Iterative Solution Methods

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Iterative Solution Methods
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Author : Owe Axelsson
language : en
Publisher: Cambridge University Press
Release Date : 1996-03-29
Iterative Solution Methods written by Owe Axelsson 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 1996-03-29 with Mathematics categories.
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.
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 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.
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 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.
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 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 Methods For Approximate Solution Of Inverse Problems
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Author : A.B. Bakushinsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-28
Iterative Methods For Approximate Solution Of Inverse Problems written by A.B. Bakushinsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-28 with Mathematics categories.
This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods. The analysis of methods includes convergence theorems as well as necessary and sufficient conditions for their convergence at a given rate. The principal groups of methods studied in the book are iterative processes based on the technique of universal linear approximations, stable gradient-type processes, and methods of stable continuous approximations. Compared to existing monographs and textbooks on ill-posed problems, the main distinguishing feature of the presented approach is that it doesn’t require any structural conditions on equations under consideration, except for standard smoothness conditions. This allows to obtain in a uniform style stable iterative methods applicable to wide classes of nonlinear inverse problems. Practical efficiency of suggested algorithms is illustrated in application to inverse problems of potential theory and acoustic scattering. The volume can be read by anyone with a basic knowledge of functional analysis. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems.