Computer Solution of Large Linear Systems
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.

1009038524
Computer Solution of Large Linear Systems
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.

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Computer Solution of Large Linear Systems

Computer Solution of Large Linear Systems

by Gerard Meurant
Computer Solution of Large Linear Systems
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Computer Solution of Large Linear Systems

Computer Solution of Large Linear Systems

by Gerard Meurant

Overview

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.

Product Details

ISBN-13: 9780444501691
Publisher: Elsevier Science
Publication date: 06/16/1999
Series: Studies in Mathematics and its Applications , #28
Pages: 776
Product dimensions: 5.94(w) x 9.00(h) x (d)

Table of Contents

Introductory MaterialGaussian elimination for general linear systemsGaussian elimination for sparse linear systemsFast solvers for separable PDEsClassical iterative methodsThe conjugate gradient and related methodsKrylov methods for non—symmetric systemsPreconditioningMultigrid methods
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