Iterative Krylov Methods for Large Linear Systems
Seiten
2009
Cambridge University Press (Verlag)
978-0-521-18370-3 (ISBN)
Cambridge University Press (Verlag)
978-0-521-18370-3 (ISBN)
Based on the author's extensive teaching experience, this book presents an overview of a number of Krylov projection methods for the solution of linear systems of equations. There are a large number of references for further reading as well as exercises to help students as they first encounter the material.
Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.
Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.
Henk A. van der Vorst is Professor Emeritus in the Mathematical Institute of Utrecht University.
Preface; 1. Introduction; 2. Mathematical preliminaries; 3. Basic iteration methods; 4. Construction of approximate solutions; 5. The conjugate gradients method; 6. GMRES and MINRES; 7. Bi-conjugate gradients; 8. How serious is irregular convergence?; 9. BI-CGSTAB; 10. Solution of singular systems; 11. Solution of f (A)x = b with Krylov subspace information; 12. Miscellaneous; 13. Preconditioning; References; Index.
| Reihe/Serie | Cambridge Monographs on Applied and Computational Mathematics ; Vol.13 |
|---|---|
| Zusatzinfo | Worked examples or Exercises; 50 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 228 mm |
| Gewicht | 390 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Iteration • Lineares System |
| ISBN-10 | 0-521-18370-7 / 0521183707 |
| ISBN-13 | 978-0-521-18370-3 / 9780521183703 |
| Zustand | Neuware |
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