Holdings: Fundamentals of matrix computations

Fundamentals of matrix computations:

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Main Author:	Watkins, David S. (Author)
Format:	Book
Language:	English
Published:	New York Wiley-Interscience 2002
Edition:	2. ed.
Series:	Pure and applied mathematics
Subjects:	Matrices Métodos numéricos de álgebra linear Sistemas lineares Matrizenrechnung Lehrbuch
Online Access:	Inhaltsverzeichnis Table of contents Inhaltsverzeichnis
Physical Description:	XIII, 618 S. graph. Darst.
ISBN:	0471213942 9780471213949

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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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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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