Software for roundoff analysis of matrix algorithms:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Academic Press
1980
|
| Series: | Computer science and applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 151 S. graph.Darst. |
| ISBN: | 0124972500 |
Staff View
MARC
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| 245 | 1 | 0 | |a Software for roundoff analysis of matrix algorithms |c Webb Miller ; Celia Wrathall |
| 264 | 1 | |a New York u.a. |b Academic Press |c 1980 | |
| 300 | |a X, 151 S. |b graph.Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Computer science and applied mathematics | |
| 650 | 4 | |a Analyse numérique matricielle - Informatique | |
| 650 | 4 | |a Erreurs d'arrondi - Informatique | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Matrices |x Data processing | |
| 650 | 4 | |a Roundoff errors |x Data processing | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface vii
1 SOME ELEMENTS OF ERROR ANALYSIS
1.1 Introduction 1
1.2 Errors in Computation 4
1.3 The Machine Rounding Unit 13
1.4 Backward Roundoff Analysis 16
1.5 Case Study 1: Triangular Matrix Inversion 22
1.6 Case Study 2: The Normal Equations 26
1.7 Case Study 3: The Hat Matrix 28
Notes and References 35
2 CONCEPTS FROM LINEAR ALGEBRA AND ANALYSIS
2.1 Introduction 37
2.2 Elementary Concepts from Analysis 38
2.3 Wilkinson Numbers 42
2.4 Norms 44
2.5 Linear Transformations 47
2.6 Minkowski Sums and Cartesian Products 52
2.7 Computing Wilkinson Numbers 53
2.8 Operator Norms 58
2.9 Differentiation 59
3 DIRECTED GRAPHS
3.1 Introduction 63
3.2 Arithmetic Graphs 66
3.3 The Weak Composition Model 71
3.4 Sums of Path Products 73
3.5 Differentiation in Graphs 77
3.6 Improved Calculation of Derivatives 82
v
vj Contents
4 SOFTWARE FOR ROUNDOFF ANALYSIS
4.1 Introduction 85
4.2 Rounding and Perturbations of the Computational
Problem 86
4.3 Comparing Rounding Errors with Problem
Sensitivity 89
4.4 The Weak Composition Model 94
4.5 Reverse Condition Numbers 96
4.6 Comparing Two Algorithms 103
4.7 Using the Software Package 105
5 CASE STUDIES
5.1 Case Study 4: The Cholesky Factorization 113
5.2 Case Study 5: Gaussian Elimination 116
5.3 Case Study 6: Gaussian Elimination with Iterative
Improvement 120
5.4 Case Study 7: Gauss Jordan Elimination 121
5.5 Case Study 8: Householder Transformations for
Least Squares Problems 122
5.6 Case Study 9: Rational QR Methods 125
5.7 Case Study 10: Downdating the QR Factorization 128
5.8 Case Study 11: The Characteristic Polynomial 129
5.9 Case Study 12: Representations of Symmetric
Matrices 131
5.10 Case Study 13: Variants of the Gram Schmidt
Method 134
5.11 Case Study 14: Cholesky Factors after Rank One
Modifications 137
Appendix: Fast Givens Transformations 141
Bibliography 143
Index 149
|
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| ctrlnum | (OCoLC)6200093 (DE-599)BVBBV001997840 |
| dewey-full | 512.9/434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 |
| dewey-search | 512.9/434 |
| dewey-sort | 3512.9 3434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| genre | Matrixalgorithmus gnd |
| genre_facet | Matrixalgorithmus |
| id | DE-604.BV001997840 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:37Z |
| institution | BVB |
| isbn | 0124972500 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001303194 |
| oclc_num | 6200093 |
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| owner_facet | DE-91G DE-BY-TUM DE-384 DE-739 DE-20 DE-29T DE-83 |
| physical | X, 151 S. graph.Darst. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Academic Press |
| record_format | marc |
| series2 | Computer science and applied mathematics |
| spelling | Miller, Webb 1892-1940 Verfasser (DE-588)126202397 aut Software for roundoff analysis of matrix algorithms Webb Miller ; Celia Wrathall New York u.a. Academic Press 1980 X, 151 S. graph.Darst. txt rdacontent n rdamedia nc rdacarrier Computer science and applied mathematics Analyse numérique matricielle - Informatique Erreurs d'arrondi - Informatique Datenverarbeitung Matrices Data processing Roundoff errors Data processing Rundungsfehler (DE-588)4465287-2 gnd rswk-swf Software (DE-588)4055382-6 gnd rswk-swf Matrixalgorithmus gnd rswk-swf Rundungsfehler (DE-588)4465287-2 s Matrixalgorithmus f Software (DE-588)4055382-6 s DE-604 Wrathall, Celia Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001303194&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Miller, Webb 1892-1940 Wrathall, Celia Software for roundoff analysis of matrix algorithms Analyse numérique matricielle - Informatique Erreurs d'arrondi - Informatique Datenverarbeitung Matrices Data processing Roundoff errors Data processing Rundungsfehler (DE-588)4465287-2 gnd Software (DE-588)4055382-6 gnd |
| subject_GND | (DE-588)4465287-2 (DE-588)4055382-6 |
| title | Software for roundoff analysis of matrix algorithms |
| title_auth | Software for roundoff analysis of matrix algorithms |
| title_exact_search | Software for roundoff analysis of matrix algorithms |
| title_full | Software for roundoff analysis of matrix algorithms Webb Miller ; Celia Wrathall |
| title_fullStr | Software for roundoff analysis of matrix algorithms Webb Miller ; Celia Wrathall |
| title_full_unstemmed | Software for roundoff analysis of matrix algorithms Webb Miller ; Celia Wrathall |
| title_short | Software for roundoff analysis of matrix algorithms |
| title_sort | software for roundoff analysis of matrix algorithms |
| topic | Analyse numérique matricielle - Informatique Erreurs d'arrondi - Informatique Datenverarbeitung Matrices Data processing Roundoff errors Data processing Rundungsfehler (DE-588)4465287-2 gnd Software (DE-588)4055382-6 gnd |
| topic_facet | Analyse numérique matricielle - Informatique Erreurs d'arrondi - Informatique Datenverarbeitung Matrices Data processing Roundoff errors Data processing Rundungsfehler Software Matrixalgorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001303194&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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