Iterative Krylov Methods for Large Linear Systems

Overview of iterative solutions methods for systems of linear equations. For graduate students and researchers.

Henk A. van der Vorst (Author)

9780521183703, Cambridge University Press

Paperback, published 1 October 2009

236 pages, 50 b/w illus. 65 exercises
22.8 x 15.2 x 1.3 cm, 0.39 kg

'… a compact but comprehensive introduction to iterative methods, also taking account of computer methods.' Mathematika

Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author 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.

Preface
1. Introduction
2. Mathematical preliminaries
3. Basic iteration methods
4. Construction of approximate solutions
5. The conjugate gradients method
6. GMRES and MINRES
7. Bi-conjugate gradients
8. How serious is irregular convergence?
9. BI-CGSTAB
10. Solution of singular systems
11. Solution of f (A)x = b with Krylov subspace information
12. Miscellaneous
13. Preconditioning
References
Index.

Subject Areas: Numerical analysis [PBKS]