Iterative Krylov Methods for Large Linear Systems

by Henk A. van der Vorst

Overview

Based on extensive research by Henk van der Vorst, this book presents an overview of a number of Krylov projection methods for the solution of linear systems of equations. Van der Vorst demonstrates how these methods can be derived from basic iteration formulas and how they are related. Focusing on the ideas behind the methods rather than a complete presentation of the theory, the volume includes a substantial amount of references for further reading as well as exercises to help students initially encountering the material.

Product Details

ISBN-13:	9780521183703
Publisher:	Cambridge University Press
Publication date:	10/01/2009
Series:	Cambridge Monographs on Applied and Computational Mathematics , #13
Pages:	236
Product dimensions:	6.00(w) x 8.90(h) x 0.40(d)

About the Author

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

Table of Contents

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.

Editorial Reviews

"The book contains basic material as well as many interesting aspects of iterative methods which may lead to new algorithms. Hence it is of interest to both students and researcher. Moreover, it is very clearly written and hence is a very good tool to use for teaching both undergraduate and postgraduate courses for mathematicians, computer scientists and engineers."
Melina A. Freitag, Mathematical Reviews

From the Publisher