Numerical linear algebra for applications in statistics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1998
|
| Series: | Statistics and computing
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 221 S. graph. Darst. |
| ISBN: | 0387985425 |
Staff View
MARC
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Record in the Search Index
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| adam_text | JAMES E. GENTLE NUMERICAL LINEAR ALGEBRA FOR APPLICATIONS IN STATISTICS
WITH 21 ILLUSTRATIONS * - - / SPRINGER CONTENTS PREFACE VN 1 COMPUTER
STORAGE AND MANIPULATION OF DATA 1 1.1 DIGITAL REPRESENTATION OF NUMERIC
DATA 3 1.2 COMPUTER OPERATIONS ON NUMERIC DATA 18 1.3 NUMERICAL
ALGORITHMS AND ANALYSIS 26 EXERCISES 41 2 BASIC VECTOR/MATRIX
COMPUTATIONS 47 2.1 NOTATION, DEFINITIONS, AND BASIC PROPERTIES 48 2.1.1
OPERATIONS ON VECTORS; VECTOR SPACES 48 2.1.2 VECTORS AND MATRICES 52
2.1.3 OPERATIONS ON VECTORS AND MATRICES 55 2.1.4 PARTITIONED MATRICES
58 2.1.5 MATRIX RANK 59 2.1.6 IDENTITY MATRICES 60 2.1.7 INVERSES 61
2.1.8 LINEAR SYSTEMS 62 2.1.9 GENERALIZED INVERSES 63 2.1.10 OTHER
SPECIAL VECTORS AND MATRICES 64 2.1.11 EIGENANALYSIS 67 2.1.12
SIMILARITY TRANSFORMATIONS 69 2.1.13 NORMS 70 2.1.14 MATRIX NORMS 72
2.1.15 ORTHOGONAL TRANSFORMATIONS 74 2.1.16 ORTHOGONALIZATION
TRANSFORMATIONS 74 2.1.17 CONDITION OF MATRICES 75 2.1.18 MATRIX
DERIVATIVES 79 2.2 COMPUTER REPRESENTATIONS AND BASIC OPERATIONS 81
2.2.1 COMPUTER REPRESENTATION OF VECTORS AND MATRICES .... 81 2.2.2
MULTIPLICATION OF VECTORS AND MATRICES 82 EXERCISES 84 XI XII CONTENTS 3
SOLUTION OF LINEAR SYSTEMS 87 3.1 GAUSSIAN ELIMINATION 87 3.2 MATRIX
FACTORIZATIONS 92 3.2.1 LU AND LDU FACTORIZATIONS 92 3.2.2 CHOLESKY
FACTORIZATION 93 3.2.3 QR FACTORIZATION 95 3.2.4 HOUSEHOLDER
TRANSFORMATIONS (REFLECTIONS) 97 3.2.5 GIVENS TRANSFORMATIONS
(ROTATIONS) 99 3.2.6 GRAM-SCHMIDT TRANSFORMATIONS 102 3.2.7 SINGULAR
VALUE FACTORIZATION 102 3.2.8 CHOICE OF DIRECT METHODS 103 3.3 ITERATIVE
METHODS 103 3.3.1 THE GAUSS-SEIDEL METHOD WITH SUCCESSIVE OVERRELAXATION
103 3.3.2 SOLUTION OF LINEAR SYSTEMS AS AN OPTIMIZATION PROBLEM;
CONJUGATE GRADIENT METHODS ^ 104 3.4 NUMERICAL ACCURACY -. 107 3.5
ITERATIVE REFINEMENT 109 3.6 UPDATING A SOLUTION 109 3.7 OVERDETERMINED
SYSTEMS; LEAST SQUARES ILL 3.7.1 FULL RANK COEFFICIENT MATRIX 112 3.7.2
COEFFICIENT MATRIX NOT OF FULL RANK 113 3.7.3 UPDATING A SOLUTION TO AN
OVERDETERMINED SYSTEM . . . .114 3.8 OTHER COMPUTATIONS FOR LINEAR
SYSTEMS 115 3.8.1 RANK DETERMINATION 115 3.8.2 COMPUTING THE DETERMINANT
115 3.8.3 COMPUTING THE CONDITION NUMBER 115 EXERCISES 117 4 COMPUTATION
OF EIGENVECTORS AND EIGENVALUES AND THE SINGULAR VALUE DECOMPOSITION 123
4.1 POWER METHOD 124 4.2 JACOBI METHOD 126 4.3 QR METHOD FOR
EIGENANALYSIS 129 4.4 SINGULAR VALUE DECOMPOSITION 131 EXERCISES 134 5
SOFTWARE FOR NUMERICAL LINEAR ALGEBRA 137 5.1 FORTRAN AND C 138 5.1.1
BLAS 140 5.1.2 FORTRAN AND C LIBRARIES 142 5.1.3 FORTRAN 90 AND 95 146
5.2 INTERACTIVE SYSTEMS FOR ARRAY MANIPULATION 148- 5.2.1 MATLAB 148
5.2.2 S, S-PLUS 151 CONTENTS XIII 5.3 HIGH-PERFORMANCE SOFTWARE 153 5.4
TEST DATA 155 EXERCISES 157 6 APPLICATIONS IN STATISTICS 161 6.1 FITTING
LINEAR MODELS WITH DATA 162 6.2 LINEAR MODELS AND LEAST SQUARES 163
6.2.1 THE NORMAL EQUATIONS AND THE SWEEP OPERATOR 165 6.2.2 LINEAR LEAST
SQUARES SUBJECT TO LINEAR EQUALITY CONSTRAINTS 166 6.2.3 WEIGHTED LEAST
SQUARES 166 6.2.4 UPDATING LINEAR REGRESSION STATISTICS 167 6.2.5 TESTS
OF HYPOTHESES 169 6.2.6 D-OPTIMAL DESIGNS 170 6.3 ILL-CONDITIONING IN
STATISTICAL APPLICATIONS 172 6.4 TESTING THE RANK OF A MATRIX 173 6.5
STOCHASTIC PROCESSES 175 EXERCISES 176 APPENDICES 183 A NOTATION AND
DEFINITIONS 183 B SOLUTIONS AND HINTS FOR SELECTED EXERCISES 191
BIBLIOGRAPHY 197 LITERATURE IN COMPUTATIONAL STATISTICS 198 WORLD WIDE
WEB, NEWS GROUPS, LIST SERVERS, AND BULLETIN BOARDS 199 REFERENCES 202
AUTHOR INDEX 213 SUBJECT INDEX 217
|
| any_adam_object | 1 |
| author | Gentle, James E. 1943- |
| author_GND | (DE-588)126727031 |
| author_facet | Gentle, James E. 1943- |
| author_role | aut |
| author_sort | Gentle, James E. 1943- |
| author_variant | j e g je jeg |
| building | Verbundindex |
| bvnumber | BV012212091 |
| callnumber-first | Q - Science |
| callnumber-label | QA184 |
| callnumber-raw | QA184.G45 1998 |
| callnumber-search | QA184.G45 1998 |
| callnumber-sort | QA 3184 G45 41998 |
| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 620f MAT 657f |
| ctrlnum | (OCoLC)38910515 (DE-599)BVBBV012212091 |
| dewey-full | 512/.5 512/.521 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.5 512/.5 21 |
| dewey-search | 512/.5 512/.5 21 |
| dewey-sort | 3512 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV012212091 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:23:41Z |
| institution | BVB |
| isbn | 0387985425 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008276128 |
| oclc_num | 38910515 |
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| physical | XIII, 221 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series2 | Statistics and computing |
| spelling | Gentle, James E. 1943- Verfasser (DE-588)126727031 aut Numerical linear algebra for applications in statistics James E. Gentle New York [u.a.] Springer 1998 XIII, 221 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics and computing Algèbre linéaire Estatística larpcal Lineaire algebra gtt Lineaire modellen gtt Modèles linéaires (Statistique) Métodos numéricos larpcal Numerieke methoden gtt Numerieke wiskunde gtt Statistiek gtt Statistik Algebras, Linear Linear models (Statistics) Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Lineares Modell (DE-588)4134827-8 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Lineares Modell (DE-588)4134827-8 s Statistik (DE-588)4056995-0 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008276128&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gentle, James E. 1943- Numerical linear algebra for applications in statistics Algèbre linéaire Estatística larpcal Lineaire algebra gtt Lineaire modellen gtt Modèles linéaires (Statistique) Métodos numéricos larpcal Numerieke methoden gtt Numerieke wiskunde gtt Statistiek gtt Statistik Algebras, Linear Linear models (Statistics) Lineare Algebra (DE-588)4035811-2 gnd Statistik (DE-588)4056995-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Lineares Modell (DE-588)4134827-8 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4056995-0 (DE-588)4128130-5 (DE-588)4134827-8 |
| title | Numerical linear algebra for applications in statistics |
| title_auth | Numerical linear algebra for applications in statistics |
| title_exact_search | Numerical linear algebra for applications in statistics |
| title_full | Numerical linear algebra for applications in statistics James E. Gentle |
| title_fullStr | Numerical linear algebra for applications in statistics James E. Gentle |
| title_full_unstemmed | Numerical linear algebra for applications in statistics James E. Gentle |
| title_short | Numerical linear algebra for applications in statistics |
| title_sort | numerical linear algebra for applications in statistics |
| topic | Algèbre linéaire Estatística larpcal Lineaire algebra gtt Lineaire modellen gtt Modèles linéaires (Statistique) Métodos numéricos larpcal Numerieke methoden gtt Numerieke wiskunde gtt Statistiek gtt Statistik Algebras, Linear Linear models (Statistics) Lineare Algebra (DE-588)4035811-2 gnd Statistik (DE-588)4056995-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Lineares Modell (DE-588)4134827-8 gnd |
| topic_facet | Algèbre linéaire Estatística Lineaire algebra Lineaire modellen Modèles linéaires (Statistique) Métodos numéricos Numerieke methoden Numerieke wiskunde Statistiek Statistik Algebras, Linear Linear models (Statistics) Lineare Algebra Numerisches Verfahren Lineares Modell |
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