A Survey of Preconditioned Iterative Methods: 1st Edition (Hardback) book cover

A Survey of Preconditioned Iterative Methods

1st Edition

By Are Magnus Bruaset

Chapman and Hall/CRC

176 pages

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Hardback: 9780582276543
pub: 1995-05-05
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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.

Reviews

"… provides an excellent orientation in the state of the art in iterative solution of linear algebraic systems …"

-Zentralblatt fur Mathematik No. 834

Table of Contents

Preface

1. Introduction

2. Iterative methods based on matrix

3. Krylov subspace methods

4. Preconditioners for linear of equations

5. Epilogue

Appendix A: Some notation and useful properties

Bibliography

Index

About the Series

Chapman & Hall/CRC Research Notes in Mathematics Series

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Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied