Iterative Methods For Solving Linear Systems
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Iterative Methods For Linear Systems
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Author : Maxim A. Olshanskii
language : en
Publisher: SIAM
Release Date : 2014-01-01
Iterative Methods For Linear Systems written by Maxim A. Olshanskii and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-01 with Mathematics categories.
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.
Iterative Methods For Solving Linear Systems
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Author : Anne Greenbaum
language : en
Publisher: SIAM
Release Date : 1997-01-01
Iterative Methods For Solving Linear Systems written by Anne Greenbaum and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Iterative Methods For Sparse Linear Systems
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Author : Yousef Saad
language : en
Publisher: SIAM
Release Date : 2003-04-01
Iterative Methods For Sparse Linear Systems written by Yousef Saad and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-01 with Mathematics categories.
Mathematics of Computing -- General.
Templates For The Solution Of Linear Systems
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Author : Richard Barrett
language : en
Publisher: SIAM
Release Date : 1994-01-01
Templates For The Solution Of Linear Systems written by Richard Barrett and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Iterative Methods For Linear And Nonlinear Equations
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Author : C. T. Kelley
language : en
Publisher: SIAM
Release Date : 1995-01-01
Iterative Methods For Linear And Nonlinear Equations written by C. T. Kelley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Iterative Krylov Methods For Large Linear Systems
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Author : H. A. van der Vorst
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-17
Iterative Krylov Methods For Large Linear Systems written by H. A. van der Vorst and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-17 with Mathematics categories.
Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.
Iterative Methods For Solving Nonlinear Equations And Systems
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Author : Juan R. Torregrosa
language : en
Publisher: MDPI
Release Date : 2019-12-06
Iterative Methods For Solving Nonlinear Equations And Systems written by Juan R. Torregrosa and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-06 with Mathematics categories.
Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.
Iterative Solution Of Large Linear Systems
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Author : David M. Young
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Iterative Solution Of Large Linear Systems written by David M. Young and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
Applied Iterative Methods
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Author : Louis A. Hageman
language : en
Publisher: Courier Corporation
Release Date : 2012-04-27
Applied Iterative Methods written by Louis A. Hageman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-27 with Mathematics categories.
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. 1981 edition. Includes 48 figures and 35 tables.
Iterative Methods For Solving Linear Systems
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Author : Anne Greenbaum
language : en
Publisher: SIAM
Release Date : 1997-01-01
Iterative Methods For Solving Linear Systems written by Anne Greenbaum and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
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.