A Survey of Preconditioned Iterative Methods / Edition 1

by Are Magnus Bruaset

Overview

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.

Product Details

ISBN-13:	9780582276543
Publisher:	Taylor & Francis
Publication date:	05/05/1995
Series:	Chapman & Hall/CRC Research Notes in Mathematics Series , #328
Pages:	174
Product dimensions:	6.88(w) x 9.69(h) x (d)

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

Editorial Reviews

"... provides an excellent orientation in the state of the art in iterative solution of linear algebraic systems ..."
-Zentralblatt fur Mathematik No. 834

From the Publisher