Iterative Solution Methods
Iterative Solution Methods
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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.
- Contains over 200 exercises
- First part includes material suitable for courses in numerical linear algebra
- Presents many of the most recent methods and results
- Can be used as a textbook for postgraduate courses in mathematics and computer science
Reviews & endorsements
"...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
Product details
- Published: March 1996
- Format: Paperback
- ISBN: 9780521555692
- Length: 672 pages
- Dimensions: 229 × 152 × 38 mm
- Weight: 0.97kg
- Contains: 14 b/w illus. 3 tables 226 exercises
- Availability: Available
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.
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