Templates for the solution of linear systems: building blocks for iterative methods
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
SIAM
1994
|
| Schriftenreihe: | Software, environments, tools
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 124 S. |
| ISBN: | 0898713285 |
Internformat
MARC
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| 245 | 1 | 0 | |a Templates for the solution of linear systems |b building blocks for iterative methods |c Richard Barrett ... |
| 264 | 1 | |a Philadelphia |b SIAM |c 1994 | |
| 300 | |a XVII, 124 S. | ||
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| 490 | 0 | |a Software, environments, tools | |
| 650 | 4 | |a Ecuaciones - Soluciones numéricas | |
| 650 | 4 | |a Métodos iterativos (Matemáticas) | |
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Datensatz im Suchindex
| _version_ | 1804125175791222784 |
|---|---|
| adam_text | Contents
List of Symbols xi
List of Figures xiii
1 Introduction 1
1.1 Why Use Templates? 2
1.2 What Methods Are Covered? 3
2 Iterative Methods 5
2.1 Overview of the Methods 5
2.2 Stationary Iterative Methods 7
2.2.1 The Jacobi Method 8
2.2.2 The Gauss Seidel Method 9
2.2.3 The Successive Overrelaxation Method 10
2.2.4 The Symmetric Successive Overrelaxation Method 12
2.2.5 Notes and References 12
2.3 Nonstationary Iterative Methods 14
2.3.1 Conjugate Gradient Method (CG) 14
2.3.2 MINRES and SYMMLQ 10
2.3.3 CG on the Normal Equations, CGNE and CGNR 18
2.3.4 Generalized Minimal Residual (GMRES) 18
2.3.5 BiConjugate Gradient (BiCG) 21
2.3.6 Quasi Minimal Residual (QMR) 23
2.3.7 Conjugate Gradient Squared Method (CGS) 25
2.3.8 BiConjugate Gradient Stabilized (Bi CGSTAB) 27
2.3.9 Chebyshev Iteration 28
2.4 Summary of the Methods 29
2.5 A short history of Krylov methods 34
2.6 Survey of recent Krylov methods 35
viii CONTENTS
3 Preconditioners 39
3.1 The why and how 39
3.1.1 Cost trade off 39
3.1.2 Theoretical prerequisites on preconditioners 40
3.2 Jacobi Preconditioning 40
3.2.1 Block Jacobi Methods 41
3.2.2 Discussion 41
3.3 SSOR preconditioning 41
3.4 Incomplete Factorization Preconditioners 42
3.4.1 Creating an incomplete factorization 42
3.4.2 Point incomplete factorizations 43
3.4.3 Block factorization methods 45
3.4.4 Incomplete LQ factorizations 48
3.5 Polynomial preconditioners 48
3.6 Other preconditioners 49
3.6.1 Preconditioning by the symmetric part 49
3.6.2 The use of fast solvers 49
3.6.3 Alternating Direction Implicit methods 50
4 Related Issues 51
4.1 Complex Systems 51
4.2 Stopping Criteria 51
4.2.1 More Details about Stopping Criteria 52
4.2.2 When r^ or ||rW|| is not readily available 55
4.2.3 Estimating ||A 1|| 56
4.2.4 Stopping when progress is no longer being made 56
4.2.5 Accounting for floating point errors 57
4.3 Data Structures 57
4.3.1 Survey of Sparse Matrix Storage Formats 58
4.3.2 Matrix vector products 62
4.3.3 Sparse Incomplete Factorizations 65
4.4 Parallelism 68
4.4.1 Inner products 68
4.4.2 Vector updates 70
4.4.3 Matrix vector products 70
4.4.4 Preconditioning 70
4.4.5 Wavefronts in the Gauss Seidel and Conjugate Gradient methods 71
4.4.6 Blocked operations in the GMRES method 72
CONTENTS ix
5 Remaining topics 73
5.1 The Lanczos Connection 73
5.2 Block Iterative Methods 74
5.3 Reduced System Preconditioning 75
5.4 Domain Decomposition Methods 76
5.4.1 Overlapping Subdomain Methods 76
5.4.2 Non overlapping Subdomain Methods 78
5.4.3 Multiplicative Schwarz Methods 80
5.5 Multigrid Methods 81
5.6 Row Projection Methods 82
A Obtaining the Software 83
B Overview of the BLAS 85
C Glossary 87
C.I Notation 92
Bibliography 95
Index 110
|
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV010698930 |
| classification_rvk | SK 915 ST 600 |
| classification_tum | DAT 310f |
| ctrlnum | (OCoLC)318260263 (DE-599)BVBBV010698930 |
| dewey-full | 511.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.4 |
| dewey-search | 511.4 |
| dewey-sort | 3511.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV010698930 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:57:23Z |
| institution | BVB |
| isbn | 0898713285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007140885 |
| oclc_num | 318260263 |
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| physical | XVII, 124 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | SIAM |
| record_format | marc |
| series2 | Software, environments, tools |
| spelling | Templates for the solution of linear systems building blocks for iterative methods Richard Barrett ... Philadelphia SIAM 1994 XVII, 124 S. txt rdacontent n rdamedia nc rdacarrier Software, environments, tools Ecuaciones - Soluciones numéricas Métodos iterativos (Matemáticas) Sistemas lineales Iteration (DE-588)4123457-1 gnd rswk-swf Lineares Gleichungssystem (DE-588)4035826-4 gnd rswk-swf Template (DE-588)4265509-2 gnd rswk-swf Lineares Gleichungssystem (DE-588)4035826-4 s Iteration (DE-588)4123457-1 s DE-604 Template (DE-588)4265509-2 s Barrett, Richard Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007140885&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Templates for the solution of linear systems building blocks for iterative methods Ecuaciones - Soluciones numéricas Métodos iterativos (Matemáticas) Sistemas lineales Iteration (DE-588)4123457-1 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Template (DE-588)4265509-2 gnd |
| subject_GND | (DE-588)4123457-1 (DE-588)4035826-4 (DE-588)4265509-2 |
| title | Templates for the solution of linear systems building blocks for iterative methods |
| title_auth | Templates for the solution of linear systems building blocks for iterative methods |
| title_exact_search | Templates for the solution of linear systems building blocks for iterative methods |
| title_full | Templates for the solution of linear systems building blocks for iterative methods Richard Barrett ... |
| title_fullStr | Templates for the solution of linear systems building blocks for iterative methods Richard Barrett ... |
| title_full_unstemmed | Templates for the solution of linear systems building blocks for iterative methods Richard Barrett ... |
| title_short | Templates for the solution of linear systems |
| title_sort | templates for the solution of linear systems building blocks for iterative methods |
| title_sub | building blocks for iterative methods |
| topic | Ecuaciones - Soluciones numéricas Métodos iterativos (Matemáticas) Sistemas lineales Iteration (DE-588)4123457-1 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Template (DE-588)4265509-2 gnd |
| topic_facet | Ecuaciones - Soluciones numéricas Métodos iterativos (Matemáticas) Sistemas lineales Iteration Lineares Gleichungssystem Template |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007140885&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT barrettrichard templatesforthesolutionoflinearsystemsbuildingblocksforiterativemethods |