Iterative methods for solving linear systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)
1997
|
| Schriftenreihe: | Frontiers in applied mathematics
17 |
| Schlagworte: | |
| Online-Zugang: | TUM01 UBW01 UBY01 UER01 Volltext |
| Beschreibung: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references (s. 205-212) and index List of algorithms -- Preface -- Chapter 1. Introduction: brief overview of the state of the art -- Part I. Krylov subspace approximations. Chapter 2. Some iteration methods: simple iteration; Chapter 3. Error bounds for CG, MINRES, and GMRES: Hermitian problems-CG and MINRES; Chapter 4. Effects of finite precision arithmetic: some numerical examples; Chapter 5. BiCG and related methods: the two-sided Lanczos algorithm; Chapter 6. Is there a short recurrence for a near-optimal approximation?; Chapter 7. Miscellaneous issues -- Part II. Preconditioners. Chapter 8. Overview and preconditioned algorithms; Chapter 9. Two example problems; Chapter 10. Comparison of preconditioners; Chapter 11. Incomplete decompositions; Chapter 12. Multigrid and domain decomposition methods 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 |
| Beschreibung: | 1 Online-Ressource (xiii, 220 Seiten) |
| ISBN: | 089871396X 9780898713961 |
| DOI: | 10.1137/1.9781611970937 |
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| 500 | |a Includes bibliographical references (s. 205-212) and index | ||
| 500 | |a List of algorithms -- Preface -- Chapter 1. Introduction: brief overview of the state of the art -- Part I. Krylov subspace approximations. Chapter 2. Some iteration methods: simple iteration; Chapter 3. Error bounds for CG, MINRES, and GMRES: Hermitian problems-CG and MINRES; Chapter 4. Effects of finite precision arithmetic: some numerical examples; Chapter 5. BiCG and related methods: the two-sided Lanczos algorithm; Chapter 6. Is there a short recurrence for a near-optimal approximation?; Chapter 7. Miscellaneous issues -- Part II. Preconditioners. Chapter 8. Overview and preconditioned algorithms; Chapter 9. Two example problems; Chapter 10. Comparison of preconditioners; Chapter 11. Incomplete decompositions; Chapter 12. Multigrid and domain decomposition methods | ||
| 500 | |a 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 | ||
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Datensatz im Suchindex
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| indexdate | 2024-07-10T00:10:18Z |
| institution | BVB |
| isbn | 089871396X 9780898713961 |
| language | English |
| lccn | 97023271 |
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| publishDateSearch | 1997 |
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| series | Frontiers in applied mathematics |
| series2 | Frontiers in applied mathematics |
| spelling | Greenbaum, Anne 1951- Verfasser (DE-588)1022363387 aut Iterative methods for solving linear systems Anne Greenbaum Philadelphia, Pa. Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) 1997 1 Online-Ressource (xiii, 220 Seiten) txt rdacontent c rdamedia cr rdacarrier Frontiers in applied mathematics 17 Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references (s. 205-212) and index List of algorithms -- Preface -- Chapter 1. Introduction: brief overview of the state of the art -- Part I. Krylov subspace approximations. Chapter 2. Some iteration methods: simple iteration; Chapter 3. Error bounds for CG, MINRES, and GMRES: Hermitian problems-CG and MINRES; Chapter 4. Effects of finite precision arithmetic: some numerical examples; Chapter 5. BiCG and related methods: the two-sided Lanczos algorithm; Chapter 6. Is there a short recurrence for a near-optimal approximation?; Chapter 7. Miscellaneous issues -- Part II. Preconditioners. Chapter 8. Overview and preconditioned algorithms; Chapter 9. Two example problems; Chapter 10. Comparison of preconditioners; Chapter 11. Incomplete decompositions; Chapter 12. Multigrid and domain decomposition methods 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 Iterative methods (Mathematics) Equations, Simultaneous / Numerical solutions Iteration (DE-588)4123457-1 gnd rswk-swf Lineares Gleichungssystem (DE-588)4035826-4 gnd rswk-swf Lineares Gleichungssystem (DE-588)4035826-4 s Iteration (DE-588)4123457-1 s DE-604 Erscheint auch als Druck-Ausgabe, Paperback 089871396X Erscheint auch als Druck-Ausgabe, Paperback 9780898713961 Frontiers in applied mathematics 17 (DE-604)BV047220606 17 https://doi.org/10.1137/1.9781611970937 Verlag Volltext |
| spellingShingle | Greenbaum, Anne 1951- Iterative methods for solving linear systems Frontiers in applied mathematics Iterative methods (Mathematics) Equations, Simultaneous / Numerical solutions Iteration (DE-588)4123457-1 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd |
| subject_GND | (DE-588)4123457-1 (DE-588)4035826-4 |
| title | Iterative methods for solving linear systems |
| title_auth | Iterative methods for solving linear systems |
| title_exact_search | Iterative methods for solving linear systems |
| title_full | Iterative methods for solving linear systems Anne Greenbaum |
| title_fullStr | Iterative methods for solving linear systems Anne Greenbaum |
| title_full_unstemmed | Iterative methods for solving linear systems Anne Greenbaum |
| title_short | Iterative methods for solving linear systems |
| title_sort | iterative methods for solving linear systems |
| topic | Iterative methods (Mathematics) Equations, Simultaneous / Numerical solutions Iteration (DE-588)4123457-1 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd |
| topic_facet | Iterative methods (Mathematics) Equations, Simultaneous / Numerical solutions Iteration Lineares Gleichungssystem |
| url | https://doi.org/10.1137/1.9781611970937 |
| volume_link | (DE-604)BV047220606 |
| work_keys_str_mv | AT greenbaumanne iterativemethodsforsolvinglinearsystems |