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Author:   Owe Axelsson (Katholieke Universiteit Nijmegen, The Netherlands)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press (Virtual Publishing)
ISBN:  

9780511624100

ISBN 10:   0511624107
Publication Date:   05 August 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Undefined
Publisher's Status:   Active
Availability:   Available To Order  
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Table of Contents

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.

Reviews

'… 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

'... 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 ...the book is the most complete and interesting study of iterative methods for systems of linear equations to date. I strongly recommend it to any researcher in the field or in any other area in which the solution of large systems of linear equations plays an important role...it will become a standard reference in numerical linear algebra... Joaquim J. Judice, Mathematical Reviews The author has done a fine job of collecting the plethora of work in this area into an up-to-date, coherent entity....I am sure that this volume is destined to be the bible of iterative methods for many years to come. T. Hopkins, Computing Reviews ...contains a wealth of relevant mathematical theory which underpins much of the development of this specific but important area of Numerical Linear Algebra. It is likely to be an important reference for theoreticians interested in the development and analysis of iterative solution methods for years to come. A. Wathen, The Bulletin of the Institute of Mathematics and its Applications

'... 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

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