Iterative Krylov Methods for Large Linear Systems / Edition 1

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Cambridge, England 2003 Hard cover New. BRAND NEW; gift quality. Sewn binding. Cloth over boards. 221 p. Contains: Illustrations. Cambridge Monographs on Applied and ... Computational Mathematics. Audience: General/trade. Read more Show Less

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More About This Textbook

Overview

The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and Bi-CGSTAB. The book also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.
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Product Details

Meet the Author

Henk A. van der Vorst is Professor Emeritus in the Mathematical Institute of Utrecht University.

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Table of Contents

Preface
1 Introduction 1
2 Mathematical preliminaries 15
3 Basic iteration methods 21
4 Construction of approximate solutions 33
5 The Conjugate Gradients method 37
6 GMRES and MINRES 65
7 Bi-Conjugate Gradients 95
8 How serious is irregular convergence? 115
9 Bi-CGSTAB 133
10 Solution of singular systems 147
11 Solution of f(A)x = b with Krylov subspace information 151
12 Miscellaneous 159
13 Preconditioning 173
References 205
Index 219
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