Iterative Solution Methods

ISBN-13: 9780521555692 / Angielski / Miękka / 1996 / 672 str.

Owe Axelsson

Opis

Large linear systems of equations arise in most scientific problems where mathematical models are used. The most efficient methods for solving these equations are iterative methods. The first part of this book contains basic and classical material from the study of linear algebra and numerical linear algebra. The second half of the book is unique among books on this topic, because it is devoted to the construction of preconditioners and iterative acceleration methods of the conjugate gradient type. This book is for graduate students and researchers in numerical analysis and applied mathematics.

Recenzje

'… likely to be an important reference for theoreticians interested in the development and analysis of iterative solution methods for years to come.' Bulletin of the Institute of Mathematics and its Applications

Spis treści

Preface; Acknowledgements; 1. Direct solution methods; 2. Theory of matrix eigenvalues; 3. Positive definite matrices, Schur complements, and generalized eigenvalue problems; 4. Reducible and irreducible matrices and the Perron–Frobenius theory for nonnegative matrices; 5. Basic iterative methods and their rates of convergence; 6. M-matrices, convergent splittings, and the SOR method; 7. Incomplete factorization preconditioning methods; 8. Approximate matrix inverses and corresponding preconditioning methods; 9. Block diagonal and Schur complement preconditionings; 10. Estimates of eigenvalues and condition numbers for preconditional matrices; 11. Conjugate gradient and Lanczos-type methods; 12. Generalized conjugate gradient methods; 13. The rate of convergence of the conjugate gradient method; Appendices.