Matrix Preconditioning Techniques and Applications
Preconditioning techniques have emerged as an essential part of successful and efficient iterative solutions of matrices. Ke Chen's book offers a comprehensive introduction to these methods. A vast range of explicit and implicit sparse preconditioners are covered, including the conjugate gradient, multi-level and fast multi-pole methods, matrix and operator splitting, fast Fourier and wavelet transforms, incomplete LU and domain decomposition, Schur complements and approximate inverses. In addition, aspects of parallel realization using the MPI are discussed. Very much a users-guide, the book provides insight to the use of these techniques in areas such as acoustic wave scattering, image restoration and bifurcation problems in electrical power stations. Supporting MATLAB files are available from the Web to support and develop readers' understanding, and provide stimulus for further study. Pitched at graduate level, the book is intended to serve as a useful guide and reference for students, computational practitioners, engineers and researchers alike.
- Comprehensive introduction to iterative methods and preconditioning with self-contained descriptions of all major techniques
- Up-to-date account of selected large scale computing applications
- Accompanying MATLAB code at www.cambridge.org/0521838282 in a friendly and easy-to-use format
Reviews & endorsements
' … packed with matehmatical description relevant for various types of preconditioning for (in particular) non-symmetric matrix equations. it could be of considerable use in introducing applicaitons scientists to possible preconditioning approaches.' Journal of Fluid Mechanics
'... a very well-written and complete book which presents a lot of recent and original algorithms of utmost importance. ...this is a good investment if you are interested in these topics or if you want to have a good overview.' Zentralblatt MATH
'… offers a comprehensive introduction to this subject … a very rich book that will serve as a reference for students in applied mathematics, numerical analysis, and applied sciences, and for engineers as well.' Numerical Algorithms
Product details
July 2005Hardback
9780521838283
592 pages
235 × 158 × 34 mm
1.085kg
95 b/w illus. 5 tables
Available
Table of Contents
- 1. Introduction
- 2. Direct methods
- 3. Iterative methods
- 4. Matrix splitting preconditioners [t1]
- 5. Approxi,ate inverse preconditioners [t2]
- 6. Multilevel methods and preconditioners [t3]
- 7. Multilevel recursive Schur complements preconditioners
- 8. Wavelet preconditioners [t5] for ˆA n x n and ˆA -1 n x n
- 9. Wavelet Schur preconditioners [t6]
- 10. Implicit wavelet preconditioners [t7]
- 11. Application I - acoustic scattering modelling
- 12. Application II - coupled matrix problems
- 13. Application III - image restoration and inverse problems
- 14. Application IV-voltage stability in electrical power systems
- 15. Parallel computing by examples.
