Afternotes goes to graduate school: lectures on advanced numerical analysis ; a series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
Siam
1998
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 245 S. graph. Darst. |
| ISBN: | 0898714044 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804126779551514624 |
|---|---|
| adam_text | G. W. STEWART UNIVERSITY OF MARYLAND COLLEGE PARK, MARYLAND AFTERNOTES
GOES TO SCHOOL LECTURES ON ADVANCED NUMERICAL ANALYSIS A SERIES OF
LECTURES ON ADVANCED NUMERICAL ANALYSIS PRESENTED AT THE UNIVERSITY OF
MARYLAND AT COLLEGE PARK AND RECORDED AFTER THE FACT. SOCIETY FOR
INDUSTRIAL AND APPLIED MATHEMATICS PHILADELPHIA CONTENTS PREFACE XI
APPROXIMATION 1 LECTURE 1 3 GENERAL OBSERVATIONS T 3 DECLINE AND FALL 3
THE LINEAR SINE 6 APPROXIMATION IN NORMED LINEAR SPACES 7 SIGNIFICANT
DIFFERENCES 9 LECTURE 2 11 THE SPACE C[0,1] 11 EXISTENCE OF BEST
APPROXIMATIONS 12 UNIQUENESS OF BEST APPROXIMATIONS 12 CONVERGENCE IN
C[0,1] 12 THE WEIERSTRASS APPROXIMATION THEOREM 13 BERNSTEIN POLYNOMIALS
14 COMMENTS 16 LECTURE 3 17 CHEBYSHEV APPROXIMATION 17 UNIQUENESS 20
CONVERGENCE OF CHEBYSHEV APPROXIMATIONS 21 RATES OF CONVERGENCE:
JACKSON S THEOREM 21 LECTURE 4 23 A THEOREM OF DE LA VALLEE POUSSIN 23 A
GENERAL APPROXIMATION STRATEGY 24 CHEBYSHEV POLYNOMIALS 25 ECONOMIZATION
OF POWER SERIES 26 FAREWELL TO C[A, B] 28 LECTURE 5 31 DISCRETE,
CONTINUOUS, AND WEIGHTED LEAST SQUARES 31 INNER-PRODUCT SPACES 32
QUASI-MATRICES 33 POSITIVE DEFINITE MATRICES 34 THE CAUCHY AND TRIANGLE
INEQUALITIES 35 ORTHOGONALITY 36 THE QR FACTORIZATION 37 LECTURE 6 39
EXISTENCE AND UNIQUENESS OF THE QR FACTORIZATION 39 THE GRAM-SCHMIDT
ALGORITHM 40 PROJECTIONS 41 BEST APPROXIMATION ON INNER-PRODUCT SPACES
43 VI AFTERNOTES GOES TO GRADUATE SCHOOL LECTURE 7 47 EXPANSIONS IN
ORTHOGONAL FUNCTIONS 47 ORTHOGONAL POLYNOMIALS 48 DISCRETE LEAST SQUARES
AND THE QR DECOMPOSITION 52 LECTURE 8 . O 57 HOUSEHOLDER TRANSFORMATIONS
57 ORTHOGONAL TRIANGULARIZATION 59 IMPLEMENTATION 62 COMMENTS ON THE
ALGORITHM 63 SOLVING LEAST SQUARES PROBLEMS 64 LECTURE 9 67 OPERATION
COUNTS 67 THE FROBENIUS AND SPECTRAL NORMS 68 STABILITY OF ORTHOGONAL
TRIANGULARIZATION 69 ERROR ANALYSIS OF THE NORMAL EQUATIONS 70
PERTURBATION OF INVERSES AND LINEAR SYSTEMS 71 PERTURBATION OF
PSEUDOINVERSES AND LEAST SQUARES SOLUTIONS ... 73 SUMMARY 77 LINEAR AND
CUBIC SPLINES 79 LECTURE 10 81 PIECEWISE LINEAR INTERPOLATION 81 THE
ERROR IN L(F) 83 APPROXIMATION IN THE OO-NORM 84 HAT FUNCTIONS 84
INTEGRATION 85 LEAST SQUARES APPROXIMATION 86 IMPLEMENTATION ISSUES 88
LECTURE 11 93 CUBIC SPLINES 93 DERIVATION OF THE CUBIC SPLINE 94 END
CONDITIONS 95 CONVERGENCE 97 LOCALITY 97 EIGENSYSTEMS 103 LECTURE 12 105
A SYSTEM OF DIFFERENTIAL EQUATIONS 105 COMPLEX VECTORS AND MATRICES 106
EIGENVALUES AND EIGENVECTORS 107 EXISTENCE AND UNIQUENESS 108 LEFT
EIGENVECTORS 108 REAL MATRICES 108 CONTENTS VII MULTIPLICITY AND
DEFECTIVE MATRICES 109 FUNCTIONS OF MATRICES 110 SIMILARITY
TRANSFORMATIONS AND DIAGONALIZATION ILL THE SCHUR DECOMPOSITION 112
LECTURE 13 115 REAL SCHUR FORM 115 BLOCK DIAGONALIZATION 116
DIAGONALIZATION 118 JORDAN CANONICAL FORM 119 HERMITIAN MATRICES 120
PERTURBATION OF A SIMPLE EIGENVALUE 120 LECTURE 14 125 A BACKWARD
PERTURBATION RESULT 125 THE RAYLEIGH QUOTIENT 126 POWERS OF MATRICES 127
THE POWER METHOD 131 LECTURE 15 135 THE INVERSE POWER METHOD 135
DERIVATION OF THE QR ALGORITHM 137 LOCAL CONVERGENCE ANALYSIS 139
PRACTICAL CONSIDERATIONS 141 HESSENBERG MATRICES 142 LECTURE 16 145
REDUCTION TO HESSENBERG FORM 145 THE HESSENBERG QR ALGORITHM 147 RETURN
TO UPPER HESSENBERG 149 LECTURE 17 151 THE IMPLICIT DOUBLE SHIFT 151
SOME IMPLEMENTATION DETAILS 153 THE SINGULAR VALUE DECOMPOSITION 155
LECTURE 18 157 RANK AND SCHMIDT S THEOREM 157 COMPUTATIONAL
CONSIDERATIONS 158 REDUCTION TO BIDIAGONAL FORM 159 PLANE ROTATIONS 161
THE IMPLICIT QR ALGORITHM FOR SINGULAR VALUES 162 KRYLOV SEQUENCE
METHODS 165 LECTURE 19 167 INTRODUCTION 167 INVARIANT SUBSPACES 167
KRYLOV SUBSPACES 170 ARNOLDI DECOMPOSITIONS 171 VIII AFTERNOTES GOES TO
GRADUATE SCHOOL IMPLICIT RESTARTING 173 -DEFLATION 174 LECTURE 20 177
THE LANCZOS ALGORITHM 177 RELATION TO ORTHOGONAL POLYNOMIALS 179
GOLUB-KAHAN-LANCZOS BIDIAGONALIZATION 180 LECTURE 21 183 LINEAR SYSTEMS,
ERRORS, AND RESIDUALS 183 DESCENDING TO A SOLUTION 183 CONJUGATE
DIRECTIONS 185 THE METHOD OF CONJUGATE GRADIENTS 187 TERMINATION 190
LECTURE 22 191 OPERATION COUNTS AND STORAGE REQUIREMENTS 191 CONJUGATE
GRADIENTS AS AN ITERATIVE METHOD 191 CONVERGENCE IN THE A-NORM 191
MONOTONE CONVERGENCE IN THE 2-NORM 194 LECTURE 23 197 PRECONDITIONED
CONJUGATE GRADIENTS 197 PRECONDITIONERS 199 INCOMPLETE LU
PRECONDITIONERS 201 LECTURE 24 205 DIAGONALLY DOMINANT MATRICES 205
RETURN TO INCOMPLETE FACTORIZATION 210 ITERATIONS, LINEAR AND NONLINEAR
213 LECTURE 25 215 SOME CLASSICAL ITERATIONS 215 SPLITTINGS AND
ITERATIVE METHODS 217 CONVERGENCE 218 IRREDUCIBILITY 218 SPLITTINGS OF
IRREDUCIBLY DIAGONALLY DOMINANT MATRICES 219 M-MATRICES AND POSITIVE
DEFINITE MATRICES 221 LECTURE 26 223 LINEAR AND NONLINEAR 223 CONTINUITY
AND DERIVATIVES 224 THE FIXED-POINT ITERATION 225 LINEAR AND NONLINEAR
ITERATIONS COMPARED 227 RATES OF CONVERGENCE 227 NEWTON S METHOD 228 THE
CONTRACTIVE MAPPING THEOREM 229 BIBLIOGRAPHY 233 CONTENTS INTRODUCTION
233 BIBLIOGRAPHY 233 INDEX 237
|
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| author | Stewart, Gilbert W. |
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| callnumber-raw | QA297.S784 1997 |
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| dewey-full | 519.4 |
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| dewey-search | 519.4 |
| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:22:53Z |
| institution | BVB |
| isbn | 0898714044 |
| language | English |
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| owner_facet | DE-29T DE-91G DE-BY-TUM DE-83 |
| physical | XII, 245 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Siam |
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| spelling | Stewart, Gilbert W. Verfasser aut Afternotes goes to graduate school lectures on advanced numerical analysis ; a series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact G. W. Stewart Philadelphia Siam 1998 XII, 245 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008242609&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stewart, Gilbert W. Afternotes goes to graduate school lectures on advanced numerical analysis ; a series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | Afternotes goes to graduate school lectures on advanced numerical analysis ; a series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact |
| title_auth | Afternotes goes to graduate school lectures on advanced numerical analysis ; a series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact |
| title_exact_search | Afternotes goes to graduate school lectures on advanced numerical analysis ; a series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact |
| title_full | Afternotes goes to graduate school lectures on advanced numerical analysis ; a series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact G. W. Stewart |
| title_fullStr | Afternotes goes to graduate school lectures on advanced numerical analysis ; a series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact G. W. Stewart |
| title_full_unstemmed | Afternotes goes to graduate school lectures on advanced numerical analysis ; a series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact G. W. Stewart |
| title_short | Afternotes goes to graduate school |
| title_sort | afternotes goes to graduate school lectures on advanced numerical analysis a series of lectures on advanced numerical analysis presented at the university of maryland at college park and recorded after the fact |
| title_sub | lectures on advanced numerical analysis ; a series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact |
| topic | Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Numerical analysis Numerische Mathematik |
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