Iterative Methods for Solving Linear Systems
Language: English
Published by Society for Industrial and Applied Mathematics,U.S., US, 1997
- Softcover
- New
Seller: Rarewaves.com UK, London, United KingdomRarewaves.com UK
AbeBooks seller since June 11, 2025
Condition: New
£ 70.80
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Add to basketItem description from seller
Much recent research has concentrated on the efficient solution of large sparse or structured linear systems using iterative methods. A language loaded with acronyms for a thousand different algorithms has developed, and it is often difficult even for specialists to identify the basic principles involved. Here is a book that focuses on the analysis of iterative methods. The author includes the most useful algorithms from a practical point of view and discusses the mathematical principles behind their derivation and analysis. Several questions are emphasized throughout: Does the method converge? If so, how fast? Is it optimal, among a certain class? If not, can it be shown to be near-optimal? The answers are presented clearly, when they are known, and remaining important open questions are laid out for further study.Greenbaum includes important material on the effect of rounding errors on iterative methods that has not appeared in other books on this subject. Additional important topics include a discussion of the open problem of finding a provably near-optimal short recurrence for non-Hermitian linear systems; the relation of matrix properties such as the field of values and the pseudospectrum to the convergence rate of iterative methods; comparison theorems for preconditioners and discussion of optimal preconditioners of specified forms; introductory material on the analysis of incomplete Cholesky, multigrid, and domain decomposition preconditioners, using the diffusion equation and the neutron transport equation as example problems. A small set of recommended algorithms and implementations is included.…
Seller Inventory # LU-9780898713961
- Title
- Iterative Methods for Solving Linear Systems
- Author
- Anne Greenbaum
- Publisher
- Society for Industrial and Applied Mathematics,U.S., US
- Publication year
- 1997
- Condition
- New
- Binding
- Paperback
- Language
- English
- ISBN 10
- 089871396X
- ISBN 13
- 9780898713961
- Item weight
- 440 grams
- Dimensions
- 17.78 x 12.7 x 26.04 cm
"Synopsis" may belong to another edition of this title.
Review
'For a course in matrix iterations, this is just the right book. It is wide-ranging, careful about details, and appealingly written - a major addition to the literature in this important area.' Nick Trefethen, Professor of Numerical Analysis, Oxford University
'This book differs substantially from other books on iterative methods, including those recently published, in that it concentrates on several principles behind the derivation and analysis of the most important methods and preconditioning techniques. Individual algorithms serve as examples illustrating the discussed ideas. Strong emphasis is given to motivation and its relation to problems in other areas of mathematics. The book speaks in clear language about principal problems in the area of iterative methods. It represents a comprehensive introduction to the field and stimulates the interest of the reader. It is valuable for students and also for experts working in the area of iterative methods.' Zdenek Strakos, Professor, Czech Academy of Sciences, Institute of Computer Science
'Anne Greenbaum is an admired authority in the field of iterative methods. Engineers and scientists often ask me about the puzzling behavior of iterative methods, which I almost always answer with a reference to Anne's work, now made easy to point to in her new book.' Paul Saylor, Department of Computer Science, University of Illinois, Urbana-Champaign
"About the title" may belong to another edition of this title.
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