickness and the incident light wavelength, in function of the light intensity and the maximum proton fluence to be supported by the device. These results minimize the effects of radiation on the total reverse current of the photodiode and maximize its response to light. The implementation of the method is useful in the design of devices whose operation point should not suffer variations due to radiation.
Savage, M. J.
2017-04-01
An iterative method was applied to daily crop reference evaporation ETo. The method correctly evaluated the slope of the saturation water vapour pressure vs temperature relationship between surface temperature and air temperature. Using daily meterological data spanning several decades from four selected locations in Australia, South Africa and USA, differences in ETo estimates were noted with and without the iteration method applied. The largest difference, which occurred under high water vapour pressure deficit conditions, ranged from 1.65 mm/day for Griffith, Australia to 0.51 mm/day for Pretoria, South Africa. The aerodynamic component of the ETo equation was more affected by not applying the spreadsheet iterative procedure compared to the radiative component. Other spreadsheet examples of the iterative method employed included obtaining the roots of a depressed cubic polynomial in the air temperature surface renewal (SR) ramp. This value was used for the measurement of sensible heat flux using surface renewal. An iterative method, together with Monin-Obukhov similarity theory (MOST) and surface-layer scintillometer (SLS) measurements in a mesic grassland, was also used to calculate the sensible heat flux. The simple iterative method is quick, accurate and convenient, easy to repeat following changes to equations or data, allows easy manipulation and allows convenient visual inspection of data and graphics. Sub-hourly measurements of sensible heat flux for the mesic grassland using SR and SLS MOST iterative methods compared favourably with Bowen ratio and eddy covariance measurements.
Bechtle, P.; Desch, K.; Wienemann, P.
2006-01-01
Provided that Supersymmetry (SUSY) is realized, the Large Hadron Collider (LHC) and the future International Linear Collider (ILC) may provide a wealth of precise data from SUSY processes. An important task will be to extract the Lagrangian parameters. On this basis the goal is to uncover the underlying symmetry breaking mechanism from the measured observables. In order to determine the SUSY parameters, the program Fittino has been developed. It uses an iterative fitting technique and a Simulated Annealing algorithm to determine the SUSY parameters directly from the observables without any a priori knowledge of the parameters, using all available loop-corrections to masses and couplings. Simulated Annealing is implemented as a stable and efficient method for finding the optimal parameter values. The theoretical predictions can be provided from any program with SUSY Les Houches Accord interface. As fit result, a set of parameters including the full error matrix and two-dimensional uncertainty contours are obtained. Pull distributions can automatically be created and allow an independent cross-check of the fit results and possible systematic shifts in the parameter determination. A determination of the importance of the individual observables for the measurement of each parameter can be performed after the fit. A flexible user interface is implemented, allowing a wide range of different types of observables and a wide range of parameters to be used. Program summaryProgram title: Fittino Catalogue identifier: ADWN Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWN Licensing provisions: GNU General Public License Programming language:C++ Computer: any computer Operating system: Linux and other Unix flavors RAM: ca. 22 MB No. of lines in distributed program, including test data, etc.: 111 962 No. of bytes in distributed program, including test data, etc.: 1 006 727 Distribution format: tar.gz Number of processors used: 1 External routines: The ROOT data analysis
Xue, Haile; Shen, Xueshun; Chou, Jifan
2015-10-01
Errors inevitably exist in numerical weather prediction (NWP) due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model (model error, denoted as ME). In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System (GRAPES-GFS) for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature (SST) were both based on NCEP (National Centers for Environmental Prediction) FNL (final) data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.
A multiscale asymptotic analysis of time evolution equations on the complex plane
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Braga, Gastão A., E-mail: gbraga@mat.ufmg.br [Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30161-970 Belo Horizonte, MG (Brazil); Conti, William R. P., E-mail: wrpconti@gmail.com [Departamento de Ciências do Mar, Universidade Federal de São Paulo, Rua Dr. Carvalho de Mendonça 144, 11070-100 Santos, SP (Brazil)
2016-07-15
Using an appropriate norm on the space of entire functions, we extend to the complex plane the renormalization group method as developed by Bricmont et al. The method is based upon a multiscale approach that allows for a detailed description of the long time asymptotics of solutions to initial value problems. The time evolution equation considered here arises in the study of iterations of the block spin renormalization group transformation for the hierarchical N-vector model. We show that, for initial conditions belonging to a certain Fréchet space of entire functions of exponential type, the asymptotics is universal in the sense that it is dictated by the fixed point of a certain operator acting on the space of initial conditions.
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Raftery Adrian E
2009-02-01
-value = 0.00139. Conclusion The strength of the iterative BMA algorithm for survival analysis lies in its ability to account for model uncertainty. The results from this study demonstrate that our procedure selects a small number of genes while eclipsing other methods in predictive performance, making it a highly accurate and cost-effective prognostic tool in the clinical setting.
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Ackroyd, R.T. (Queen Mary Coll., London (UK). Dept. of Nuclear Engineering); Riyait, N.S. (Imperial Coll. of Science and Technology, London (UK). Nuclear Power Group)
1989-01-01
Conventional finite-element solutions of the even-parity transport equation for systems with voids treat the void as a region of low absorption. This treatment tends to give physically-unacceptable solutions to void problems as the void cross-section tends to zero. An explanation for the effect is proposed. Biased finite elements are used in two ways to obtain physically-acceptable solutions for the void regions. Two new methods are described and tested. The iterative method synthesizes finite-element solution using a sequence of problems with constant absorptions in the void regions. The sequence is terminated when the fluxes in the void regions become steady. The extrapolation method obtains a best approximation to the void solution by combining two or more independent biased trial functions in an optimum way. The extrapolation method is further subdivided into elementary and nodal or multiparameter extrapolation. The relevant theory of both the iteration and extrapolation methods is given. Several 2-D test problems using the above methods have been investigated. Results are compared with those obtained with other numerical methods and almost analytical results of the point kernel method for voids surrounded by purely absorbing media. (author).
Improving Convergence of Iterative Feedback Tuning using Optimal External Perturbations
DEFF Research Database (Denmark)
Huusom, Jakob Kjøbsted; Hjalmarsson, Håkon; Poulsen, Niels Kjølstad
2008-01-01
Iterative feedback tuning constitutes an attractive control loop tuning method for processes in the absence of sufficient process insight. It is a purely data driven approach to optimization of the loop performance. The standard formulation ensures an unbiased estimate of the loop performance cost...... function gradient, which is used in a search algorithm. A slow rate of convergence of the tuning method is often experienced when tuning for disturbance rejection. This is due to a poor signal to noise ratio in the process data. A method is proposed for increasing the information content in data...... by introducing an optimal perturbation signal in the tuning algorithm. For minimum variance control design the optimal design of an external perturbation signal is derived in terms of the asymptotic accuracy of the iterative feedback tuning method....
Wazwaz, Abdul-Majid
2017-07-01
In this work we address the Lane-Emden boundary value problems which appear in chemical applications, biochemical applications, and scientific disciplines. We apply the variational iteration method to solve two specific models. The first problem models reaction-diffusion equation in a spherical catalyst, while the second problem models the reaction-diffusion process in a spherical biocatalyst. We obtain reliable analytical expressions of the concentrations and the effectiveness factors. Proper graphs will be used to illustrate the obtained results. The proposed analysis demonstrates reliability and efficiency applicability of the employed method.
Directory of Open Access Journals (Sweden)
Shyam B. Dhage
2016-03-01
Full Text Available In this paper authors prove the existence as well as approximation of the positive solutions for a periodic boundary value problem of first order ordinary nonlinear quadratic differential equations with maxima. An algorithm for the solutions is developed and it is shown that certain sequence of successive approximations converges monotonically to the positive solution of considered quadratic differential equations under some suitable mixed hybrid conditions. Our results rely on the Dhage iteration principle embodied in a recent hybrid fixed point theorem of Dhage (2014. A numerical example is also provided to illustrate the hypotheses and abstract theory developed in this paper.
The Normalized-Rate Iterative Algorithm: A Practical Dynamic Spectrum Management Method for DSL
Directory of Open Access Journals (Sweden)
Statovci Driton
2006-01-01
Full Text Available We present a practical solution for dynamic spectrum management (DSM in digital subscriber line systems: the normalized-rate iterative algorithm (NRIA. Supported by a novel optimization problem formulation, the NRIA is the only DSM algorithm that jointly addresses spectrum balancing for frequency division duplexing systems and power allocation for the users sharing a common cable bundle. With a focus on being implementable rather than obtaining the highest possible theoretical performance, the NRIA is designed to efficiently solve the DSM optimization problem with the operators' business models in mind. This is achieved with the help of two types of parameters: the desired network asymmetry and the desired user priorities. The NRIA is a centralized DSM algorithm based on the iterative water-filling algorithm (IWFA for finding efficient power allocations, but extends the IWFA by finding the achievable bitrates and by optimizing the bandplan. It is compared with three other DSM proposals: the IWFA, the optimal spectrum balancing algorithm (OSBA, and the bidirectional IWFA (bi-IWFA. We show that the NRIA achieves better bitrate performance than the IWFA and the bi-IWFA. It can even achieve performance almost as good as the OSBA, but with dramatically lower requirements on complexity. Additionally, the NRIA can achieve bitrate combinations that cannot be supported by any other DSM algorithm.
Tian, Zhen; Jia, Xun; Jiang, Steve B
2013-01-01
In the treatment plan optimization for intensity modulated radiation therapy (IMRT), dose-deposition coefficient (DDC) matrix is often pre-computed to parameterize the dose contribution to each voxel in the volume of interest from each beamlet of unit intensity. However, due to the limitation of computer memory and the requirement on computational efficiency, in practice matrix elements of small values are usually truncated, which inevitably compromises the quality of the resulting plan. A fixed-point iteration scheme has been applied in IMRT optimization to solve this problem, which has been reported to be effective and efficient based on the observations of the numerical experiments. In this paper, we aim to point out the mathematics behind this scheme and to answer the following three questions: 1) whether the fixed-point iteration algorithm converges or not? 2) when it converges, whether the fixed point solution is same as the original solution obtained with the complete DDC matrix? 3) if not the same, wh...
Optimal asymptotic cloning machines
Chiribella, Giulio; Yang, Yuxiang
2014-06-01
We pose the question whether the asymptotic equivalence between quantum cloning and quantum state estimation, valid at the single-clone level, still holds when all clones are examined globally. We conjecture that the answer is affirmative and present a large amount of evidence supporting our conjecture, developing techniques to derive optimal asymptotic cloners and proving their equivalence with estimation in virtually all scenarios considered in the literature. Our analysis covers the case of arbitrary finite sets of states, arbitrary families of coherent states, arbitrary phase- and multiphase-covariant sets of states, and two-qubit maximally entangled states. In all these examples we observe that the optimal asymptotic cloners enjoy a universality property, consisting in the fact that scaling of their fidelity does not depend on the specific details of the input states, but only on the number of free parameters needed to specify them.
Chiba, Shuntaro; Ishida, Takashi; Ikeda, Kazuyoshi; Mochizuki, Masahiro; Teramoto, Reiji; Taguchi, Y-H; Iwadate, Mitsuo; Umeyama, Hideaki; Ramakrishnan, Chandrasekaran; Thangakani, A Mary; Velmurugan, D; Gromiha, M Michael; Okuno, Tatsuya; Kato, Koya; Minami, Shintaro; Chikenji, George; Suzuki, Shogo D; Yanagisawa, Keisuke; Shin, Woong-Hee; Kihara, Daisuke; Yamamoto, Kazuki Z; Moriwaki, Yoshitaka; Yasuo, Nobuaki; Yoshino, Ryunosuke; Zozulya, Sergey; Borysko, Petro; Stavniichuk, Roman; Honma, Teruki; Hirokawa, Takatsugu; Akiyama, Yutaka; Sekijima, Masakazu
2017-09-20
We propose a new iterative screening contest method to identify target protein inhibitors. After conducting a compound screening contest in 2014, we report results acquired from a contest held in 2015 in this study. Our aims were to identify target enzyme inhibitors and to benchmark a variety of computer-aided drug discovery methods under identical experimental conditions. In both contests, we employed the tyrosine-protein kinase Yes as an example target protein. Participating groups virtually screened possible inhibitors from a library containing 2.4 million compounds. Compounds were ranked based on functional scores obtained using their respective methods, and the top 181 compounds from each group were selected. Our results from the 2015 contest show an improved hit rate when compared to results from the 2014 contest. In addition, we have successfully identified a statistically-warranted method for identifying target inhibitors. Quantitative analysis of the most successful method gave additional insights into important characteristics of the method used.
Asymptotic prime partitions of integers
Bartel, Johann; Bhaduri, R. K.; Brack, Matthias; Murthy, M. V. N.
2017-05-01
In this paper, we discuss P (n ) , the number of ways a given integer n may be written as a sum of primes. In particular, an asymptotic form Pas(n ) valid for n →∞ is obtained analytically using standard techniques of quantum statistical mechanics. First, the bosonic partition function of primes, or the generating function of unrestricted prime partitions in number theory, is constructed. Next, the density of states is obtained using the saddle-point method for Laplace inversion of the partition function in the limit of large n . This gives directly the asymptotic number of prime partitions Pas(n ) . The leading term in the asymptotic expression grows exponentially as √{n /ln(n ) } and agrees with previous estimates. We calculate the next-to-leading-order term in the exponent, proportional to ln[ln(n )]/ln(n ) , and we show that an earlier result in the literature for its coefficient is incorrect. Furthermore, we also calculate the next higher-order correction, proportional to 1 /ln(n ) and given in Eq. (43), which so far has not been available in the literature. Finally, we compare our analytical results with the exact numerical values of P (n ) up to n ˜8 ×106 . For the highest values, the remaining error between the exact P (n ) and our Pas(n ) is only about half of that obtained with the leading-order approximation. But we also show that, unlike for other types of partitions, the asymptotic limit for the prime partitions is still quite far from being reached even for n ˜107 .
Bruder, H; Raupach, R; Sunnegardh, J; Allmendinger, T; Klotz, E; Stierstorfer, K; Flohr, T
2015-11-07
In CT imaging, a variety of applications exist which are strongly SNR limited. However, in some cases redundant data of the same body region provide additional quanta. Examples in dual energy CT, the spatial resolution has to be compromised to provide good SNR for material decomposition. However, the respective spectral dataset of the same body region provides additional quanta which might be utilized to improve SNR of each spectral component. Perfusion CT is a high dose application, and dose reduction is highly desirable. However, a meaningful evaluation of perfusion parameters might be impaired by noisy time frames. On the other hand, the SNR of the average of all time frames is extremely high.In redundant CT acquisitions, multiple image datasets can be reconstructed and averaged to composite image data. These composite image data, however, might be compromised with respect to contrast resolution and/or spatial resolution and/or temporal resolution. These observations bring us to the idea of transferring high SNR of composite image data to low SNR 'source' image data, while maintaining their resolution.It has been shown that the noise characteristics of CT image data can be improved by iterative reconstruction (Popescu et al 2012 Book of Abstracts, 2nd CT Meeting (Salt Lake City, UT) p 148). In case of data dependent Gaussian noise it can be modelled with image-based iterative reconstruction at least in an approximate manner (Bruder et al 2011 Proc. SPIE 7961 79610J). We present a generalized update equation in image space, consisting of a linear combination of the previous update, a correction term which is constrained by the source image data, and a regularization prior, which is initialized by the composite image data. This iterative reconstruction approach we call bimodal reconstruction (BMR). Based on simulation data it is shown that BMR can improve low contrast detectability, substantially reduces the noise power and has the potential to recover spatial
Energy Technology Data Exchange (ETDEWEB)
Dubina, Sean Hyun, E-mail: sdubin2@uic.edu; Wedgewood, Lewis Edward, E-mail: wedge@uic.edu [Department of Chemical Engineering, University of Illinois at Chicago, 810 S. Clinton St. (MC 110), Chicago, Illinois 60607-4408 (United States)
2016-07-15
Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.
Asymptotic freedom, asymptotic flatness and cosmology
Kiritsis, Elias
2013-01-01
Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free $\\beta$-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this class of models. The Starobinsky inflationary model as well as the recently proposed models of T-inflation are members of this class. The holographic setup gives a completely new (and contrasting) view to the stability and other problems of such inflationary models.
Library designs for generic C++ sparse matrix computations of iterative methods
Energy Technology Data Exchange (ETDEWEB)
Pozo, R.
1996-12-31
A new library design is presented for generic sparse matrix C++ objects for use in iterative algorithms and preconditioners. This design extends previous work on C++ numerical libraries by providing a framework in which efficient algorithms can be written *independent* of the matrix layout or format. That is, rather than supporting different codes for each (element type) / (matrix format) combination, only one version of the algorithm need be maintained. This not only reduces the effort for library developers, but also simplifies the calling interface seen by library users. Furthermore, the underlying matrix library can be naturally extended to support user-defined objects, such as hierarchical block-structured matrices, or application-specific preconditioners. Utilizing optimized kernels whenever possible, the resulting performance of such framework can be shown to be competitive with optimized Fortran programs.
Directory of Open Access Journals (Sweden)
Phayap Katchang
2010-01-01
Full Text Available The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusions with set-valued maximal monotone mappings and inverse-strongly monotone mappings, and the set of fixed points of a family of finitely nonexpansive mappings in the setting of Hilbert spaces. We propose a new iterative scheme for finding the common element of the above three sets. Our results improve and extend the corresponding results of the works by Zhang et al. (2008, Peng et al. (2008, Peng and Yao (2009, as well as Plubtieng and Sriprad (2009 and some well-known results in the literature.
An iterative learning control method with application for CNC machine tools
Energy Technology Data Exchange (ETDEWEB)
Kim, D.I.; Kim, S. [Samsung Electronics, Suwon (Korea, Republic of)
1996-01-01
A proportional, integral, and derivative (PID) type iterative learning controller is proposed for precise tracking control of industrial robots and computer numerical controller (CNC) machine tools performing repetitive tasks. The convergence of the output error by the proposed learning controller is guaranteed under a certain condition even when the system parameters are not known exactly and unknown external disturbances exist. As the proposed learning controller is repeatedly applied to the industrial robot or the CNC machine tool with the path-dependent repetitive task, the distance difference between the desired path and the actual tracked or machined path, which is one of the most significant factors in the evaluation of control performance, is progressively reduced. The experimental results demonstrate that the proposed learning controller can improve machining accuracy when the CNC machine tool performs repetitive machining tasks.
Bhaskaran-Nair, Kiran; Brabec, Jiří; Aprà, Edoardo; van Dam, Hubertus J J; Pittner, Jiří; Kowalski, Karol
2012-09-07
In this paper we discuss the performance of the non-iterative state-specific multireference coupled cluster (SS-MRCC) methods accounting for the effect of triply excited cluster amplitudes. The corrections to the Brillouin-Wigner and Mukherjee's MRCC models based on the manifold of singly and doubly excited cluster amplitudes (BW-MRCCSD and Mk-MRCCSD, respectively) are tested and compared with exact full configuration interaction results for small systems (H(2)O, N(2), and Be(3)). For the larger systems (naphthyne isomers) the BW-MRCC and Mk-MRCC methods with iterative singles, doubles, and non-iterative triples (BW-MRCCSD(T) and Mk-MRCCSD(T)) are compared against the results obtained with single reference coupled cluster methods. We also report on the parallel performance of the non-iterative implementations based on the use of processor groups.
Energy Technology Data Exchange (ETDEWEB)
Zayed, Elsayed M.E. [Dept. of Mathematics, Zagazig Univ. (Egypt); Abdel Rahman, Hanan M. [Dept. of Basic Sciences, Higher Technological Inst., Tenth of Ramadan City (Egypt)
2010-01-15
In this article, two powerful analytical methods called the variational iteration method (VIM) and the variational homotopy perturbation method (VHPM) are introduced to obtain the exact and the numerical solutions of the (2+1)-dimensional Korteweg-de Vries-Burgers (KdVB) equation and the (1+1)-dimensional Sharma-Tasso-Olver equation. The main objective of the present article is to propose alternative methods of solutions, which avoid linearization and physical unrealistic assumptions. The results show that these methods are very efficient, convenient and can be applied to a large class of nonlinear problems. (orig.)
Subber, Waad; Sarkar, Abhijit
2014-01-01
Recent advances in high performance computing systems and sensing technologies motivate computational simulations with extremely high resolution models with capabilities to quantify uncertainties for credible numerical predictions. A two-level domain decomposition method is reported in this investigation to devise a linear solver for the large-scale system in the Galerkin spectral stochastic finite element method (SSFEM). In particular, a two-level scalable preconditioner is introduced in order to iteratively solve the large-scale linear system in the intrusive SSFEM using an iterative substructuring based domain decomposition solver. The implementation of the algorithm involves solving a local problem on each subdomain that constructs the local part of the preconditioner and a coarse problem that propagates information globally among the subdomains. The numerical and parallel scalabilities of the two-level preconditioner are contrasted with the previously developed one-level preconditioner for two-dimensional flow through porous media and elasticity problems with spatially varying non-Gaussian material properties. A distributed implementation of the parallel algorithm is carried out using MPI and PETSc parallel libraries. The scalabilities of the algorithm are investigated in a Linux cluster.
Directory of Open Access Journals (Sweden)
Louis H. Kauffman
2017-07-01
Full Text Available We give an exposition of iterant algebra, a generalization of matrix algebra that is motivated by the structure of measurement for discrete processes. We show how Clifford algebras and matrix algebras arise naturally from iterants, and we then use this point of view to discuss the Schrödinger and Dirac equations, Majorana Fermions, representations of the braid group and the framed braids in relation to the structure of the Standard Model for physics.
Hubeny, I.; Lanz, T.
1995-01-01
A new munerical method for computing non-Local Thermodynamic Equilibrium (non-LTE) model stellar atmospheres is presented. The method, called the hybird complete linearization/accelerated lambda iretation (CL/ALI) method, combines advantages of both its constituents. Its rate of convergence is virtually as high as for the standard CL method, while the computer time per iteration is almost as low as for the standard ALI method. The method is formulated as the standard complete lineariation, the only difference being that the radiation intensity at selected frequency points is not explicity linearized; instead, it is treated by means of the ALI approach. The scheme offers a wide spectrum of options, ranging from the full CL to the full ALI method. We deonstrate that the method works optimally if the majority of frequency points are treated in the ALI mode, while the radiation intensity at a few (typically two to 30) frequency points is explicity linearized. We show how this method can be applied to calculate metal line-blanketed non-LTE model atmospheres, by using the idea of 'superlevels' and 'superlines' introduced originally by Anderson (1989). We calculate several illustrative models taking into accont several tens of thosands of lines of Fe III to Fe IV and show that the hybrid CL/ALI method provides a robust method for calculating non-LTE line-blanketed model atmospheres for a wide range of stellar parameters. The results for individual stellar types will be presented in subsequent papers in this series.
Asymptotic stability of a catalyst particle
DEFF Research Database (Denmark)
Wedel, Stig; Michelsen, Michael L.; Villadsen, John
1977-01-01
The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0. These a......The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0...
Energy Technology Data Exchange (ETDEWEB)
Reitz, Irmtraud; Hesse, Bernd-Michael; Nill, Simeon; Tuecking, Thomas; Oelfke, Uwe [DKFZ, Heidelberg (Germany)
2009-07-01
The problem of the enormous amount of scattered radiation in kV CBCT (kilo voltage cone beam computer tomography) is addressed. Scatter causes undesirable streak- and cup-artifacts and results in a quantitative inaccuracy of reconstructed CT numbers, so that an accurate dose calculation might be impossible. Image contrast is also significantly reduced. Therefore we checked whether an appropriate implementation of the fast iterative scatter correction algorithm we have developed for MV (mega voltage) CBCT reduces the scatter contribution in a kV CBCT as well. This scatter correction method is based on a superposition of pre-calculated Monte Carlo generated pencil beam scatter kernels. The algorithm requires only a system calibration by measuring homogeneous slab phantoms with known water-equivalent thicknesses. In this study we compare scatter corrected CBCT images of several phantoms to the fan beam CT images acquired with a reduced cone angle (a slice-thickness of 14 mm in the isocenter) at the same system. Additional measurements at a different CBCT system were made (different energy spectrum and phantom-to-detector distance) and a first order approach of a fast beam hardening correction will be introduced. The observed, image quality of the scatter corrected CBCT images is comparable concerning resolution, noise and contrast-to-noise ratio to the images acquired in fan beam geometry. Compared to the CBCT without any corrections the contrast of the contrast-and-resolution phantom with scatter correction and additional beam hardening correction is improved by a factor of about 1.5. The reconstructed attenuation coefficients and the CT numbers of the scatter corrected CBCT images are close to the values of the images acquired in fan beam geometry for the most pronounced tissue types. Only for extreme dense tissue types like cortical bone we see a difference in CT numbers of 5.2%, which can be improved to 4.4% with the additional beam hardening correction. Cupping
Reitz, Irmtraud; Hesse, Bernd-Michael; Nill, Simeon; Tücking, Thomas; Oelfke, Uwe
2009-01-01
The problem of the enormous amount of scattered radiation in kV CBCT (kilo voltage cone beam computer tomography) is addressed. Scatter causes undesirable streak- and cup-artifacts and results in a quantitative inaccuracy of reconstructed CT numbers, so that an accurate dose calculation might be impossible. Image contrast is also significantly reduced. Therefore we checked whether an appropriate implementation of the fast iterative scatter correction algorithm we have developed for MV (mega voltage) CBCT reduces the scatter contribution in a kV CBCT as well. This scatter correction method is based on a superposition of pre-calculated Monte Carlo generated pencil beam scatter kernels. The algorithm requires only a system calibration by measuring homogeneous slab phantoms with known water-equivalent thicknesses. In this study we compare scatter corrected CBCT images of several phantoms to the fan beam CT images acquired with a reduced cone angle (a slice-thickness of 14 mm in the isocenter) at the same system. Additional measurements at a different CBCT system were made (different energy spectrum and phantom-to-detector distance) and a first order approach of a fast beam hardening correction will be introduced. The observed image quality of the scatter corrected CBCT images is comparable concerning resolution, noise and contrast-to-noise ratio to the images acquired in fan beam geometry. Compared to the CBCT without any corrections the contrast of the contrast-and-resolution phantom with scatter correction and additional beam hardening correction is improved by a factor of about 1.5. The reconstructed attenuation coefficients and the CT numbers of the scatter corrected CBCT images are close to the values of the images acquired in fan beam geometry for the most pronounced tissue types. Only for extreme dense tissue types like cortical bone we see a difference in CT numbers of 5.2%, which can be improved to 4.4% with the additional beam hardening correction. Cupping is
Scheven, U. M.; Harris, R.; Johns, M. L.
2008-12-01
The experimental characterization of voidspaces in porous media generally includes measurements of volume averaged scalar properties such as porosity, dispersivity, or the hydrodynamic radius rh = V/S, where V and S are the volume and surface area of the pore space respectively. Displacement encoding NMR experiments have made significant contributions to this characterization. It is clear, however, that NMR derived dispersivities in packed beds—the one random porous system for which there exist canonical but incompatible theoretical predictions with few or no adjustable parameters—can be affected by the same experimental complications which have substantially contributed to the puzzling scatter in published dispersion results based on elution experiments. Notable among these are macroscopic flow heterogeneities near walls, and inhomogeneous flow injection. Using the first three cumulants we delineate a transition from a pre-asymptotic to a quasi-asymptotic dispersion regime and determine the true dispersivity of the random pack of spheres.
Singh, Randhir; Das, Nilima; Kumar, Jitendra
2017-06-01
An effective analytical technique is proposed for the solution of the Lane-Emden equations. The proposed technique is based on the variational iteration method (VIM) and the convergence control parameter h . In order to avoid solving a sequence of nonlinear algebraic or complicated integrals for the derivation of unknown constant, the boundary conditions are used before designing the recursive scheme for solution. The series solutions are found which converges rapidly to the exact solution. Convergence analysis and error bounds are discussed. Accuracy, applicability of the method is examined by solving three singular problems: i) nonlinear Poisson-Boltzmann equation, ii) distribution of heat sources in the human head, iii) second-kind Lane-Emden equation.
Application of Gauss's law space-charge limited emission model in iterative particle tracking method
Energy Technology Data Exchange (ETDEWEB)
Altsybeyev, V.V., E-mail: v.altsybeev@spbu.ru; Ponomarev, V.A.
2016-11-01
The particle tracking method with a so-called gun iteration for modeling the space charge is discussed in the following paper. We suggest to apply the emission model based on the Gauss's law for the calculation of the space charge limited current density distribution using considered method. Based on the presented emission model we have developed a numerical algorithm for this calculations. This approach allows us to perform accurate and low time consumpting numerical simulations for different vacuum sources with the curved emitting surfaces and also in the presence of additional physical effects such as bipolar flows and backscattered electrons. The results of the simulations of the cylindrical diode and diode with elliptical emitter with the use of axysimmetric coordinates are presented. The high efficiency and accuracy of the suggested approach are confirmed by the obtained results and comparisons with the analytical solutions.
A new non-iterative reconstruction method for the electrical impedance tomography problem
Ferreira, A. D.; Novotny, A. A.
2017-03-01
The electrical impedance tomography (EIT) problem consists in determining the distribution of the electrical conductivity of a medium subject to a set of current fluxes, from measurements of the corresponding electrical potentials on its boundary. EIT is probably the most studied inverse problem since the fundamental works by Calderón from the 1980s. It has many relevant applications in medicine (detection of tumors), geophysics (localization of mineral deposits) and engineering (detection of corrosion in structures). In this work, we are interested in reconstructing a number of anomalies with different electrical conductivity from the background. Since the EIT problem is written in the form of an overdetermined boundary value problem, the idea is to rewrite it as a topology optimization problem. In particular, a shape functional measuring the misfit between the boundary measurements and the electrical potentials obtained from the model is minimized with respect to a set of ball-shaped anomalies by using the concept of topological derivatives. It means that the objective functional is expanded and then truncated up to the second order term, leading to a quadratic and strictly convex form with respect to the parameters under consideration. Thus, a trivial optimization step leads to a non-iterative second order reconstruction algorithm. As a result, the reconstruction process becomes very robust with respect to noisy data and independent of any initial guess. Finally, in order to show the effectiveness of the devised reconstruction algorithm, some numerical experiments into two spatial dimensions are presented, taking into account total and partial boundary measurements.
Energy Technology Data Exchange (ETDEWEB)
Litim, Daniel F. [Department of Physics and Astronomy, University of Sussex,Falmer Campus, Brighton, BN1 9QH (United Kingdom); Sannino, Francesco [CP-Origins & the Danish Institute for Advanced Study Danish IAS, University of Southern Denmark,Campusvej 55, DK-5230 Odense (Denmark)
2014-12-31
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.
DEFF Research Database (Denmark)
Litim, Daniel F.; Sannino, Francesco
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet...... fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed....
Yu, Lifeng; Fletcher, Joel G.; Shiung, Maria; Thomas, Kristen B.; Matsumoto, Jane M.; Zingula, Shannon N.; McCollough, Cynthia H.
2016-01-01
OBJECTIVE The objective of this study was to evaluate the radiation dose reduction potential of a novel image-based denoising technique in pediatric abdominopelvic and chest CT examinations and compare it with a commercial iterative reconstruction method. MATERIALS AND METHODS Data were retrospectively collected from 50 (25 abdominopelvic and 25 chest) clinically indicated pediatric CT examinations. For each examination, a validated noise-insertion tool was used to simulate half-dose data, which were reconstructed using filtered back-projection (FBP) and sinogram-affirmed iterative reconstruction (SAFIRE) methods. A newly developed denoising technique, adaptive nonlocal means (aNLM), was also applied. For each of the 50 patients, three pediatric radiologists evaluated four datasets: full dose plus FBP, half dose plus FBP, half dose plus SAFIRE, and half dose plus aNLM. For each examination, the order of preference for the four datasets was ranked. The organ-specific diagnosis and diagnostic confidence for five primary organs were recorded. RESULTS The mean (± SD) volume CT dose index for the full-dose scan was 5.3 ± 2.1 mGy for abdominopelvic examinations and 2.4 ± 1.1 mGy for chest examinations. For abdominopelvic examinations, there was no statistically significant difference between the half dose plus aNLM dataset and the full dose plus FBP dataset (3.6 ± 1.0 vs 3.6 ± 0.9, respectively; p = 0.52), and aNLM performed better than SAFIRE. For chest examinations, there was no statistically significant difference between the half dose plus SAFIRE and the full dose plus FBP (4.1 ± 0.6 vs 4.2 ± 0.6, respectively; p = 0.67), and SAFIRE performed better than aNLM. For all organs, there was more than 85% agreement in organ-specific diagnosis among the three half-dose configurations and the full dose plus FBP configuration. CONCLUSION Although a novel image-based denoising technique performed better than a commercial iterative reconstruction method in pediatric
Zhang, Bin; Zeng, Gengsheng L
2006-11-21
Spherically symmetric volume elements (blobs) have better resolution-noise performance than voxels because of the overlapping of their rotational symmetric basis functions; however, using blobs is more computationally expensive than using voxels due to blob overlap. In this paper, we propose an immediate after-backprojection filtering method (ABF) with blob-shaped window functions for a voxel-based reconstruction. We compared this method with the general voxel-based method (without filtering), the blob-based method, the voxel-based method with between-iteration filtering (BIF) and with post-filtering (POF), using computer simulations. Both the quality of the reconstruction and the computational cost were evaluated. The reconstruction quality was measured by the contrast recovery coefficient (CRC) versus the background noise. It is shown that images reconstructed using this method are characterized by less image noise and preserved image contrast in comparison with both the general voxel-based method and the voxel-based method with BIF. The improvement in image quality achieved by this method varies with the parameters chosen for the Kaiser-Bessel (KB) windows. As with blobs, wider KB windows achieve better contrast-noise trade-offs in the reconstructed images, but are more computationally expensive. When using a KB window of a = 2.0, alpha = 10.4 and m = 2, known as the basis function of a 'standard' blob, this new method achieves identical CRC-noise features to the blob-based method with 'standard' blobs. In addition, the ABF method can be combined with the post-filtering method to achieve better noise-resolution performance than the general voxel-based post-filtering method. The computational cost of the ABF method is slightly greater than that of the general voxel-based method, but much less than that of the blob-based method.
Kourakos, G.; Harter, T.
2012-12-01
Groundwater contamination in semi-arid agricultural regions is increasing around the globe. Communities in such areas typically rely on groundwater resources for domestic and irrigation uses. Intensive farming practices are a significant source of groundwater contamination, which affects communities via well pumping and ecosystems via groundwater return flow to streams. Agricultural contamination or diffuse pollution is generally difficult to simulate due to large amount of sources and the large number of distributed wells, requiring high resolution flow and transport simulations. Individual contributing sources are on the order of few hectare to a few tens of hectare, while many of the larger agricultural groundwater basins encompass hundreds to thousands of square kilometers. Classical 3D transport modeling approaches are intractable across such scales with the current computing power. In this study we develop an efficient, highly parallelizable transport method known as streamline transport simulation. The approach decomposes a multi-dimensional problem into multiple one-dimensional subproblems which are trivial to solve. The streamline modeling requires a highly detailed 3D velocity field. The simulation of highly detailed groundwater flow in large agricultural basin is achieved by developing a substructuring iterative domain decomposition method or Complement Schur method for obtaining the velocity field. For unconfined aquifers, we illustrate that it is critical to use a moving mesh such that finite element adapts according to the head field. We therefore combined an iterative moving mesh approach with the Complement Schur domain decomposition method. The importance of using the moving mesh approach is illustrated with a hypothetical example and with an application to a real case study in the southern Central Valley, California.
Strong convergence of modified Ishikawa iterations for nonlinear ...
Indian Academy of Sciences (India)
(1.3) where PK denotes the metric projection from H onto a closed convex subset K of H and proved that sequence {xn} converges strongly to PF (T )x0. Recently, Kim and Xu [13] has adapted the iteration (1.1) in a Hilbert space. More precisely, they introduced the following iteration process for asymptotically nonexpansive.
Yu, Lifeng; Fletcher, Joel G; Shiung, Maria; Thomas, Kristen B; Matsumoto, Jane M; Zingula, Shannon N; McCollough, Cynthia H
2015-11-01
The objective of this study was to evaluate the radiation dose reduction potential of a novel image-based denoising technique in pediatric abdominopelvic and chest CT examinations and compare it with a commercial iterative reconstruction method. Data were retrospectively collected from 50 (25 abdominopelvic and 25 chest) clinically indicated pediatric CT examinations. For each examination, a validated noise-insertion tool was used to simulate half-dose data, which were reconstructed using filtered back-projection (FBP) and sinogram-affirmed iterative reconstruction (SAFIRE) methods. A newly developed denoising technique, adaptive nonlocal means (aNLM), was also applied. For each of the 50 patients, three pediatric radiologists evaluated four datasets: full dose plus FBP, half dose plus FBP, half dose plus SAFIRE, and half dose plus aNLM. For each examination, the order of preference for the four datasets was ranked. The organ-specific diagnosis and diagnostic confidence for five primary organs were recorded. The mean (± SD) volume CT dose index for the full-dose scan was 5.3 ± 2.1 mGy for abdominopelvic examinations and 2.4 ± 1.1 mGy for chest examinations. For abdominopelvic examinations, there was no statistically significant difference between the half dose plus aNLM dataset and the full dose plus FBP dataset (3.6 ± 1.0 vs 3.6 ± 0.9, respectively; p = 0.52), and aNLM performed better than SAFIRE. For chest examinations, there was no statistically significant difference between the half dose plus SAFIRE and the full dose plus FBP (4.1 ± 0.6 vs 4.2 ± 0.6, respectively; p = 0.67), and SAFIRE performed better than aNLM. For all organs, there was more than 85% agreement in organ-specific diagnosis among the three half-dose configurations and the full dose plus FBP configuration. Although a novel image-based denoising technique performed better than a commercial iterative reconstruction method in pediatric abdominopelvic CT examinations, it performed worse in
Three New Optimal Fourth-Order Iterative Methods to Solve Nonlinear Equations
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Gustavo Fernández-Torres
2013-01-01
Full Text Available We present new modifications to Newton's method for solving nonlinear equations. The analysis of convergence shows that these methods have fourth-order convergence. Each of the three methods uses three functional evaluations. Thus, according to Kung-Traub's conjecture, these are optimal methods. With the previous ideas, we extend the analysis to functions with multiple roots. Several numerical examples are given to illustrate that the presented methods have better performance compared with Newton's classical method and other methods of fourth-order convergence recently published.
Directory of Open Access Journals (Sweden)
Akira Maebatake
2016-07-01
Full Text Available Objective(s: The aim of this study was to determine the optimal reconstruction parameters for iterative reconstruction in different devices and collimators for dopamine transporter (DaT single-photon emission computed tomography (SPECT. The results were compared between filtered back projection (FBP and different attenuation correction (AC methods.Methods: An anthropomorphic striatal phantom was filled with 123I solutions at different striatum-to-background radioactivity ratios. Data were acquired using two SPECT/CT devices, equipped with a low-to-medium-energy general-purpose collimator (cameras A-1 and B-1 and a low-energy high-resolution (LEHR collimator (cameras A-2 and B-2.The SPECT images were once reconstructed by FBP using Chang’s AC and once by ordered subset expectation maximization (OSEM using both CTAC and Chang’s AC; moreover, scatter correction was performed. OSEM on cameras A-1 and A-2 included resolution recovery (RR. The images were analyzed, using the specific binding ratio (SBR. Regions of interest for the background were placed on both frontal and occipital regions.Results: The optimal number of iterations and subsets was 10i10s on camera A-1, 10i5s on camera A-2, and 7i6s on cameras B-1 and B-2. The optimal full width at half maximum of the Gaussian filter was 2.5 times the pixel size. In the comparison between FBP and OSEM, the quality was superior on OSEM-reconstructed images, although edge artifacts were observed in cameras A-1 and A-2. The SBR recovery of OSEM was higher than that of FBP on cameras A-1 and A-2, while no significant difference was detected on cameras B-1 and B-2. Good linearity of SBR was observed in all cameras. Inthe comparison between Chang’s AC and CTAC, a significant correlation was observed on all cameras. The difference in the background region influenced SBR differently in Chang’s AC and CTAC on cameras A-1 and B-1.Conclusion: Iterative reconstruction improved image quality on all cameras
Comparative Analysis of Software Development Methods between Parallel, V-Shaped and Iterative
Nugroho, Suryanto; Waluyo, Sigit Hadi; Hakim, Luqman
2017-01-01
Any organization that will develop software is faced with a difficult choice of choosing the right software development method. Whereas the software development methods used, play a significant role in the overall software development process. Software development methods are needed so that the software development process can be systematic so that it is not only completed within the right time frame but also must have good quality. There are various methods of software development in System ...
ASYMPTOTICS OF a PARTICLES TRANSPORT PROBLEM
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Kuzmina Ludmila Ivanovna
2017-11-01
Full Text Available Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck in the pores. It is assumed that size distributions of the solid particles and the pores overlap. In this case, the main mechanism of particle retention is a size-exclusion: the particles pass freely through the large pores and get stuck at the inlet of the tiny pores that are smaller than the particle diameter. The concentrations of suspended and retained particles satisfy two quasi-linear differential equations of the first order. To solve the filtration problem, methods of nonlinear asymptotic analysis are used. Results: in a mathematical model of filtration of suspensions, which takes into account the dependence of the porosity and permeability of the porous medium on concentration of retained particles, the boundary between two phases is moving with variable velocity. The asymptotic solution to the problem is constructed for a small filtration coefficient. The theorem of existence of the asymptotics is proved. Analytical expressions for the principal asymptotic terms are presented for the case of linear coefficients and initial conditions. The asymptotics of the boundary of two phases is given in explicit form. Conclusions: the filtration problem under study can be solved analytically.
Energy Technology Data Exchange (ETDEWEB)
Pérez, Germán, E-mail: german.perez.pichel@gmail.com; Mitteau, Raphaël; Eaton, Russell; Raffray, René
2015-12-15
Highlights: • Bonding defects at the ITER first wall beryllium armour are studied. • Experimental and analytical methods are combined. • Models supporting test results interpretation are proposed. • Guidelines for new experimental protocols are suggested. • Contribution to the definition of defects acceptance criteria. - Abstract: The reliability of the plasma facing components (PFCs) is essential for the efficient plasma operation in a fusion machine. This concerns especially the bond between the armour tiles facing the plasma and the heat sink material (copper alloy). The different thermal expansions of the bonded materials cause a stress distribution in the bond, which peaks at the bond edge. Under cyclic heat flux and accounting for the possible presence of bonding defects, this stress could reach a level where the component might be jeopardised. Because of the complexity of describing realistically by analyses and models the stress evolution in the bond, “design by experiments” is the main procedure for defining and qualifying the armour joint. Most of the existing plasma operation know-how on actively cooled PFCs has been obtained with carbon composite armour tiles. In ITER, the tiles of the first wall are made out of beryllium, which means that the know-how is progressively adapted to this specific bimetallic pair. Nonetheless, analyses are still performed for supporting the R&D experimental programme. This paper: explores methods for combining experimental results with finite element and statistical analyses; benchmarks test results; proposes hypothesis and rationales consistent with test results interpretations; suggests guidelines for defining possible further experimental protocols; and contributes to the definition of defects acceptance criteria.
Term structure extrapolation and asymptotic forward rates
de Kort, J.; Vellekoop, M.H.
2015-01-01
We investigate different inter- and extrapolation methods for term structures under different constraints in order to generate market-consistent estimates which describe the asymptotic behavior of forward rates. Our starting point is the method proposed by Smith and Wilson, which is used by the
Directory of Open Access Journals (Sweden)
Banan Maayah
2014-01-01
Full Text Available A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillator’s models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of convergence for the series solution. The numerical results demonstrate the validity and the applicability of the new technique. A very good agreement was found between the results obtained using the presented algorithm and the Runge-Kutta method, which shows that the multistep reproducing kernel Hilbert space method is very efficient and convenient for solving nonlinear oscillator’s models.
Iteratively reweighted generalized rank annihilation method 1. Improved handling of prediction bias
Faber, N.M.; Ferre, J.; Boque, R.
2001-01-01
The generalized rank annihilation method (GRAM) is a method for curve resolution and calibration that uses two bilinear matrices simultaneously, i.e., one for the unknown and one for the calibration sample. A GRAM calculation amounts to solving an eigenvalue problem for which the eigenvalues are
Asymptotically flat multiblack lenses
Tomizawa, Shinya; Okuda, Taika
2017-03-01
We present an asymptotically flat and stationary multiblack lens solution with biaxisymmetry of U (1 )×U (1 ) as a supersymmetric solution in the five-dimensional minimal ungauged supergravity. We show that the spatial cross section of each degenerate Killing horizon admits different lens space topologies of L (n ,1 )=S3/Zn as well as a sphere S3. Moreover, we show that, in contrast to the higher-dimensional Majumdar-Papapetrou multiblack hole and multi-Breckenridge-Myers-Peet-Vafa (BMPV) black hole spacetime, the metric is smooth on each horizon even if the horizon topology is spherical.
Asymptotic structures of cardinals
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Oleksandr Petrenko
2014-07-01
Full Text Available A ballean is a set X endowed with some family F of its subsets, called the balls, in such a way that (X,F can be considered as an asymptotic counterpart of a uniform topological space. Given a cardinal k, we define F using a natural order structure on k. We characterize balleans up to coarse equivalence, give the criterions of metrizability and cellularity, calculate the basic cardinal invariant of these balleans. We conclude the paper with discussion of some special ultrafilters on cardinal balleans.
Ho, Pei-Ming
2017-04-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
Energy Technology Data Exchange (ETDEWEB)
Bhaskaran-Nair, Kiran; Brabec, Jiri; Apra, Edoardo; van Dam, Hubertus JJ; Pittner, Jiri; Kowalski, Karol
2012-09-07
In this paper we discuss the performance of the non-iterative State-Specific Mul- tireference Coupled Cluster (SS-MRCC) methods accounting for the effect of triply excited cluster amplitudes. The corrections to the Brillouin-Wigner and Mukherjee MRCC models based on the manifold of singly and doubly excited cluster amplitudes (BW-MRCCSD and Mk-MRCCSD, respectively) are tested and compared with the exact full configuration interaction results (FCI) for small systems (H2O, N2, and Be3). For larger systems (naphthyne isomers and -carotene), the non-iterative BW-MRCCSD(T) and Mk-MRCCSD(T) methods are compared against the results obtained with the single reference coupled cluster methods. We also report on the parallel performance of the non-iterative implementations based on the use of pro- cessor groups.
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Chi-Chang Wang
2013-09-01
Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.
Frenod, Emmanuel
2013-01-01
In this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods; H-Measure-Based Numerical Methods; Two-Scale Numerical Methods and TSAPS: Two-Scale Asymptotic Preserving Schemes.
An Iterative Method for Estimating Airfoil Deformation due to Solid Particle Erosion
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Valeriu DRAGAN
2014-04-01
Full Text Available Helicopter blades are currently constructed with composite materials enveloping honeycomb cores with only the leading and trailing edges made of metal alloys. In some cases, the erosive wear of the bound between the composite skin and metallic leading edge leads to full blade failure. It is therefore the goal of this paper to provide a method for simulating the way an airfoil is deformed through the erosion process. The method involves computational fluid dynamics simulations, scripts for automatic meshing and spreadsheet calculators for estimating the erosion and, ultimately, the airfoil deformation. Further work could include more complex meshing scripts allowing the use of similar methods for turbo-machineries.
Solving Nondifferentiable Nonlinear Equations by New Steffensen-Type Iterative Methods with Memory
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J. P. Jaiswal
2014-01-01
Full Text Available It is attempted to present two derivative-free Steffensen-type methods with memory for solving nonlinear equations. By making use of a suitable self-accelerator parameter in the existing optimal fourth- and eighth-order without memory methods, the order of convergence has been increased without any extra function evaluation. Therefore, its efficiency index is also increased, which is the main contribution of this paper. The self-accelerator parameters are estimated using Newton’s interpolation. To show applicability of the proposed methods, some numerical illustrations are presented.
Stability analysis of a partitioned iterative method for steady free surface flow
Demeester, Toon; Degroote, Joris; Vierendeels, Jan
2018-02-01
This note considers the steady free surface (FS) flow problem as encountered in the paper by van Brummelen et al. [1]. In that paper, steady flow of water in a two-dimensional slice of an infinitely wide open channel with a particular bottom wall is calculated as the first step in the development of a 3D surface fitting method for steady flow around ships. In these water-air flows, the influence of air is usually negligible due to the large difference in density. Contrary to surface capturing methods which are typically multiphase techniques (such as the volume-of-fluid method), fitting methods usually consider only the water phase. The latter approach requires appropriate FS boundary conditions. The dynamic boundary condition (DBC) used here assumes that the pressure is constant (atmospheric) at the FS and the shear stresses are zero. The kinematic boundary condition (KBC) states that the FS is impermeable.
Inverse Free Iterative Methods for Nonlinear Ill-Posed Operator Equations
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Ioannis K. Argyros
2014-01-01
ill-posed operator equation F(x=y. The proposed method is a modified form of Tikhonov gradient (TIGRA method considered by Ramlau (2003. The regularization parameter is chosen according to the balancing principle considered by Pereverzev and Schock (2005. The error estimate is derived under a general source condition and is of optimal order. Some numerical examples involving integral equations are also given in this paper.
Visser, R; Godart, J; Wauben, D J L; Langendijk, J A; Van't Veld, A A; Korevaar, E W
2016-05-21
The objective of this study was to introduce a new iterative method to reconstruct multi leaf collimator (MLC) positions based on low resolution ionization detector array measurements and to evaluate its error detection performance. The iterative reconstruction method consists of a fluence model, a detector model and an optimizer. Expected detector response was calculated using a radiotherapy treatment plan in combination with the fluence model and detector model. MLC leaf positions were reconstructed by minimizing differences between expected and measured detector response. The iterative reconstruction method was evaluated for an Elekta SLi with 10.0 mm MLC leafs in combination with the COMPASS system and the MatriXX Evolution (IBA Dosimetry) detector with a spacing of 7.62 mm. The detector was positioned in such a way that each leaf pair of the MLC was aligned with one row of ionization chambers. Known leaf displacements were introduced in various field geometries ranging from -10.0 mm to 10.0 mm. Error detection performance was tested for MLC leaf position dependency relative to the detector position, gantry angle dependency, monitor unit dependency, and for ten clinical intensity modulated radiotherapy (IMRT) treatment beams. For one clinical head and neck IMRT treatment beam, influence of the iterative reconstruction method on existing 3D dose reconstruction artifacts was evaluated. The described iterative reconstruction method was capable of individual MLC leaf position reconstruction with millimeter accuracy, independent of the relative detector position within the range of clinically applied MU's for IMRT. Dose reconstruction artifacts in a clinical IMRT treatment beam were considerably reduced as compared to the current dose verification procedure. The iterative reconstruction method allows high accuracy 3D dose verification by including actual MLC leaf positions reconstructed from low resolution 2D measurements.
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Vasyl Chekurin
2017-01-01
Full Text Available The mathematical model for describing combined conductive-radiative heat transfer in a dielectric layer, which emits, absorbs, and scatters IR radiation both in its volume and on the boundary, has been considered. A nonlinear stationary boundary-value problem for coupled heat and radiation transfer equations for the layer, which exchanges by energy with external medium by convection and radiation, has been formulated. In the case of optically thick layer, when its thickness is much more of photon-free path, the problem becomes a singularly perturbed one. In the inverse case of optically thin layer, the problem is regularly perturbed, and it becomes a regular (unperturbed one, when the layer’s thickness is of order of several photon-free paths. An iterative method for solving of the unperturbed problem has been developed and its convergence has been tested numerically. With the use of the method, the temperature field and radiation fluxes have been studied. The model and method can be used for development of noncontact methods for temperature testing in dielectrics and for nondestructive determination of its radiation properties on the base of the data obtained by remote measuring of IR radiation emitted by the layer.
Energy Technology Data Exchange (ETDEWEB)
Vandewalle, S. [Caltech, Pasadena, CA (United States)
1994-12-31
Time-stepping methods for parabolic partial differential equations are essentially sequential. This prohibits the use of massively parallel computers unless the problem on each time-level is very large. This observation has led to the development of algorithms that operate on more than one time-level simultaneously; that is to say, on grids extending in space and in time. The so-called parabolic multigrid methods solve the time-dependent parabolic PDE as if it were a stationary PDE discretized on a space-time grid. The author has investigated the use of multigrid waveform relaxation, an algorithm developed by Lubich and Ostermann. The algorithm is based on a multigrid acceleration of waveform relaxation, a highly concurrent technique for solving large systems of ordinary differential equations. Another method of this class is the time-parallel multigrid method. This method was developed by Hackbusch and was recently subject of further study by Horton. It extends the elliptic multigrid idea to the set of equations that is derived by discretizing a parabolic problem in space and in time.
Vorst, H.A. van der; Ye, Q.
1999-01-01
In this paper, a strategy is proposed for alternative computations of the residual vectors in Krylov subspace methods, which improves the agreement of the computed residuals and the true residuals to the level of O(u)kAkkxk. Building on earlier ideas on residual replacement and on insights in
Büsing, Henrik
2014-05-01
The geological sequestration of CO2 is considered as one option to mitigate anthropogenic effects on climate change. To describe the behavior of CO2 underground we consider mass balance equations for the two phases, CO2 and brine, which include the dissolution of CO2 into the brine phase and of H2O into the gas phase (c.f. [1]). After discretization in time with the implicit Euler method and in space with the Box method (c.f. [2]), we end up with a nonlinear system of equations. Newton's method is used to solve these systems, where the required Jacobians are obtained by automatic differentiation (AD) (c.f. [3]). In contrast to approximate Jacobians via finite differences, AD gives exact Jacobians through a source code transformation. These exact Jacobians have the advantage that no additional errors are introduced by the derivative computation. In consequence, fewer Newton iterations are needed and a performance increase during derivative computation can be observed (c.f. [4]). During the initial stage of a CO2 sequestration scenario the movement of the CO2 plume is driven by advective and buoyancy forces. After injection is finished solubility and density driven flow become dominant. We examine the performance of different iterative solvers and preconditioners for these two stages. To this end, we consider standard ILU preconditioning with BiCGStab as iterative solver, as well as GMRES, and algebraic and geometric multigrid methods. Our test example considers, on the one hand, a homogeneous permeability distribution and, on the other hand, a heterogeneous one. In the latter case we sample a heterogeneous porosity field from a Gaussian distribution and, subsequently, derive the corresponding permeabilities after [5]. Finally, we examine to which extent the amount of dissolved CO2 depends on the heterogeneities in the reservoir. References [1] Spycher, N., Pruess, K., & Ennis-King, J., 2003. CO2-H2O mixtures in the geological sequestration of CO2. I. Assessment and
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
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Mohamed Mostafa R.
2016-01-01
Full Text Available Self-Excited Permanent Magnet Induction Generator (PMIG is commonly used in wind energy generation systems. The difficulty of Self-Excited Permanent Magnet Induction Generator (SEPMIG modeling is the circuit parameters of the generator vary at each load conditions due to the a change in the frequency and stator voltage. The paper introduces a new modeling for SEPMIG using Gauss-sidle relaxation method. The SEPMIG characteristics using the proposed method are studied at different load conditions according to the wind speed variation, load impedance changes and different shunted capacitor values. The system modeling is investigated due to the magnetizing current variation, the efficiency variation, the power variation and power factor variation. The proposed modeling system satisfies high degree of simplicity and accuracy.
Zhang, Songchuan; Xia, Youshen
2018-01-01
Much research has been devoted to complex-variable optimization problems due to their engineering applications. However, the complex-valued optimization method for solving complex-variable optimization problems is still an active research area. This paper proposes two efficient complex-valued optimization methods for solving constrained nonlinear optimization problems of real functions in complex variables, respectively. One solves the complex-valued nonlinear programming problem with linear equality constraints. Another solves the complex-valued nonlinear programming problem with both linear equality constraints and an -norm constraint. Theoretically, we prove the global convergence of the proposed two complex-valued optimization algorithms under mild conditions. The proposed two algorithms can solve the complex-valued optimization problem completely in the complex domain and significantly extend existing complex-valued optimization algorithms. Numerical results further show that the proposed two algorithms have a faster speed than several conventional real-valued optimization algorithms.
Nonlinear microwave imaging using Levenberg-Marquardt method with iterative shrinkage thresholding
Desmal, Abdulla
2014-07-01
Development of microwave imaging methods applicable in sparse investigation domains is becoming a research focus in computational electromagnetics (D.W. Winters and S.C. Hagness, IEEE Trans. Antennas Propag., 58(1), 145-154, 2010). This is simply due to the fact that sparse/sparsified domains naturally exist in many applications including remote sensing, medical imaging, crack detection, hydrocarbon reservoir exploration, and see-through-the-wall imaging.
Iterative Reconstruction Methods to Reduce Respiratory Motion Artifacts in Cartesian Coronary MRI
Forman, Christoph
2017-01-01
Cardiovascular diseases and coronary artery disease (CAD) in particular are the leading cause of death in most developed countries worldwide. Although CAD progresses slowly over several years, it often remains unnoticed and may lead to myocardial infarction in a sudden event. For this reason, there is a strong clinical need for the development of non-invasive and radiation-free screening methods allowing for an early diagnosis of these diseases. In this context, magnetic resonance imaging (MR...
Iterative methods for solving Ax=b, GMRES/FOM versus QMR/BiCG
Energy Technology Data Exchange (ETDEWEB)
Cullum, J. [IBM Research Division, Yorktown Heights, NY (United States)
1996-12-31
We study the convergence of GMRES/FOM and QMR/BiCG methods for solving nonsymmetric Ax=b. We prove that given the results of a BiCG computation on Ax=b, we can obtain a matrix B with the same eigenvalues as A and a vector c such that the residual norms generated by a FOM computation on Bx=c are identical to those generated by the BiCG computations. Using a unitary equivalence for each of these methods, we obtain test problems where we can easily vary certain spectral properties of the matrices. We use these test problems to study the effects of nonnormality on the convergence of GMRES and QMR, to study the effects of eigenvalue outliers on the convergence of QMR, and to compare the convergence of restarted GMRES, QMR, and BiCGSTAB across a family of normal and nonnormal problems. Our GMRES tests on nonnormal test matrices indicate that nonnormality can have unexpected effects upon the residual norm convergence, giving misleading indications of superior convergence over QMR when the error norms for GMRES are not significantly different from those for QMR. Our QMR tests indicate that the convergence of the QMR residual and error norms is influenced predominantly by small and large eigenvalue outliers and by the character, real, complex, or nearly real, of the outliers and the other eigenvalues. In our comparison tests QMR outperformed GMRES(10) and GMRES(20) on both the normal and nonnormal test matrices.
Numerical algorithms for uniform Airy-type asymptotic expansions
N.M. Temme (Nico)
1997-01-01
textabstractAiry-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
Sachdev, PL
2010-01-01
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/boundary conditions. This title presents the constructive mathematical techniques. It deals with the asymptotic methods which include self-similarity, balancing argument, and matched asymptotic expansions
How to co-add images? I. A new iterative method for image reconstruction of dithered observations
Wang, Lei; Li, Guo-Liang
2017-09-01
By employing the previous Voronoi approach and replacing its nearest neighbor approximation with Drizzle in iterative signal extraction, we develop a fast iterative Drizzle algorithm, named fiDrizzle, to reconstruct the underlying band-limited image from undersampled dithered frames. Compared with the existing iDrizzle, the new algorithm improves rate of convergence and accelerates the computational speed. Moreover, under the same conditions (e.g. the same number of dithers and iterations), fiDrizzle can make a better quality reconstruction than iDrizzle, due to the newly discovered High Sampling caused Decelerating Convergence (HSDC) effect in the iterative signal extraction process. fiDrizzle demonstrates its powerful ability to perform image deconvolution from undersampled dithers.
Energy Technology Data Exchange (ETDEWEB)
Gwynllyw, D.Rh.; Phillips, T.N. [Univ. of Wales, Aberystwyth (United Kingdom)
1994-12-31
The journal bearing is an essential part of all internal combustion engines as a means of transferring the energy from the piston rods to the rotating crankshaft. It consists essentially of an inner cylinder (the journal), which is part of the crankshaft, and an outer cylinder (the bearing), which is at the end of the piston rod. In general, the two cylinders are eccentric and there is a lubricating film of oil separating the two surfaces. The addition of polymers to mineral (Newtonian) oils to minimize the variation of viscosity with temperature has the added effect of introducing strain-dependent viscosity and elasticity. The physical problem has many complicating features which need to be modelled. It is a fully three-dimensional problem which means that significant computational effort is required to solve the problem numerically. The system is subject to dynamic loading in which the journal is allowed to move under the forces the fluid imparts on it and also any other loads such as that imparted by the engine force. The centre of the journal traces out a nontrivial locus in space. In addition, there is significant deformation of the bearing and journal and extensive cavitation of the oil lubricant. In the present study the authors restrict themselves to the two-dimensional statically loaded problem. In previous work a single domain spectral method was used which employed a bipolar coordinate transformation to map the region between the journal and the bearing onto a rectangle. The flow variables were then approximated on this rectangle using Fourier-Chebyshev expansions. However, to allow for future possible deformation of the journal and bearing surfaces due to increased load in the dynamically loaded case they have decided to use a more versatile spectral element formulation.
Miéville, Frédéric A; Gudinchet, François; Rizzo, Elena; Ou, Phalla; Brunelle, Francis; Bochud, François O; Verdun, Francis R
2011-09-01
Radiation dose exposure is of particular concern in children due to the possible harmful effects of ionizing radiation. The adaptive statistical iterative reconstruction (ASIR) method is a promising new technique that reduces image noise and produces better overall image quality compared with routine-dose contrast-enhanced methods. To assess the benefits of ASIR on the diagnostic image quality in paediatric cardiac CT examinations. Four paediatric radiologists based at two major hospitals evaluated ten low-dose paediatric cardiac examinations (80 kVp, CTDI(vol) 4.8-7.9 mGy, DLP 37.1-178.9 mGy·cm). The average age of the cohort studied was 2.6 years (range 1 day to 7 years). Acquisitions were performed on a 64-MDCT scanner. All images were reconstructed at various ASIR percentages (0-100%). For each examination, radiologists scored 19 anatomical structures using the relative visual grading analysis method. To estimate the potential for dose reduction, acquisitions were also performed on a Catphan phantom and a paediatric phantom. The best image quality for all clinical images was obtained with 20% and 40% ASIR (p ASIR above 50%, image quality significantly decreased (p ASIR, a strong noise-free appearance of the structures reduced image conspicuity. A potential for dose reduction of about 36% is predicted for a 2- to 3-year-old child when using 40% ASIR rather than the standard filtered back-projection method. Reconstruction including 20% to 40% ASIR slightly improved the conspicuity of various paediatric cardiac structures in newborns and children with respect to conventional reconstruction (filtered back-projection) alone.
Asymptotic independence for unimodal densities
Balkema, G.; Nolde, N.
2010-01-01
Asymptotic independence of the components of random vectors is a concept used in many applications. The standard criteria for checking asymptotic independence are given in terms of distribution functions (DFs). DFs are rarely available in an explicit form, especially in the multivariate case. Often
Asymptotic Safety, Fractals, and Cosmology
Reuter, Martin; Saueressig, Frank
These lecture notes introduce the basic ideas of the asymptotic safety approach to quantum Einstein gravity (QEG). In particular they provide the background for recent work on the possibly multi-fractal structure of the QEG space-times. Implications of asymptotic safety for the cosmology of the early Universe are also discussed.
Essentially asymptotically stable homoclinic networks
Driesse, R.; Homburg, A.J.
2009-01-01
Melbourne [An example of a nonasymptotically stable attractor, Nonlinearity 4(3) (1991), pp. 835-844] discusses an example of a robust heteroclinic network that is not asymptotically stable but which has the strong attracting property called essential asymptotic stability. We establish that this
Directory of Open Access Journals (Sweden)
Tongchun Li
2015-01-01
element is proposed to solve the safety factor of local discontinuous rock mass. Slope system is divided into several continuous bodies and local discontinuous interface boundaries. Each block is treated as a partition of the system and contacted by discontinuous joints. The displacements of blocks are chosen as basic variables and the rigid displacements in the centroid of blocks are chosen as motion variables. The contact forces on interface boundaries and the rigid displacements to the centroid of each body are chosen as mixed variables and solved iteratively using the interface boundary equations. Flexibility matrix is formed through PFE according to the contact states of nodal pairs and spring flexibility is used to reflect the influence of weak structural plane so that nonlinear iteration is only limited to the possible contact region. With cohesion and friction coefficient reduced gradually, the states of all nodal pairs at the open or slip state for the first time are regarded as failure criterion, which can decrease the effect of subjectivity in determining safety factor. Examples are used to verify the validity of the proposed method.
Asymptotic theory of weakly dependent random processes
Rio, Emmanuel
2017-01-01
Presenting tools to aid understanding of asymptotic theory and weakly dependent processes, this book is devoted to inequalities and limit theorems for sequences of random variables that are strongly mixing in the sense of Rosenblatt, or absolutely regular. The first chapter introduces covariance inequalities under strong mixing or absolute regularity. These covariance inequalities are applied in Chapters 2, 3 and 4 to moment inequalities, rates of convergence in the strong law, and central limit theorems. Chapter 5 concerns coupling. In Chapter 6 new deviation inequalities and new moment inequalities for partial sums via the coupling lemmas of Chapter 5 are derived and applied to the bounded law of the iterated logarithm. Chapters 7 and 8 deal with the theory of empirical processes under weak dependence. Lastly, Chapter 9 describes links between ergodicity, return times and rates of mixing in the case of irreducible Markov chains. Each chapter ends with a set of exercises. The book is an updated and extended ...
Barua, Gautam; Patidar, M. K.
2017-03-01
An iterative procedure is worked out for estimating solute travel times in a subsurface system by making use of the velocity and streamline distributions pertinent to the system. The developed method is then being applied to study the solute travel times to ditch drains originating from a field being subjected to a uniform (1) recharge and (2) ponding field over the surface of the soil. For case (1), both single and layered soils are being considered to estimate the travel times. The developed mathematical procedure is simple to use, robust, reasonably accurate even if being used with a lesser division of a streamline and completely eliminates the necessity of determination of any integrals for estimating the travel times—integrals which, in the methods generally been employed for estimating the travel times from steady-state analytical groundwater models, would otherwise need be evaluated. The study shows that travel times of water particles traversing through a layered soil being subjected to a uniform recharge at the surface are sensitive to the directional conductivities, anisotropy ratio (defined here as the ratio between horizontal and vertical hydraulic conductivities of soil) and thickness of individual layers of a soil profile as well as to the magnitude of the steady-state recharge on the surface of the soil. For the ponded drainage scenarios also, directional conductivities and thickness of a soil profile, extent of partial penetration and width of the ditch drains, levels of water head at the surface of the soil as well as on the ditches are observed to influence the travel times in a noticeable way. The proposed method is important as it provides simple and accurate estimations of migration times of pollutants to subsurface drains under different drainage situations; it can also be used to assess the time of reclamation of a salt-affected or waterlogged soil being drained by a network of subsurface drains being installed for the purpose from the
Directory of Open Access Journals (Sweden)
Safa Bozkurt Coşkun
2007-01-01
Full Text Available In order to enhance heat transfer between primary surface and the environment, radiating extended surfaces are commonly utilized. Especially in the case of large temperature differences, variable thermal conductivity has a strong effect on performance of such a surface. In this paper, variational iteration method is used to analyze convective straight and radial fins with temperature-dependent thermal conductivity. In order to show the efficiency of variational iteration method (VIM, the results obtained from VIM analysis are compared with previously obtained results using Adomian decomposition method (ADM and the results from finite element analysis. VIM produces analytical expressions for the solution of nonlinear differential equations. However, these expressions obtained from VIM must be tested with respect to the results obtained from a reliable numerical method or analytical solution. This work assures that VIM is a promising method for the analysis of convective straight and radial fin problems.
AbouEisha, Hassan M.
2016-06-02
In this paper we present a multi-criteria optimization of element partition trees and resulting orderings for multi-frontal solver algorithms executed for two dimensional h adaptive finite element method. In particular, the problem of optimal ordering of elimination of rows in the sparse matrices resulting from adaptive finite element method computations is reduced to the problem of finding of optimal element partition trees. Given a two dimensional h refined mesh, we find all optimal element partition trees by using the dynamic programming approach. An element partition tree defines a prescribed order of elimination of degrees of freedom over the mesh. We utilize three different metrics to estimate the quality of the element partition tree. As the first criterion we consider the number of floating point operations(FLOPs) performed by the multi-frontal solver. As the second criterion we consider the number of memory transfers (MEMOPS) performed by the multi-frontal solver algorithm. As the third criterion we consider memory usage (NONZEROS) of the multi-frontal direct solver. We show the optimization results for FLOPs vs MEMOPS as well as for the execution time estimated as FLOPs+100MEMOPS vs NONZEROS. We obtain Pareto fronts with multiple optimal trees, for each mesh, and for each refinement level. We generate a library of optimal elimination trees for small grids with local singularities. We also propose an algorithm that for a given large mesh with identified local sub-grids, each one with local singularity. We compute Schur complements over the sub-grids using the optimal trees from the library, and we submit the sequence of Schur complements into the iterative solver ILUPCG.
Directory of Open Access Journals (Sweden)
2009-03-01
Full Text Available We introduce a new approximation scheme combining the viscosity method with parallel method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a family of finitely strict pseudocontractions. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. Based on this result, we also get some new and interesting results. The results in this paper extend and improve some well-known results in the literature.
AL-Jawary, M. A.; AL-Qaissy, H. R.
2015-04-01
In this paper, we implement the new iterative method proposed by Daftardar-Gejji and Jafari namely new iterative method (DJM) to solve the linear and non-linear Volterra integro-differential equations and systems of linear and non-linear Volterra integro-differential equations. The applications of the DJM for solving the resulting equations of the non-linear Volterra integro-differential equations forms of the Lane-Emden equations are presented. The Volterra integro-differential equations forms of the Lane-Emden equation overcome the singular behaviour at the origin x = 0 of the original differential equation. Some examples are solved and different cases of the Lane-Emden equations of first kind are presented. Moreover, the DJM is applied to solve the system of the linear and non-linear Volterra integro-differential forms of the Lane-Emden equations. The results demonstrate that the method has many merits such as being derivative-free, and overcoming the difficulty arising in calculating Adomian polynomials to handle the non-linear terms in Adomian Decomposition Method (ADM). It does not require to calculate Lagrange multiplier in Variational Iteration Method (VIM) and no need to construct a homotopy in Homotopy Perturbation Method (HPM) and solve the corresponding algebraic equations.
DEFF Research Database (Denmark)
Dieterle, Mischa; Horstmeyer, Thomas; Berthold, Jost
2012-01-01
to successively improving data, the repeated instantiation of a skeleton incurs a certain overhead that could be saved by reusing existing processes, threads and communication structures. This is especially important when running parallel applications in a distributed environment. However, customising......Skeleton-based programming is an area of increasing relevance with upcoming highly parallel hardware, since it substantially facilitates parallel programming and separates concerns. When parallel algorithms expressed by skeletons involve iterations – applying the same algorithm repeatedly...... a particular skeleton ad-hoc for repeated execution turns out to be considerably complicated, and raises general questions about introducing state into a stateless parallel computation. In addition, one would strongly prefer an approach which leaves the original skeleton intact, and only uses it as a building...
Kassam-Adams, Nancy; Marsac, Meghan L; Kohser, Kristen L; Kenardy, Justin A; March, Sonja; Winston, Flaura K
2015-04-15
The advent of eHealth interventions to address psychological concerns and health behaviors has created new opportunities, including the ability to optimize the effectiveness of intervention activities and then deliver these activities consistently to a large number of individuals in need. Given that eHealth interventions grounded in a well-delineated theoretical model for change are more likely to be effective and that eHealth interventions can be costly to develop, assuring the match of final intervention content and activities to the underlying model is a key step. We propose to apply the concept of "content validity" as a crucial checkpoint to evaluate the extent to which proposed intervention activities in an eHealth intervention program are valid (eg, relevant and likely to be effective) for the specific mechanism of change that each is intended to target and the intended target population for the intervention. The aims of this paper are to define content validity as it applies to model-based eHealth intervention development, to present a feasible method for assessing content validity in this context, and to describe the implementation of this new method during the development of a Web-based intervention for children. We designed a practical 5-step method for assessing content validity in eHealth interventions that includes defining key intervention targets, delineating intervention activity-target pairings, identifying experts and using a survey tool to gather expert ratings of the relevance of each activity to its intended target, its likely effectiveness in achieving the intended target, and its appropriateness with a specific intended audience, and then using quantitative and qualitative results to identify intervention activities that may need modification. We applied this method during our development of the Coping Coach Web-based intervention for school-age children. In the evaluation of Coping Coach content validity, 15 experts from five countries
Asymptotic Solution of the Theory of Shells Boundary Value Problem
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I. V. Andrianov
2007-01-01
Full Text Available This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i it is devoted to the fundamental principles of asymptotic approaches, and (ii it deals with both traditional approaches, and less widely used, new approaches. The authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.
Vinas, A. F.; Scudder, J. D.
1986-01-01
A new, definitive, reliable and fast iterative method is described for determining the geometrical properties of a shock (i.e., theta sub Bn, yields N, V sub s and M sub A), the conservation constants and the self-consistent asymptotic magnetofluid variables, that uses the three dimensional magnetic field and plasma observations. The method is well conditioned and reliable at all theta sub Bn angles regardless of the shock strength or geometry. Explicit proof of uniqueness of the shock geometry solution by either analytical or graphical methods is given. The method is applied to synthetic and real shocks, including a bow shock event and the results are then compared with those determined by preaveraging methods and other iterative schemes. A complete analysis of the confidence region and error bounds of the solution is also presented.
Li, Zhong-xiao; Li, Zhen-chun
2017-08-01
Adaptive multiple subtraction is an important step for successfully conducting surface-related multiple elimination in marine seismic exploration. 2D adaptive multiple subtraction conducted in the parabolic Radon domain has been proposed to better separate primaries and multiples than 2D adaptive multiple subtraction conducted in the time-offset domain. Additionally, the parabolic Radon domain hybrid demultiple method combining parabolic Radon filtering and parabolic Radon domain 2D adaptive multiple subtraction can better remove multiples than the cascaded demultiple method using time-offset domain 2D adaptive multiple subtraction and the parabolic Radon transform method sequentially. To solve the matching filter in the optimization problem with L1 norm minimization constraint of primaries, traditional parabolic Radon domain 2D adaptive multiple subtraction uses the iterative reweighted least squares (IRLS) algorithm, which is computationally expensive for solving a weighted LS inversion in each iteration. In this paper we introduce the fast iterative shrinkage thresholding algorithm (FISTA) as a faster alternative to the IRLS algorithm for parabolic Radon domain 2D adaptive multiple subtraction. FISTA uses the shrinkage-thresholding operator to promote the sparsity of estimated primaries and solves the 2D matching filter with iterative steps. FISTA based parabolic Radon domain 2D adaptive multiple subtraction reduces the computation time effectively while achieving similar accuracy compared with IRLS based parabolic Radon domain 2D adaptive multiple subtraction. Additionally, the provided examples show that FISTA based parabolic Radon domain 2D adaptive multiple subtraction can better separate primaries and multiples than FISTA based time-offset domain 2D adaptive multiple subtraction. Furthermore, we introduce FISTA based parabolic Radon domain 2D adaptive multiple subtraction into the parabolic Radon domain hybrid demultiple method to improve its computation
Comparison of the asymptotic stability properties for two multirate strategies
Savcenco, V Valeriu
2007-01-01
textabstractThis paper contains a comparison of the asymptotic stability properties for two multirate strategies. For each strategy, the asymptotic stability regions are presented for a 2 x 2 test problem and the differences between the results are discussed. The considered multirate schemes use Rosenbrock type methods as the main time integration method and have one level of temporal local refinement. Some remarks on the relevance of the results for 2 x 2 test problems are presented.
Iterative supervirtual refraction interferometry
Al-Hagan, Ola
2014-05-02
In refraction tomography, the low signal-to-noise ratio (S/N) can be a major obstacle in picking the first-break arrivals at the far-offset receivers. To increase the S/N, we evaluated iterative supervirtual refraction interferometry (ISVI), which is an extension of the supervirtual refraction interferometry method. In this method, supervirtual traces are computed and then iteratively reused to generate supervirtual traces with a higher S/N. Our empirical results with both synthetic and field data revealed that ISVI can significantly boost up the S/N of far-offset traces. The drawback is that using refraction events from more than one refractor can introduce unacceptable artifacts into the final traveltime versus offset curve. This problem can be avoided by careful windowing of refraction events.
Top mass from asymptotic safety
Eichhorn, Astrid; Held, Aaron
2018-02-01
We discover that asymptotically safe quantum gravity could predict the top-quark mass. For a broad range of microscopic gravitational couplings, quantum gravity could provide an ultraviolet completion for the Standard Model by triggering asymptotic freedom in the gauge couplings and bottom Yukawa and asymptotic safety in the top-Yukawa and Higgs-quartic coupling. We find that in a part of this range, a difference of the top and bottom mass of approximately 170GeV is generated and the Higgs mass is determined in terms of the top mass. Assuming no new physics below the Planck scale, we construct explicit Renormalization Group trajectories for Standard Model and gravitational couplings which link the transplanckian regime to the electroweak scale and yield a top pole mass of Mt,pole ≈ 171GeV.
An asymptotically exact theory of functionally graded piezoelectric shells
Le, Khanh Chau
2016-01-01
An asymptotically exact two-dimensional theory of functionally graded piezoelectric shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application, analytical solution to the problem of forced vibration of a functionally graded piezoceramic cylindrical shell with thickness polarization fully covered by electrodes and excited by a harmonic voltage is found.
Asymptotic vacua with higher derivatives
Energy Technology Data Exchange (ETDEWEB)
Cotsakis, Spiros, E-mail: skot@aegean.gr [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kadry, Seifedine, E-mail: Seifedine.Kadry@aum.edu.kw [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kolionis, Georgios, E-mail: gkolionis@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece); Tsokaros, Antonios, E-mail: atsok@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece)
2016-04-10
We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
Iterative optimization in inverse problems
Byrne, Charles L
2014-01-01
Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author's considerable research in the field, including his recently developed class of SUMMA algorithms. Related to sequential unconstrained minimization methods, the SUMMA class includes a wide range of iterative algorithms well known to researchers in various areas, such as statistics and image processing. Organizing the topics from general to more
Directory of Open Access Journals (Sweden)
R. Ingram
2012-01-01
Full Text Available We present a general theory for regularization models of the Navier-Stokes equations based on the Leray deconvolution model with a general deconvolution operator designed to fit a few important key properties. We provide examples of this type of operator, such as the (modified Tikhonov-Lavrentiev and (modified Iterated Tikhonov-Lavrentiev operators, and study their mathematical properties. An existence theory is derived for the family of models and a rigorous convergence theory is derived for the resulting algorithms. Our theoretical results are supported by numerical testing with the Taylor-Green vortex problem, presented for the special operator cases mentioned above.
Iterative initial condition reconstruction
Schmittfull, Marcel; Baldauf, Tobias; Zaldarriaga, Matias
2017-07-01
Motivated by recent developments in perturbative calculations of the nonlinear evolution of large-scale structure, we present an iterative algorithm to reconstruct the initial conditions in a given volume starting from the dark matter distribution in real space. In our algorithm, objects are first moved back iteratively along estimated potential gradients, with a progressively reduced smoothing scale, until a nearly uniform catalog is obtained. The linear initial density is then estimated as the divergence of the cumulative displacement, with an optional second-order correction. This algorithm should undo nonlinear effects up to one-loop order, including the higher-order infrared resummation piece. We test the method using dark matter simulations in real space. At redshift z =0 , we find that after eight iterations the reconstructed density is more than 95% correlated with the initial density at k ≤0.35 h Mpc-1 . The reconstruction also reduces the power in the difference between reconstructed and initial fields by more than 2 orders of magnitude at k ≤0.2 h Mpc-1 , and it extends the range of scales where the full broadband shape of the power spectrum matches linear theory by a factor of 2-3. As a specific application, we consider measurements of the baryonic acoustic oscillation (BAO) scale that can be improved by reducing the degradation effects of large-scale flows. In our idealized dark matter simulations, the method improves the BAO signal-to-noise ratio by a factor of 2.7 at z =0 and by a factor of 2.5 at z =0.6 , improving standard BAO reconstruction by 70% at z =0 and 30% at z =0.6 , and matching the optimal BAO signal and signal-to-noise ratio of the linear density in the same volume. For BAO, the iterative nature of the reconstruction is the most important aspect.
Asymptotics of weighted random sums
DEFF Research Database (Denmark)
Corcuera, José Manuel; Nualart, David; Podolskij, Mark
2014-01-01
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral...
Thermodynamics of asymptotically safe theories
DEFF Research Database (Denmark)
Rischke, Dirk H.; Sannino, Francesco
2015-01-01
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze...
Naturalness of asymptotically safe Higgs
DEFF Research Database (Denmark)
Pelaggi, Giulio M.; Sannino, Francesco; Strumia, Alessandro
2017-01-01
that the scalars can be lighter than Λ. Although we do not have an answer to whether the Standard Model hypercharge coupling growth toward a Landau pole at around Λ ~ 1040GeV can be tamed by non-perturbative asymptotic safety, our results indicate that such a possibility is worth exploring. In fact, if successful...
Ruin problems and tail asymptotics
DEFF Research Database (Denmark)
Rønn-Nielsen, Anders
The thesis Ruin Problems and Tail Asymptotics provides results on ruin problems for several classes of Markov processes. For a class of diffusion processes with jumps an explicit expression for the joint Laplace transform of the first passage time and the corresponding undershoot is derived...
Energy Technology Data Exchange (ETDEWEB)
Ortiz, J. F.; Grau, A.
1985-07-01
In the present paper an iterative method is applied to study the variation of dynode response in the multiplier phototube. Three different situation 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 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) 11 refs.
Energy Technology Data Exchange (ETDEWEB)
T' Jampens, B
2002-12-15
Precise knowledge of cold-atom collision properties is essential for the studies of Bose-Einstein condensation or cold molecule formation. In such experiments, the interaction mainly occurs at rather large interatomic distance, in the so-called asymptotic region. We have developed a purely asymptotic method which allows us to fully describe the collision properties of cold alkali atoms without using the inner part of the molecular potentials, which is often known with a poor precision. The key point of the method is the setting of nodal lines, which are the lines connecting the nodes of successive radial wavefunctions near the ground state threshold. Within the framework of Born-Oppenheimer approximation, computing such nodal lines, by numerical integration of the radial Schroedinger equation in the asymptotic region only, provides a very simple way to derive scattering lengths from observed bound level positions. The method has been extended to the multichannel case and appears now as a genuine parametric method, in which a few parameters (some chosen nodal lines) replace the inner part of the potentials. These nodal lines are used as fitting parameters, which are adjusted on experimental results. Once these parameters have been determined, any collision property such as scattering lengths, clock shifts or magnetic field induced Feshbach resonances can be deduced in principle. This method has been applied to obtain the collision properties of ultracold sodium and cesium atoms. (author)
Asymptotic granularity reduction and its application
Su, Shenghui; Lü, Shuwang; Fan, Xiubin
2011-01-01
It is well known that the inverse function of y = x with the derivative y' = 1 is x = y, the inverse function of y = c with the derivative y' = 0 is inexistent, and so on. Hence, on the assumption that the noninvertibility of the univariate increasing function y = f(x) with x > 0 is in direct proportion to the growth rate reflected by its derivative, the authors put forward a method of comparing difficulties in inverting two functions on a continuous or discrete interval called asymptotic gra...
On the Asymptotics of Takeuchi Numbers
Prellberg, Thomas
2000-01-01
I present an asymptotic formula for the Takeuchi numbers $T_n$. In particular, I give compelling numerical evidence and present a heuristic argument showing that $$T_n\\sim C_T B_n\\exp{1\\over2}{W(n)}^2$$as $n$ tends to infinity, where $B_n$ are the Bell numbers, W(n) is Lambert's $W$ function, and $C_T=2.239...$ is a constant. Moreover, I show that the method presented here can be generalized to derive conjectures for related problems.
Asymptotic symmetries and electromagnetic memory
Pasterski, Sabrina
2017-09-01
Recent investigations into asymptotic symmetries of gauge theory and gravity have illuminated connections between gauge field zero-mode sectors, the corresponding soft factors, and their classically observable counterparts — so called "memories". Namely, low frequency emissions in momentum space correspond to long time integrations of the corre-sponding radiation in position space. Memory effect observables constructed in this manner are non-vanishing in typical scattering processes, which has implications for the asymptotic symmetry group. Here we complete this triad for the case of large U(1) gauge symmetries at null infinity. In particular, we show that the previously studied electromagnetic memory effect, whereby the passage of electromagnetic radiation produces a net velocity kick for test charges in a distant detector, is the position space observable corresponding to th Weinberg soft photon pole in momentum space scattering amplitudes.
Directory of Open Access Journals (Sweden)
Mladenović Vladimir
2016-01-01
Full Text Available In this paper, a new approach in solving and analysing the performances of the digital telecommunication non-coherent FSK/ASK system in the presence of noise is derived, by using a computer algebra system. So far, most previous solutions cannot be obtained in closed form, which can be a problem for detailed analysis of complex communication systems. In this case, there is no insight into the influence of certain parameters on the performance of the system. The analysis, modelling and design can be time-consuming. One of the main reasons is that these solutions are obtained by utilising traditional numerical tools in the shape of closed-form expressions. Our results were obtained in closed-form solutions. They are resolved by the introduction of an iteration-based simulation method. The Wolfram language is used for describing applied symbolic tools, and SchematicSolver application package has been used for designing. In a new way, the probability density function and the impact of the newly introduced parameter of iteration are performed when errors are calculated. Analyses of the new method are applied to several scenarios: without fading, in the presence of Rayleigh fading, Rician fading, and in cases when the signals are correlated and uncorrelated. [Projekat Ministarstva nauke Republike Srbije, br. TR 32023
Root Asymptotics of Spectral Polynomials
Directory of Open Access Journals (Sweden)
B. Shapiro
2007-01-01
Full Text Available We have been studying the asymptotic energy distribution of the algebraic part of the spectrum of the one-dimensional sextic anharmonic oscillator. We review some (both old and recent results on the multiparameter spectral problem and show that our problem ranks among the degenerate cases of Heine-Stieltjes spectral problem, and we derive the density of the corresponding probability measure.
Elser, V.; Rankenburg, I.; Thibault, P.
2007-01-01
In many problems that require extensive searching, the solution can be described as satisfying two competing constraints, where satisfying each independently does not pose a challenge. As an alternative to tree-based and stochastic searching, for these problems we propose using an iterated map built from the projections to the two constraint sets. Algorithms of this kind have been the method of choice in a large variety of signal-processing applications; we show here that the scope of these algorithms is surprisingly broad, with applications as diverse as protein folding and Sudoku. PMID:17202267
An asymptotic expansion for product integration applied to Cauchy principal value integrals
Wesseling, P.
1975-01-01
Product integration methods for Cauchy principal value integrals based on piecewise Lagrangian interpolation are studied. It is shown that for this class of quadrature methods the truncation error has an asymptotic expansion in integer powers of the step-size, and that a method with an asymptotic
Dhruv, Akash; Blower, Christopher; Wickenheiser, Adam M.
2015-03-01
The ability of UAVs to operate in complex and hostile environments makes them useful in military and civil operations concerning surveillance and reconnaissance. However, limitations in size of UAVs and communication delays prohibit their operation close to the ground and in cluttered environments, which increase risks associated with turbulence and wind gusts that cause trajectory deviations and potential loss of the vehicle. In the last decade, scientists and engineers have turned towards bio-inspiration to solve these issues by developing innovative flow control methods that offer better stability, controllability, and maneuverability. This paper presents an aerodynamic load solver for bio-inspired wings that consist of an array of feather-like flaps installed across the upper and lower surfaces in both the chord- and span-wise directions, mimicking the feathers of an avian wing. Each flap has the ability to rotate into both the wing body and the inbound airflow, generating complex flap configurations unobtainable by traditional wings that offer improved aerodynamic stability against gusting flows and turbulence. The solver discussed is an unsteady three-dimensional iterative doublet panel method with vortex particle wakes. This panel method models the wake-body interactions between multiple flaps effectively without the need to define specific wake geometries, thereby eliminating the need to manually model the wake for each configuration. To incorporate viscous flow characteristics, an iterative boundary layer theory is employed, modeling laminar, transitional and turbulent regions over the wing's surfaces, in addition to flow separation and reattachment locations. This technique enables the boundary layer to influence the wake strength and geometry both within the wing and aft of the trailing edge. The results obtained from this solver are validated using experimental data from a low-speed suction wind tunnel operating at Reynolds Number 300,000. This method
Numerical Relativity and Asymptotic Flatness
Deadman, E.; Stewart, J. M.
2009-01-01
It is highly plausible that the region of space-time far from an isolated gravitating body is, in some sense, asymptotically Minkowskian. However theoretical studies of the full nonlinear theory, initiated by Bondi et al. (1962), Sachs (1962) and Newman & Unti (1962), rely on careful, clever, a-priori choices of chart (and tetrad) and so are not readily accessible to the numerical relativist, who chooses her/his chart on the basis of quite different grounds. This paper seeks to close this gap...
Ultraviolet asymptotics of glueball propagators
Bochicchio, Marco; Muscinelli, Samuele P.
2013-08-01
We point out that perturbation theory in conjunction with the renormalization group ( RG) puts a severe constraint on the structure of the large- N non-perturbative glueball propagators in SU( N) pure Y M, in QCD and in = 1 SU SY QCD with massless quarks, or in any confining asymptotically-free gauge theory massless in perturbation theory. For the scalar and pseudoscalar glueball propagators in pure Y M and QCD with massless quarks we check in detail the RG-improved estimate to the order of the leading and next-to-leading logarithms by means of a remarkable three-loop computation by Chetyrkin et al. We investigate as to whether the aforementioned constraint is satisfied by any of the scalar or pseudoscalar glueball propagators computed in the framework of the AdS String/ large- N Gauge Theory correspondence and of a recent proposal based on a Topological Field Theory underlying the large- N limit of Y M . We find that none of the proposals for the scalar or the pseudoscalar glueball propagators based on the AdS String/large- N Gauge Theory correspondence satisfies the constraint, actually as expected, since the gravity side of the correspondence is in fact strongly coupled in the ultraviolet. On the contrary, the Topological Field Theory satisfies the constraint that follows by the asymptotic freedom.
Asymptotically Free Gauge Theories. I
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Asymptotic chaos expansions in finance theory and practice
Nicolay, David
2014-01-01
Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (suc...
Kozhinov, Anton N; Zhurov, Konstantin O; Tsybin, Yury O
2013-07-02
We describe a mass spectra recalibration method, which enables analysis of petroleum samples with Orbitrap FTMS. In this method, the mass calibration function is estimated on the basis of mass-to-charge ratios and abundances of internal calibrants without a need for theoretical description of residual mass errors. Importantly, to maximize the estimation accuracy of the mass calibration function, an iterative approach is implemented to obtain sufficiently high number of internal calibrants covering the entire ranges of mass-to-charge ratios and abundances of interest. For petroleomic samples, the method routinely provides root-mean-square (RMS) mass accuracies at sub-ppm level and hence allows for reliable assignment of elemental compositions. Moreover, since the achieved mass accuracies are normally limited only by random errors of low-abundance analytes, the method maximizes the range of abundances of assignable species for a given signal-to-noise ratio of experimental data. Additionally, despite being initially developed for Orbitrap FTMS, the method is likewise applicable for ion cyclotron resonance FTMS.
Tamboer, Peter; Vorst, Harrie C. M.; Oort, Frans J.
2014-01-01
Methods for identifying dyslexia in adults vary widely between studies. Researchers have to decide how many tests to use, which tests are considered to be the most reliable, and how to determine cut-off scores. The aim of this study was to develop an objective and powerful method for diagnosing dyslexia. We took various methodological measures,…
Huijssen, J.; Verweij, M.D.
2010-01-01
The development and optimization of medical ultrasound transducers and imaging modalities require a computational method that accurately predicts the nonlinear acoustic pressure field. A prospective method should provide the wide-angle, pulsed field emitted by an arbitrary planar source distribution
The ITER project technological challenges
CERN. Geneva; Lister, Joseph; Marquina, Miguel A; Todesco, Ezio
2005-01-01
The first lecture reminds us of the ITER challenges, presents hard engineering problems, typically due to mechanical forces and thermal loads and identifies where the physics uncertainties play a significant role in the engineering requirements. The second lecture presents soft engineering problems of measuring the plasma parameters, feedback control of the plasma and handling the physics data flow and slow controls data flow from a large experiment like ITER. The last three lectures focus on superconductors for fusion. The third lecture reviews the design criteria and manufacturing methods for 6 milestone-conductors of large fusion devices (T-7, T-15, Tore Supra, LHD, W-7X, ITER). The evolution of the designer approach and the available technologies are critically discussed. The fourth lecture is devoted to the issue of performance prediction, from a superconducting wire to a large size conductor. The role of scaling laws, self-field, current distribution, voltage-current characteristic and transposition are...
Maerten, F.; Maerten, L.; Pollard, D. D.
2014-11-01
Most analytical solutions to engineering or geological problems are limited to simple geometries. For example, analytical solutions have been found to solve for stresses around a circular hole in a plate. To solve more complex problems, mathematicians and engineers have developed powerful computer-aided numerical methods, which can be categorized into two main types: differential methods and integral methods. The finite element method (FEM) is a differential method that was developed in the 1950s and is one of the most commonly used numerical methods today. Since its development, other differential methods, including the boundary element method (BEM), have been developed to solve different types of problems. The purpose of this paper is to describe iBem3D, formally called Poly3D, a C++ and modular 3D boundary element computer program based on the theory of angular dislocations for modeling three-dimensional (3D) discontinuities in an elastic, heterogeneous, isotropic whole- or half-space. After 20 years and more than 150 scientific publications, we present in detail the formulation behind this method, its enhancements over the years as well as some important applications in several domains of the geosciences. The main advantage of using this formulation, for describing geological objects such as faults, resides in the possibility of modeling complex geometries without gaps and overlaps between adjacent triangular dislocation elements, which is a significant shortcoming for models using rectangular dislocation elements. Reliability, speed, simplicity, and accuracy are enhanced in the latest version of the computer code. Industrial applications include subseismic fault modeling, fractured reservoir modeling, interpretation and validation of fault connectivity and reservoir compartmentalization, depleted area and fault reactivation, and pressurized wellbore stability. Academic applications include earthquake and volcano monitoring, hazard mitigation, and slope
DEFF Research Database (Denmark)
Spietz, Henrik Juul; Hejlesen, Mads Mølholm; Walther, Jens Honore
The ability to predict aerodynamic forces, due to the interaction of a fluid flow with a solid body, is central in many fields of engineering and is necessary to identify error-prone structural designs. In bluff-body flows the aerodynamic forces oscillate due to vortex shedding and variations...... in the oncoming flow. This may lead to structural instability e.g. when the shedding frequency aligns with the natural frequency of the structure. Fluid structure interaction must especially be considered when designing long span bridges. A three dimensional vortex-in-cell method is applied for the direct...... numerical simulation of the flow past a bodies of arbitrary shape. Vortex methods use a simple formulation where only the trajectories of discrete vortex particles are simulated. The Lagrangian formulation eliminates the CFL type condition that Eulerian methods have to satisfy. This allows vortex methods...
Benali, Abdelmajid
2013-01-01
When running a groundwater flow model, a recurrent and seemingly subsidiary question arises at the starting step of computations: what value of acceleration parameter do we need to optimize the numerical solver? A method is proposed to provide a practical estimate of the optimal acceleration parameter via a geostatistical analysis of the spatial variability of the logarithm of the transmissivity field Y. The background of the approach is illustrated on the successive over-relaxation method (SOR) used, either as a stand-alone solver, or as a symmetric preconditioner (SSOR) to the gradient conjugate method, or as a smoother in multigrid methods. It shows that this optimum acceleration factor is a function of the standard deviation and the correlation length of Y. This provides an easy-to-use heuristic procedure to estimate the acceleration factors, which could even be incorporated in the software package. A case study illustrates the steps needed to perform this estimation.
Directory of Open Access Journals (Sweden)
Shenghua Wang
2013-01-01
Full Text Available We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.
The Asymptotic Solution for the Steady Variable-Viscosity Free ...
African Journals Online (AJOL)
Under an arbitrary time-dependent heating of an infinite vertical plate (or wall), the steady viscosity-dependent free convection flow of a viscous incompressible fluid is investigated. Using the asymptotic method of solution on the governing equations of motion and energy, the resulting Ordinary differential equations were ...
A Novel Non-Iterative Method for Real-Time Parameter Estimation of the Fricke-Morse Model
Directory of Open Access Journals (Sweden)
SIMIC, M.
2016-11-01
Full Text Available Parameter estimation of Fricke-Morse model of biological tissue is widely used in bioimpedance data processing and analysis. Complex nonlinear least squares (CNLS data fitting is often used for parameter estimation of the model, but limitations such as high processing time, converging into local minimums, need for good initial guess of model parameters and non-convergence have been reported. Thus, there is strong motivation to develop methods which can solve these flaws. In this paper a novel real-time method for parameter estimation of Fricke-Morse model of biological cells is presented. The proposed method uses the value of characteristic frequency estimated from the measured imaginary part of bioimpedance, whereupon the Fricke-Morse model parameters are calculated using the provided analytical expressions. The proposed method is compared with CNLS in frequency ranges of 1 kHz to 10 MHz (beta-dispersion and 10 kHz to 100 kHz, which is more suitable for low-cost microcontroller-based bioimpedance measurement systems. The obtained results are promising, and in both frequency ranges, CNLS and the proposed method have accuracies suitable for most electrical bioimpedance (EBI applications. However, the proposed algorithm has significantly lower computation complexity, so it was 20-80 times faster than CNLS.
Directory of Open Access Journals (Sweden)
Zhanhua Yu
2011-01-01
Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.
Archimedes' Pi--An Introduction to Iteration.
Lotspeich, Richard
1988-01-01
One method (attributed to Archimedes) of approximating pi offers a simple yet interesting introduction to one of the basic ideas of numerical analysis, an iteration sequence. The method is described and elaborated. (PK)
Preasymptotic convergence of randomized Kaczmarz method
Jiao, Yuling; Jin, Bangti; Lu, Xiliang
2017-12-01
Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the method enjoys an exponential convergence for well-posed problems, and the convergence rate is determined by a variant of the condition number. In this work, we analyze the preasymptotic convergence behavior of the randomized Kaczmarz method, and show that the low-frequency error (with respect to the right singular vectors) decays faster during first iterations than the high-frequency error. Under the assumption that the initial error is smooth (e.g. sourcewise representation), the result explains the fast empirical convergence behavior, thereby shedding new insights into the excellent performance of the randomized Kaczmarz method in practice. Further, we propose a simple strategy to stabilize the asymptotic convergence of the iteration by means of variance reduction. We provide extensive numerical experiments to confirm the analysis and to elucidate the behavior of the algorithms.
Directory of Open Access Journals (Sweden)
Jarmo Partanen
2013-11-01
Full Text Available A forecasting methodology for prediction of both normal prices and price spikes in the day-ahead energy market is proposed. The method is based on an iterative strategy implemented as a combination of two modules separately applied for normal price and price spike predictions. The normal price module is a mixture of wavelet transform, linear AutoRegressive Integrated Moving Average (ARIMA and nonlinear neural network models. The probability of a price spike occurrence is produced by a compound classifier in which three single classification techniques are used jointly to make a decision. Combined with the spike value prediction technique, the output from the price spike module aims to provide a comprehensive price spike forecast. The overall electricity price forecast is formed as combined normal price and price spike forecasts. The forecast accuracy of the proposed method is evaluated with real data from the Finnish Nord Pool Spot day-ahead energy market. The proposed method provides significant improvement in both normal price and price spike prediction accuracy compared with some of the most popular forecast techniques applied for case studies of energy markets.