A survey of preconditioned iterative methods:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harlow, Essex
Longman Scientific & Technical
1995
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Pitman research notes in mathematics series
328 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 162 S. graph. Darst. |
| ISBN: | 0582276543 0470235543 |
Internformat
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| 245 | 1 | 0 | |a A survey of preconditioned iterative methods |c Are Magnus Bruaset |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow, Essex |b Longman Scientific & Technical |c 1995 | |
| 300 | |a XII, 162 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman research notes in mathematics series |v 328 | |
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| 650 | 7 | |a Itération (Mathématiques) |2 ram | |
| 650 | 7 | |a Numerieke wiskunde |2 gtt | |
| 650 | 7 | |a grand système |2 inriac | |
| 650 | 7 | |a matrice creuse |2 inriac | |
| 650 | 7 | |a méthode itérative |2 inriac | |
| 650 | 7 | |a sous-espace Krylov |2 inriac | |
| 650 | 7 | |a système linéaire |2 inriac | |
| 650 | 7 | |a équation algébrique |2 inriac | |
| 650 | 4 | |a Equations |x Numerical solutions | |
| 650 | 4 | |a Iterative methods (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804124741937659904 |
|---|---|
| adam_text | Contents
Preface xi
Chapter 1. Introduction 1
1.1 A model problem 1
1.2 Direct versus iterative methods 3
1.3 Outline 8
Chapter 2. Iterative methods based on matrix splittings 10
2.1 Stationary iterative, methods 13
2.1.1 The Jacobi and Gauss Seidel iterations 13
2.1.2 Overrelaxed iterations 15
2.1.3 Extrapolation and other methods 17
2.2 Nonstationary iterative methods 19
2.3 Remarks on implementation and efficiency 22
Chapter 3. Krylov subspace methods 25
3.1 Basic principles of Krylov projection methods 27
3.2 Algorithmic frameworks 33
3.3 Symmetric problems 36
3.3.1 Symmetric positive definite problems 36
3.3.2 Symmetric indefinite problems 42
3.4 Nonsymmetric problems 44
3.4.1 Orthogonalization methods 44
3.4.2 Biorthogonalization and Lanczos algorithms 53
3.4.3 Solving the normal equations 60
3.5 Termination procedures for iterative solvers 62
3.6 Remarks on implementation and efficiency 66
Chapter 4. Preconditioners for linear systems of equations 72
4.1 Basic iterations revisited 73
4.2 Preconditioners based on incomplete factorizations 76
4.2.1 Pointwise incomplete factorizations 77
4.2.2 Blockwise incomplete factorizations 86
4.2.3 Remarks on implementation and efficiency 92
4.3 Preconditioners based on approximate inversion 98
ix
4.3.1 Polynomial approximations 99
4.3.2 Sparse approximate inverses 108
4.3.3 Remarks on implementation and efficiency 110
4.4 Iterative solvers in terms of the PDE 112
4.4.1 Fast direct methods used as preconditioners 113
4.4.2 Multilevel and domain decomposition methods 114
Chapter 5. Epilogue 126
Appendix A. Some notation and useful properties 131
Bibliography 136
Index 159
x
|
| any_adam_object | 1 |
| author | Bruaset, Are Magnus 1963- |
| author_GND | (DE-588)130663867 |
| author_facet | Bruaset, Are Magnus 1963- |
| author_role | aut |
| author_sort | Bruaset, Are Magnus 1963- |
| author_variant | a m b am amb |
| building | Verbundindex |
| bvnumber | BV010321808 |
| callnumber-first | Q - Science |
| callnumber-label | QA297 |
| callnumber-raw | QA297.8 |
| callnumber-search | QA297.8 |
| callnumber-sort | QA 3297.8 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 880 SK 915 |
| classification_tum | MAT 410f |
| ctrlnum | (OCoLC)32199271 (DE-599)BVBBV010321808 |
| dewey-full | 512/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.5 |
| dewey-search | 512/.5 |
| dewey-sort | 3512 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV010321808 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:50:29Z |
| institution | BVB |
| isbn | 0582276543 0470235543 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006869139 |
| oclc_num | 32199271 |
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| owner_facet | DE-12 DE-355 DE-BY-UBR DE-739 DE-703 DE-29T DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-706 DE-83 DE-11 |
| physical | XII, 162 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Longman Scientific & Technical |
| record_format | marc |
| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Bruaset, Are Magnus 1963- Verfasser (DE-588)130663867 aut A survey of preconditioned iterative methods Are Magnus Bruaset 1. publ. Harlow, Essex Longman Scientific & Technical 1995 XII, 162 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 328 Equations - Solutions numériques ram Iteratief oplossen gtt Itération (Mathématiques) ram Numerieke wiskunde gtt grand système inriac matrice creuse inriac méthode itérative inriac sous-espace Krylov inriac système linéaire inriac équation algébrique inriac Equations Numerical solutions Iterative methods (Mathematics) Iteration (DE-588)4123457-1 gnd rswk-swf Schwach besetzte Matrix (DE-588)4056053-3 gnd rswk-swf Lineares Gleichungssystem (DE-588)4035826-4 gnd rswk-swf Lineares System (DE-588)4125617-7 gnd rswk-swf Präkonditionierung (DE-588)4255669-7 gnd rswk-swf Lineares System (DE-588)4125617-7 s Iteration (DE-588)4123457-1 s DE-604 Lineares Gleichungssystem (DE-588)4035826-4 s Schwach besetzte Matrix (DE-588)4056053-3 s Präkonditionierung (DE-588)4255669-7 s Pitman research notes in mathematics series 328 (DE-604)BV000022845 328 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006869139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bruaset, Are Magnus 1963- A survey of preconditioned iterative methods Pitman research notes in mathematics series Equations - Solutions numériques ram Iteratief oplossen gtt Itération (Mathématiques) ram Numerieke wiskunde gtt grand système inriac matrice creuse inriac méthode itérative inriac sous-espace Krylov inriac système linéaire inriac équation algébrique inriac Equations Numerical solutions Iterative methods (Mathematics) Iteration (DE-588)4123457-1 gnd Schwach besetzte Matrix (DE-588)4056053-3 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Lineares System (DE-588)4125617-7 gnd Präkonditionierung (DE-588)4255669-7 gnd |
| subject_GND | (DE-588)4123457-1 (DE-588)4056053-3 (DE-588)4035826-4 (DE-588)4125617-7 (DE-588)4255669-7 |
| title | A survey of preconditioned iterative methods |
| title_auth | A survey of preconditioned iterative methods |
| title_exact_search | A survey of preconditioned iterative methods |
| title_full | A survey of preconditioned iterative methods Are Magnus Bruaset |
| title_fullStr | A survey of preconditioned iterative methods Are Magnus Bruaset |
| title_full_unstemmed | A survey of preconditioned iterative methods Are Magnus Bruaset |
| title_short | A survey of preconditioned iterative methods |
| title_sort | a survey of preconditioned iterative methods |
| topic | Equations - Solutions numériques ram Iteratief oplossen gtt Itération (Mathématiques) ram Numerieke wiskunde gtt grand système inriac matrice creuse inriac méthode itérative inriac sous-espace Krylov inriac système linéaire inriac équation algébrique inriac Equations Numerical solutions Iterative methods (Mathematics) Iteration (DE-588)4123457-1 gnd Schwach besetzte Matrix (DE-588)4056053-3 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Lineares System (DE-588)4125617-7 gnd Präkonditionierung (DE-588)4255669-7 gnd |
| topic_facet | Equations - Solutions numériques Iteratief oplossen Itération (Mathématiques) Numerieke wiskunde grand système matrice creuse méthode itérative sous-espace Krylov système linéaire équation algébrique Equations Numerical solutions Iterative methods (Mathematics) Iteration Schwach besetzte Matrix Lineares Gleichungssystem Lineares System Präkonditionierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006869139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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