Fundamentals of matrix computations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Wiley-Interscience
2002
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| Ausgabe: | 2. ed. |
| Schriftenreihe: | Pure and applied mathematics
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Table of contents Inhaltsverzeichnis |
| Beschreibung: | XIII, 618 S. graph. Darst. |
| ISBN: | 0471213942 9780471213949 |
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Datensatz im Suchindex
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| adam_text | FUNDAMENTALS OF MATRIX COMPUTATIONS SECOND EDITION DAVID S. WATKINS
WILEY INTERSGIENCE A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS
PREFACE IX ACKNOWLEDGMENTS XIII 1 GAUSSIAN ELIMINATION AND ITS VARIANTS
1 1.1 MATRIX MULTIPLICATION ; 1 1.2 SYSTEMS OF LINEAR EQUATIONS 11 1.3
TRIANGULAR SYSTEMS 23 1.4 POSITIVE DEFINITE SYSTEMS; CHOLESKY
DECOMPOSITION 32 1.5 BANDED POSITIVE DEFINITE SYSTEMS 54 1.6 SPARSE
POSITIVE DEFINITE SYSTEMS 63 1.7 GAUSSIAN ELIMINATION AND THE LU
DECOMPOSITION 70 1.8 GAUSSIAN ELIMINATION WITH PIVOTING 93 1.9 SPARSE
GAUSSIAN ELIMINATION 106 2 SENSITIVITY OF LINEAR SYSTEMS 111 2.1 VECTOR
AND MATRIX NORMS 112 2.2 CONDITION NUMBERS 120 W CONTENTS 2.3 PERTURBING
THE COEFFICIENT MATRIX 133 2.4 A POSTERIORI ERROR ANALYSIS USING THE
RESIDUAL 137 2.5 ROUNDOFF ERRORS; BACKWARD STABILITY 139 2.6 PROPAGATION
OF ROUNDOFF ERRORS 148 2.7 BACKWARD ERROR ANALYSIS OF GAUSSIAN
ELIMINATION 157 2.8 SCALING 171 2.9 COMPONENTWISE SENSITIVITY ANALYSIS
175 3 THE LEAST SQUARES PROBLEM 181 3.1 THE DISCRETE LEAST SQUARES
PROBLEM 181 3.2 ORTHOGONAL MATRICES, ROTATORS, AND REFLECTORS 185 3.3
SOLUTION OF THE LEAST SQUARES PROBLEM 212 3.4 THE GRAM-SCHMIDT PROCESS
220 3.5 GEOMETRIC APPROACH 239 3.6 UPDATING THE QR DECOMPOSITION 249 4
THE SINGULAR VALUE DECOMPOSITION 261 4.1 INTRODUCTION 262 4.2 SOME BASIC
APPLICATIONS OF SINGULAR VALUES 266 4.3 THE SVD AND THE LEAST SQUARES
PROBLEM 275 4.4 SENSITIVITY OF THE LEAST SQUARES PROBLEM 281 5
EIGENVALUES AND EIGENVECTORS I 289 5.1 SYSTEMS OF DIFFERENTIAL EQUATIONS
289 5.2 BASIC FACTS 305 5.3 THE POWER METHOD AND SOME SIMPLE EXTENSIONS
314 5.4 SIMILARITY TRANSFORMS 334 5.5 *- REDUCTION TO HESSENBERG AND
TRIDIAGONAL FORMS 349 5.6 THE QR ALGORITHM 356 5.7 IMPLEMENTATION OF THE
QR ALGORITHM 372 5.8 USE OF THE QR ALGORITHM TO CALCULATE EIGENVECTORS
392 5.9 THE SVD REVISITED 396 CONTENTS VII 6 EIGENVALUES AND
EIGENVECTORS II 413 6.1 EIGENSPACES AND INVARIANT SUBSPACES 413 6.2
SUBSPACE ITERATION, SIMULTANEOUS ITERATION, AND THE QR ALGORITHM 420 6.3
EIGENVALUES OF LARGE, SPARSE MATRICES, I 433 6.4 EIGENVALUES OF LARGE,
SPARSE MATRICES, II 451 6.5 SENSITIVITY OF EIGENVALUES AND EIGENVECTORS
462 6.6 METHODS FOR THE SYMMETRIC EIGENVALUE PROBLEM 476 6.7 THE
GENERALIZED EIGENVALUE PROBLEM 502 7 ITERATIVE METHODS FOR LINEAR
SYSTEMS 521 7.1 A MODEL PROBLEM 521 7.2 THE CLASSICAL ITERATIVE METHODS
530 7.3 CONVERGENCE OF ITERATIVE METHODS 544 7.4 DESCENT METHODS;
STEEPEST DESCENT 559 7.5 PRECONDITIONERS 571 7.6 THE CONJUGATE-GRADIENT
METHOD 576 7.7 DERIVATION OF THE CG ALGORITHM 581 7.8 CONVERGENCE OF THE
CG ALGORITHM 590 7.9 INDEFINITE AND NONSYMMETRIC PROBLEMS 596 APPENDIX
SOME SOURCES OF SOFTWARE FOR MATRIX COMPUTATIONS 603 REFERENCES 605
INDEX 611 INDEX OFMATLAB TERMS 617
|
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| 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 |
| edition | 2. ed. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:03:21Z |
| institution | BVB |
| isbn | 0471213942 9780471213949 |
| language | English |
| lccn | 2002071332 |
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| physical | XIII, 618 S. graph. Darst. |
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| series2 | Pure and applied mathematics |
| spelling | Watkins, David S. Verfasser aut Fundamentals of matrix computations David S. Watkins 2. ed. New York Wiley-Interscience 2002 XIII, 618 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics Matrices Métodos numéricos de álgebra linear larpcal Sistemas lineares larpcal Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Matrizenrechnung (DE-588)4126963-9 s DE-604 http://www3.interscience.wiley.com/cgi-bin/booktext/109855329/BOOKPDFSTART Inhaltsverzeichnis http://www.loc.gov/catdir/toc/wiley023/2002071332.html Table of contents HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009891341&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Watkins, David S. Fundamentals of matrix computations Matrices Métodos numéricos de álgebra linear larpcal Sistemas lineares larpcal Matrizenrechnung (DE-588)4126963-9 gnd |
| subject_GND | (DE-588)4126963-9 (DE-588)4123623-3 |
| title | Fundamentals of matrix computations |
| title_auth | Fundamentals of matrix computations |
| title_exact_search | Fundamentals of matrix computations |
| title_full | Fundamentals of matrix computations David S. Watkins |
| title_fullStr | Fundamentals of matrix computations David S. Watkins |
| title_full_unstemmed | Fundamentals of matrix computations David S. Watkins |
| title_short | Fundamentals of matrix computations |
| title_sort | fundamentals of matrix computations |
| topic | Matrices Métodos numéricos de álgebra linear larpcal Sistemas lineares larpcal Matrizenrechnung (DE-588)4126963-9 gnd |
| topic_facet | Matrices Métodos numéricos de álgebra linear Sistemas lineares Matrizenrechnung Lehrbuch |
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