Computer Solution of Large Linear Systems, Volume 28

1st Edition

Authors: Gerard Meurant
Hardcover ISBN: 9780444501691
eBook ISBN: 9780080529516
Imprint: North Holland
Published Date: 16th June 1999
Page Count: 776
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Table of Contents

Introductory Material. Vector and matrices norms.
Eigenvalues.
Irreducibility and diagonal dominance.
M--Matrices and generalizations.
Splittings.
Positive definite matrices.
The graph of a matrix.
Chebyshev polynomials
Discretization methods for partial diffential equations.
Eigenvalues and Fourier analysis.
Floating point arithmetic.
Vector and parallel computers.
BLAS and LAPACK.
Bibliographical comments.
Gaussian elimination for general linear systems.
Introduction to Gaussian elimination.
Gaussian elimination without permutations.
Gaussian elimination with permutations (partial piv- oting).
Gaussian elimination with other pivoting strategies.
Operation counts.
Gaussian elimination for symmetric systems.
The outer product algorithm.
The bordering algorithm.
The inner product algorithm.
Coding the three factorization algorithms.
Positive definite systems.
Indefinite systems.
Gaussian elimination for H-matrices.
Block methods.
Tridiagonal and block tridiagonal systems.
Roundoff error analysis.
Perturbation analysis.
Scaling.
Iterative refinement.
Parallel solution of general linear systems.
Bibliographical comments. <BR


Description

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.


Details

No. of pages:
776
Language:
English
Copyright:
© North Holland 1999
Published:
Imprint:
North Holland
eBook ISBN:
9780080529516
Hardcover ISBN:
9780444501691

About the Authors

Gerard Meurant Author