Iterative Methods And Preconditioners For Systems Of Linear Equations

Author : Gabriele Ciaramella,Martin J. Gander
Publisher : SIAM
Page : 285 pages
File Size : 49,6 Mb
Release : 2022-02-08
Category : Mathematics
ISBN : 9781611976908

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Iterative Methods and Preconditioners for Systems of Linear Equations by Gabriele Ciaramella,Martin J. Gander Pdf

Iterative methods use successive approximations to obtain more accurate solutions. This book gives an introduction to iterative methods and preconditioning for solving discretized elliptic partial differential equations and optimal control problems governed by the Laplace equation, for which the use of matrix-free procedures is crucial. All methods are explained and analyzed starting from the historical ideas of the inventors, which are often quoted from their seminal works. Iterative Methods and Preconditioners for Systems of Linear Equations grew out of a set of lecture notes that were improved and enriched over time, resulting in a clear focus for the teaching methodology, which derives complete convergence estimates for all methods, illustrates and provides MATLAB codes for all methods, and studies and tests all preconditioners first as stationary iterative solvers. This textbook is appropriate for undergraduate and graduate students who want an overview or deeper understanding of iterative methods. Its focus on both analysis and numerical experiments allows the material to be taught with very little preparation, since all the arguments are self-contained, and makes it appropriate for self-study as well. It can be used in courses on iterative methods, Krylov methods and preconditioners, and numerical optimal control. Scientists and engineers interested in new topics and applications will also find the text useful.

Author : Yousef Saad
Publisher : SIAM
Page : 537 pages
File Size : 43,8 Mb
Release : 2003-04-01
Category : Mathematics
ISBN : 9780898715347

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Iterative Methods for Sparse Linear Systems by Yousef Saad Pdf

Mathematics of Computing -- General.

Author : Daniele Bertaccini,Fabio Durastante
Publisher : CRC Press
Page : 366 pages
File Size : 50,7 Mb
Release : 2018-02-19
Category : Mathematics
ISBN : 9781351649612

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Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications by Daniele Bertaccini,Fabio Durastante Pdf

This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.

Author : Maxim A. Olshanskii,Eugene E. Tyrtyshnikov
Publisher : SIAM
Page : 244 pages
File Size : 41,5 Mb
Release : 2014-07-21
Category : Mathematics
ISBN : 9781611973464

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Iterative Methods for Linear Systems by Maxim A. Olshanskii,Eugene E. Tyrtyshnikov Pdf

Iterative Methods for Linear Systems÷offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.÷÷

Author : Anne Greenbaum
Publisher : SIAM
Page : 235 pages
File Size : 53,9 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 1611970938

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Iterative Methods for Solving Linear Systems by Anne Greenbaum Pdf

Much recent research has concentrated on the efficient solution of large sparse or structured linear systems using iterative methods. A language loaded with acronyms for a thousand different algorithms has developed, and it is often difficult even for specialists to identify the basic principles involved. Here is a book that focuses on the analysis of iterative methods. The author includes the most useful algorithms from a practical point of view and discusses the mathematical principles behind their derivation and analysis. Several questions are emphasized throughout: Does the method converge? If so, how fast? Is it optimal, among a certain class? If not, can it be shown to be near-optimal? The answers are presented clearly, when they are known, and remaining important open questions are laid out for further study. Greenbaum includes important material on the effect of rounding errors on iterative methods that has not appeared in other books on this subject. Additional important topics include a discussion of the open problem of finding a provably near-optimal short recurrence for non-Hermitian linear systems; the relation of matrix properties such as the field of values and the pseudospectrum to the convergence rate of iterative methods; comparison theorems for preconditioners and discussion of optimal preconditioners of specified forms; introductory material on the analysis of incomplete Cholesky, multigrid, and domain decomposition preconditioners, using the diffusion equation and the neutron transport equation as example problems. A small set of recommended algorithms and implementations is included.

Author : Richard Barrett,Michael W. Berry,Tony F. Chan,James Demmel,June Donato,Jack Dongarra,Victor Eijkhout,Roldan Pozo,Charles Romine,Henk van der Vorst
Publisher : SIAM
Page : 130 pages
File Size : 42,9 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 9780898713282

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Templates for the Solution of Linear Systems by Richard Barrett,Michael W. Berry,Tony F. Chan,James Demmel,June Donato,Jack Dongarra,Victor Eijkhout,Roldan Pozo,Charles Romine,Henk van der Vorst Pdf

Mathematics of Computing -- Numerical Analysis.

Author : Are Magnus Bruaset
Publisher : Routledge
Page : 140 pages
File Size : 54,7 Mb
Release : 2018-12-13
Category : Mathematics
ISBN : 9781351469364

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A Survey of Preconditioned Iterative Methods by Are Magnus Bruaset Pdf

The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are w

Author : Owe Axelsson
Publisher : Cambridge University Press
Page : 676 pages
File Size : 44,9 Mb
Release : 1996-03-29
Category : Mathematics
ISBN : 0521555698

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Iterative Solution Methods by Owe Axelsson Pdf

This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for students who are not afraid of theory. To assist the reader, the more difficult passages have been marked, the definitions for each chapter are collected at the beginning of the chapter, and numerous exercises are included throughout the text. The second part of the book serves as a monograph introducing recent results in the iterative solution of linear systems, mainly using preconditioned conjugate gradient methods. This book should be a valuable resource for students and researchers alike wishing to learn more about iterative methods.

Author : David R. Kincaid,Linda J. Hayes
Publisher : Academic Press
Page : 350 pages
File Size : 44,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483260204

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Iterative Methods for Large Linear Systems by David R. Kincaid,Linda J. Hayes Pdf

Iterative Methods for Large Linear Systems contains a wide spectrum of research topics related to iterative methods, such as searching for optimum parameters, using hierarchical basis preconditioners, utilizing software as a research tool, and developing algorithms for vector and parallel computers. This book provides an overview of the use of iterative methods for solving sparse linear systems, identifying future research directions in the mainstream of modern scientific computing with an eye to contributions of the past, present, and future. Different iterative algorithms that include the successive overrelaxation (SOR) method, symmetric and unsymmetric SOR methods, local (ad-hoc) SOR scheme, and alternating direction implicit (ADI) method are also discussed. This text likewise covers the block iterative methods, asynchronous iterative procedures, multilevel methods, adaptive algorithms, and domain decomposition algorithms. This publication is a good source for mathematicians and computer scientists interested in iterative methods for large linear systems.

Author : H. A. van der Vorst
Publisher : Cambridge University Press
Page : 242 pages
File Size : 53,6 Mb
Release : 2003-04-17
Category : Mathematics
ISBN : 0521818281

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Iterative Krylov Methods for Large Linear Systems by H. A. van der Vorst Pdf

Table of contents

Author : Yousef Saad
Publisher : SIAM
Page : 546 pages
File Size : 53,9 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0898718007

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Iterative Methods for Sparse Linear Systems by Yousef Saad Pdf

Since the first edition of this book was published in 1996, tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of the new generation of linear and nonlinear systems arising in typical applications has grown. Solving the three-dimensional models of these problems using direct solvers is no longer effective. At the same time, parallel computing has penetrated these application areas as it became less expensive and standardized. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods. Iterative Methods for Sparse Linear Systems, Second Edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. These equations can number in the millions and are sparse in the sense that each involves only a small number of unknowns. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.

Author : Gerard Meurant
Publisher : Elsevier
Page : 777 pages
File Size : 49,6 Mb
Release : 1999-06-16
Category : Mathematics
ISBN : 9780080529516

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Computer Solution of Large Linear Systems by Gerard Meurant Pdf

This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.

Author : C. T. Kelley
Publisher : SIAM
Page : 169 pages
File Size : 41,6 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 9780898713527

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Iterative Methods for Linear and Nonlinear Equations by C. T. Kelley Pdf

Mathematics of Computing -- Numerical Analysis.

Author : David M. Young
Publisher : Elsevier
Page : 598 pages
File Size : 52,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483274133

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Iterative Solution of Large Linear Systems by David M. Young Pdf

Iterative Solution of Large Linear Systems describes the systematic development of a substantial portion of the theory of iterative methods for solving large linear systems, with emphasis on practical techniques. The focal point of the book is an analysis of the convergence properties of the successive overrelaxation (SOR) method as applied to a linear system where the matrix is "consistently ordered". Comprised of 18 chapters, this volume begins by showing how the solution of a certain partial differential equation by finite difference methods leads to a large linear system with a sparse matrix. The next chapter reviews matrix theory and the properties of matrices, as well as several theorems of matrix theory without proof. A number of iterative methods, including the SOR method, are then considered. Convergence theorems are also given for various iterative methods under certain assumptions on the matrix A of the system. Subsequent chapters deal with the eigenvalues of the SOR method for consistently ordered matrices; the optimum relaxation factor; nonstationary linear iterative methods; and semi-iterative methods. This book will be of interest to students and practitioners in the fields of computer science and applied mathematics.

Author : A. de la Garza
Publisher : Unknown
Page : 12 pages
File Size : 55,6 Mb
Release : 1951
Category : Iterative methods (Mathematics)
ISBN : UOM:39015094990911

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An Iterative Method for Solving Systems of Linear Equations by A. de la Garza Pdf