Lectures on finite precision computations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
SIAM
1996
|
| Schriftenreihe: | Software, environments, tools
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 235 S. graph. Darst. |
| ISBN: | 0898713587 |
Internformat
MARC
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| 100 | 1 | |a Chatelin, Françoise |e Verfasser |0 (DE-588)1022352814 |4 aut | |
| 245 | 1 | 0 | |a Lectures on finite precision computations |c Françoise Chaitin-Chatelin ; Valérie Frayssé |
| 264 | 1 | |a Philadelphia, Pa. |b SIAM |c 1996 | |
| 300 | |a XIV, 235 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Software, environments, tools | |
| 650 | 7 | |a Análise de erros |2 larpcal | |
| 650 | 7 | |a Calcul d'erreur |2 ram | |
| 650 | 7 | |a Calculs numériques - Informatique |2 ram | |
| 650 | 7 | |a Cálculo numérico |2 larpcal | |
| 650 | 7 | |a Processamento eletrônico de dados |2 larpcal | |
| 650 | 7 | |a calculabilité |2 inriac | |
| 650 | 7 | |a précise |2 inriac | |
| 650 | 7 | |a stabilité |2 inriac | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Error analysis (Mathematics) | |
| 650 | 4 | |a Numerical calculations |x Data processing | |
| 700 | 1 | |a Frayssé, Valérie |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008544998&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-008544998 | ||
Datensatz im Suchindex
| _version_ | 1804127232055050240 |
|---|---|
| adam_text | Contents
Foreword xi
Preface xiii
Notation xv
1 General Presentation 1
1.1 Coupling 1
1.2 Chaotic computations 2
1.3 Computability in finite precision 2
1.4 Numerical quality of computations 2
1.5 Role of singularities 3
1.6 Spectral instability and nonnormality 3
1.7 Influence on numerical software 4
1.8 Qualitative computing 4
1.9 Experimental mathematics 5
1.10 Sense of errors: For a rehabilitation of finite precision computa¬
tions 5
2 Computability in Finite Precision 7
2.1 Well posed problems 7
2.2 Approximations 8
2.3 Convergence in exact arithmetic 8
2.4 Computability in finite precision 11
2.5 Gaussian elimination 15
2.6 Forward error analysis 17
2.7 The influence of singularities 24
2.8 Numerical stability in exact arithmetic 27
2.9 Computability in finite precision for iterative and approximate
methods 28
2.10 The limit of numerical stability in finite precision 30
2.11 Arithmetically robust convergence 31
2.12 The computed logistic 33
2.13 Bibliographical comments 37
vii
viii CONTENTS
3 Measures of Stability for Regular Problems 39
3.1 Choice of data and class of perturbations 40
3.2 Choice of norms: Scaling 40
3.3 Conditioning of regular problems 43
3.4 Simple roots of polynomials 45
3.5 Factorizations of a complex matrix 48
3.6 Solving linear systems 49
3.7 Functions of a square matrix 52
3.8 Concluding remarks 55
3.9 Bibliographical comments 56
4 Computation in the Neighbourhood of a Singularity 57
4.1 Singular problems that are well posed 57
4.2 Condition numbers of Holder singularities 58
4.3 Computability of ill posed problems 60
4.4 Singularities of z h A — zl 60
4.5 Distances to singularity 65
4.6 Unfolding of singularity 69
4.7 Spectral portraits 69
4.8 Bibliographical comments 70
5 Arithmetic Quality of Reliable Algorithms 71
5.1 Forward and backward analyses 71
5.2 Backward error 71
5.3 Quality of reliable software 72
5.4 Formulae for backward errors 74
5.5 Influence of the class of perturbations 78
5.6 Iterative refinement for backward stability 82
5.7 Robust reliability and arithmetic quality 84
5.8 Bibliographical comments 85
6 Numerical Stability in Finite Precision 87
6.1 Iterative and approximate methods 87
6.2 Numerical convergence of iterative solvers 87
6.3 Stopping criteria in finite precision 89
6.4 Robust convergence 91
6.5 The computed logistic revisited 94
6.6 Care of use 95
6.7 Bibliographical comments 96
7 Software Tools for Round off Error Analysis in Algorithms 97
7.1 A historical perspective 97
7.2 Assessment of the quality of numerical software 98
7.3 Backward error analysis in libraries 99
7.4 Sensitivity analysis 99
7.5 Interval analysis 100
CONTENTS ix
7.6 Probabilistic models 100
7.7 Computer algebra 102
7.8 Bibliographical comments 102
8 The Toolbox PRECISE for Computer Experimentation 103
8.1 What is PRECISE? 104
8.2 Module for backward error analysis 105
8.3 Sample size 114
8.4 Backward analysis with PRECISE 115
8.5 Dangerous border and unfolding of a singularity 120
8.6 Summary of module 1 123
8.7 Bibliographical comments 124
9 Experiments with PRECISE 125
9.1 Format of the examples 125
9.2 Backward error analysis for linear systems 126
9.3 Computer unfolding of singularity 136
9.4 Dangerous border and distance to singularity 140
9.5 Roots of polynomials 144
9.6 Eigenvalue problems 150
9.7 Conclusion 157
9.8 Bibliographical comments 157
10 Robustness to Nonnormality 159
10.1 Nonnormality and spectral instability 159
10.2 Nonnormality in physics and technology 164
10.3 Convergence of numerical methods in exact arithmetic 166
10.4 Influence on numerical software 167
10.5 Bibliographical comments 173
11 Qualitative Computing 175
11.1 Sensitivity of pseudosolutions for F(x) = y 176
11.2 Pseudospectra of matrices 177
11.3 Pseudozeroes of polynomials 182
11.4 Divergence portrait for the complex logistic iteration 188
11.5 Qualitative assessment of a Jordan form 189
11.6 Beyond linear perturbation theory 194
11.7 Bibliographical comments 197
12 More Numerical Illustrations with PRECISE 199
Annex: The Toolbox PRECISE with PRECISE 211
Bibliography 219
Index 233
|
| any_adam_object | 1 |
| author | Chatelin, Françoise Frayssé, Valérie |
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| ctrlnum | (OCoLC)33405700 (DE-599)BVBBV012581848 |
| dewey-full | 519.4/0285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4/0285 |
| dewey-search | 519.4/0285 |
| dewey-sort | 3519.4 3285 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012581848 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:30:04Z |
| institution | BVB |
| isbn | 0898713587 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008544998 |
| oclc_num | 33405700 |
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| owner_facet | DE-91G DE-BY-TUM DE-706 DE-83 |
| physical | XIV, 235 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | SIAM |
| record_format | marc |
| series2 | Software, environments, tools |
| spelling | Chatelin, Françoise Verfasser (DE-588)1022352814 aut Lectures on finite precision computations Françoise Chaitin-Chatelin ; Valérie Frayssé Philadelphia, Pa. SIAM 1996 XIV, 235 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Software, environments, tools Análise de erros larpcal Calcul d'erreur ram Calculs numériques - Informatique ram Cálculo numérico larpcal Processamento eletrônico de dados larpcal calculabilité inriac précise inriac stabilité inriac Datenverarbeitung Error analysis (Mathematics) Numerical calculations Data processing Frayssé, Valérie Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008544998&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chatelin, Françoise Frayssé, Valérie Lectures on finite precision computations Análise de erros larpcal Calcul d'erreur ram Calculs numériques - Informatique ram Cálculo numérico larpcal Processamento eletrônico de dados larpcal calculabilité inriac précise inriac stabilité inriac Datenverarbeitung Error analysis (Mathematics) Numerical calculations Data processing |
| title | Lectures on finite precision computations |
| title_auth | Lectures on finite precision computations |
| title_exact_search | Lectures on finite precision computations |
| title_full | Lectures on finite precision computations Françoise Chaitin-Chatelin ; Valérie Frayssé |
| title_fullStr | Lectures on finite precision computations Françoise Chaitin-Chatelin ; Valérie Frayssé |
| title_full_unstemmed | Lectures on finite precision computations Françoise Chaitin-Chatelin ; Valérie Frayssé |
| title_short | Lectures on finite precision computations |
| title_sort | lectures on finite precision computations |
| topic | Análise de erros larpcal Calcul d'erreur ram Calculs numériques - Informatique ram Cálculo numérico larpcal Processamento eletrônico de dados larpcal calculabilité inriac précise inriac stabilité inriac Datenverarbeitung Error analysis (Mathematics) Numerical calculations Data processing |
| topic_facet | Análise de erros Calcul d'erreur Calculs numériques - Informatique Cálculo numérico Processamento eletrônico de dados calculabilité précise stabilité Datenverarbeitung Error analysis (Mathematics) Numerical calculations Data processing |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008544998&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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