Fundamentos matemáticos para la resolución de sistemas de ecuaciones lineales por iteración ; Los métodos iterativos en la solución del problema estructural PDF Download
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Author: Paul Lustgarten
Publisher:
ISBN:
Category :
Languages : es
Pages : 0
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Book Description
Author: Paul Lustgarten
Publisher:
ISBN:
Category :
Languages : es
Pages : 0
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Book Description
Author: Paul Lustgarten
Publisher:
ISBN:
Category :
Languages : es
Pages : 36
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Author:
Publisher:
ISBN:
Category : Equations, Simultaneous
Languages : es
Pages : 36
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Author:
Publisher:
ISBN:
Category : Catalogs, Publishers'
Languages : es
Pages : 1418
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Book Description
Author: C. T. Kelley
Publisher: SIAM
ISBN: 0898713528
Category : Mathematics
Languages : en
Pages : 169
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Book Description
Mathematics of Computing -- Numerical Analysis.
Author: Owe Axelsson
Publisher: Cambridge University Press
ISBN: 9780521555692
Category : Mathematics
Languages : en
Pages : 676
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Book Description
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: S. Manrique Catalán
Publisher:
ISBN:
Category :
Languages : es
Pages : 69
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Author: Anne Greenbaum
Publisher: SIAM
ISBN: 9781611970937
Category : Mathematics
Languages : en
Pages : 235
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Book Description
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: David M. Young
Publisher: Courier Corporation
ISBN: 9780486425481
Category : Mathematics
Languages : en
Pages : 612
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Book Description
This self-contained treatment offers a systematic development of the theory of iterative methods. Its focal point resides in an analysis of the convergence properties of the successive overrelaxation (SOR) method, as applied to a linear system with a consistently ordered matrix. The text explores the convergence properties of the SOR method and related techniques in terms of the spectral radii of the associated matrices as well as in terms of certain matrix norms. Contents include a review of matrix theory and general properties of iterative methods; SOR method and stationary modified SOR method for consistently ordered matrices; nonstationary methods; generalizations of SOR theory and variants of method; second-degree methods, alternating direction-implicit methods, and a comparison of methods. 1971 edition.
Author: Are Magnus Bruaset
Publisher: CRC Press
ISBN: 9780582276543
Category : Mathematics
Languages : en
Pages : 180
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Book Description
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 well suited for the kind of systems arising from the discretization of partial differential equations. The focus of this presentation is on the family of Krylov subspace solvers, of which the Conjugate Gradient algorithm is a typical example. In addition to an introduction to the basic principles of such methods, a large number of specific algorithms for symmetric and nonsymmetric problems are discussed. When solving linear systems by iteration, a preconditioner is usually introduced in order to speed up convergence. In many cases, the selection of a proper preconditioner is crucial to the resulting computational performance. For this reason, this book pays special attention to different preconditioning strategies. Although aimed at a wide audience, the presentation assumes that the reader has basic knowledge of linear algebra, and to some extent, of partial differential equations. The comprehensive bibliography in this survey is provides an entry point to the enormous amount of published research in the field of iterative methods.
