Parameter free iterative linear solvers: [with 11 tables]
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin
Akad.-Verl.
1996
|
| Edition: | 1. ed. |
| Series: | Mathematical research
97 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 194 - 213 |
| Physical Description: | 217 S. graph. Darst. |
| ISBN: | 3055017633 |
Staff View
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| 245 | 1 | 0 | |a Parameter free iterative linear solvers |b [with 11 tables] |c Rüdiger Weiss |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1996 | |
| 300 | |a 217 S. |b graph. Darst. | ||
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| 490 | 1 | |a Mathematical research |v 97 | |
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Record in the Search Index
| _version_ | 1804125340858056704 |
|---|---|
| adam_text | Contents
1 Necessities and Criterions 11
2 Introduction to Iterative Methods 14
2.1 Iterates, Residuals and Errors 14
2.2 Classical Iterative Methods 1G
2.2.1 Matrix Splittings 17
2.2.2 Method of Steepest Descent 19
2.2.3 Classical Conjugate Gradients (CG) 21
2.2.4 Review of Classical Iterative Methods 27
3 Orthogonalization Methods 28
3.1 General Concept 28
3.2 Convergence and Geometric Properties 31
3.3 Matrix Notation and Short Recurrences 39
4 Krylov Subspace Methods 43
4.1 Conjugate Krylov Subspace Methods (CKS) 44
4.1.1 The Lanczos Connection 45
4.1.2 Convergence Properties • !
4.1.3 Short Recurrences 59
4.1.4 Generalized Conjugate Gradient Methods 62
4.1.5 Biconjugate Gradient based Methods 70
4.1.G Rank j Updates 91
4.1.7 Overview of CKS methods 97
4.1.8 Poly and Hybrid Algorithms 101
4.2 Generalized Minimal Error Methods 102
4.3 Broyden and Eirola Xovanlinna Methods 107
4.4 Classification in Terms of Orthogonalization Methods 108
4.4.1 Special Methods 108
4.4.2 Relations between Methods 115
4.5 A Sample Problem 116
4.6 Discussion 121
8 Contents
5 Transformation of Methods 131
5.1 Residual Minimizing Smoothing 132
5.2 Quasi Residual Smoothing 139
5.3 Error Minimizing Smoothing 141
5.4 Review and Comparison of Smoothing 143
6 Preconditioning 145
6.1 Constant Preconditioning 145
6.2 Step Dependent Preconditioning 147
6.3 Preconditioned Orthogonalization Methods 150
6.4 Overview of Preconditioners 154
6.5 Special Preconditioners 154
6.5.1 Normalization 155
6.5.2 Polynomial Preconditioners 158
6.5.3 Normal Equations 159
6.5.4 Incomplete Lf/ Decomposition (ILU) 159
6.5.5 Incomplete Cholesky (IC) 161
6.5.6 Incomplete (^ Decomposition (IQR) 162
6.5.7 Incomplete Gauss Jordan 163
6.5.8 Incomplete Probenius Inverse 165
6.5.9 Projection Methods 166
6.5.10 Iterative Methods as Preconditioners 167
6.5.11 Multi Level Methods 167
6.6 Discussion 171
7 Numerical Stability 174
7.1 Arithmetic and Accuracy 174
7.2 Variants and Different Implementations 175
8 Efficiency on Supercomputers 178
8.1 Vectorization and Parallelization 178
8.2 Latency Hiding 179
8.3 Scalability 179
8.4 Matrix Vector Multiplication 180
8.5 Dot Products 182
9 Remarks and Annotations 185
9.1 Review and Practical Advices 185
9.2 Open Questions and Trends 187
Contents 9
Time Table 190
Notation 191
Bibliography 194
Index 214
|
| any_adam_object | 1 |
| author | Weiss, Rüdiger |
| author_facet | Weiss, Rüdiger |
| author_role | aut |
| author_sort | Weiss, Rüdiger |
| author_variant | r w rw |
| building | Verbundindex |
| bvnumber | BV010853807 |
| 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 858 SK 640 SK 915 SK 920 |
| classification_tum | MAT 657f |
| ctrlnum | (OCoLC)35562976 (DE-599)BVBBV010853807 |
| dewey-full | 003.74 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003.74 |
| dewey-search | 003.74 |
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| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV010853807 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:00:01Z |
| institution | BVB |
| isbn | 3055017633 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007255498 |
| oclc_num | 35562976 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-703 DE-824 DE-20 DE-521 DE-634 DE-83 DE-11 DE-188 |
| physical | 217 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Akad.-Verl. |
| record_format | marc |
| series | Mathematical research |
| series2 | Mathematical research |
| spelling | Weiss, Rüdiger Verfasser aut Parameter free iterative linear solvers [with 11 tables] Rüdiger Weiss 1. ed. Berlin Akad.-Verl. 1996 217 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical research 97 Literaturverz. S. 194 - 213 Iterative methods (Mathematics) Linear systems Lineares Gleichungssystem (DE-588)4035826-4 gnd rswk-swf Lineares System (DE-588)4125617-7 gnd rswk-swf Gradientenverfahren (DE-588)4157995-1 gnd rswk-swf Iteration (DE-588)4123457-1 gnd rswk-swf Lineares Gleichungssystem (DE-588)4035826-4 s Iteration (DE-588)4123457-1 s DE-188 Lineares System (DE-588)4125617-7 s 1\p DE-604 Gradientenverfahren (DE-588)4157995-1 s 2\p DE-604 Mathematical research 97 (DE-604)BV000008585 97 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007255498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Weiss, Rüdiger Parameter free iterative linear solvers [with 11 tables] Mathematical research Iterative methods (Mathematics) Linear systems Lineares Gleichungssystem (DE-588)4035826-4 gnd Lineares System (DE-588)4125617-7 gnd Gradientenverfahren (DE-588)4157995-1 gnd Iteration (DE-588)4123457-1 gnd |
| subject_GND | (DE-588)4035826-4 (DE-588)4125617-7 (DE-588)4157995-1 (DE-588)4123457-1 |
| title | Parameter free iterative linear solvers [with 11 tables] |
| title_auth | Parameter free iterative linear solvers [with 11 tables] |
| title_exact_search | Parameter free iterative linear solvers [with 11 tables] |
| title_full | Parameter free iterative linear solvers [with 11 tables] Rüdiger Weiss |
| title_fullStr | Parameter free iterative linear solvers [with 11 tables] Rüdiger Weiss |
| title_full_unstemmed | Parameter free iterative linear solvers [with 11 tables] Rüdiger Weiss |
| title_short | Parameter free iterative linear solvers |
| title_sort | parameter free iterative linear solvers with 11 tables |
| title_sub | [with 11 tables] |
| topic | Iterative methods (Mathematics) Linear systems Lineares Gleichungssystem (DE-588)4035826-4 gnd Lineares System (DE-588)4125617-7 gnd Gradientenverfahren (DE-588)4157995-1 gnd Iteration (DE-588)4123457-1 gnd |
| topic_facet | Iterative methods (Mathematics) Linear systems Lineares Gleichungssystem Lineares System Gradientenverfahren Iteration |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007255498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000008585 |
| work_keys_str_mv | AT weissrudiger parameterfreeiterativelinearsolverswith11tables |