Computational methods for matrix eigenproblems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Wiley
1973
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 132 S. |
| ISBN: | 0471319155 0471275867 |
Internformat
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| 100 | 1 | |a Gourlay, Alexander R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Computational methods for matrix eigenproblems |c Alexander R. Gourlay ; George A. Watson |
| 264 | 1 | |a London |b Wiley |c 1973 | |
| 300 | |a XI, 132 S. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
1 Introduction
1.1 Introduction ......... 1
1.2 A geometrical example 1
1.3 Small vibrations ........ 3
1.4 An example in information system design . ... 5
1.5 An eigenproblem in non linear optimization ... 6
1.6 An example from mathematical economics ... 7
1.7 A Sturm Liouville problem 8
2 Background theory
2.1 Introduction 11
2.2 Eigenvalues and eigenvectors . . . . . .13
2.3 Similarity transformations 15
2.4 The Jordan canonical form 17
2.5 Some properties of Hermitian matrices . . . .19
2.6 Vector and matrix norms 20
2.7 Theorems on bounds for the eigenvalues .... 22
2.8 Condition of the eigenvalue problem . . . .23
2.9 Stability of similarity transformation methods ... 24
3 Reductions and transformations
3.1 Introduction 26
3.2 Elementary operation matrices 26
3.3 Elementary unitary matrices ...... 28
3.4 Elementary Hermitian matrices 29
3.5 Gaussian elimination 30
3.6 Unitary decomposition of a matrix 31
3.7 Elementary similarity transformations .... 35
4 Methods for the dominant eigenvalue
4.1 Introduction 38
4.2 The power method 38
4.3 Shift of origin 42
4.4 Aitken s acceleration device 43
4.5 The Rayleigh quotient 45
ix
x Contents
5 Methods for the subdominant eigenvalue
5.1 Introduction 47
5.2 Deflation 47
5.3 Simultaneous iteration for real symmetric matrices . . 51
6 Inverse iteration
6.1 Introduction 56
6.2 Inverse iteration for an eigenvalue 56
6.3 Computational procedure for inverse iteration ... 58
7 Jacobi s method
7.1 Introduction 63
7.2 Jacobi s algorithm 64
7.3 Variants of the Jacobi algorithm 67
7.4 The maximizing property of the classical Jacobi algorithm . 68
7.5 Calculation of the eigenvectors 69
8 Givens and Householder s methods
8.1 Introduction 71
8.2 Givens method 71
8.3 Householder s method 74 _
8.4 Reduction of a Hermitian matrix 77
i
9 Eigeasystem of a symmetric tridiagonal matrix
9.1 Introduction 79
9.2 Sturm sequences and bisection 80
9.3 Eigenvectors of a tridiagonal matrix..... 84
10 The LR and QR algorithms
10.1 Introduction ........ 85
10.2 The LR algorithm 85
10.3 The QR algorithm 87
10.4 The QR algorithm with shifts 89
10.5 Analysis of convergence 90
11 Extensions of Jacobi s method
11.1 Introduction 97
11.2 Normal matrices 97 .
11.3 General matrices 99 i
Contents xi
12 Extensions of Givens and Householder s methods
12.1 Introduction 102
12.2 Reduction to upper Hessenberg form .... 102
12.3 Further reduction to tridiagonal form .... 105
12.4 Evaluation of the characteristic polynomial . . . 106
12.5 Computation of the eigenvalues 109
12.6 Evaluation of eigenvectors 113
13 QR algorithm for Hessenberg matrices
13.1 Introduction 114
13.2 QR algorithm for a complex Hessenberg matrix . .114
13.3 Double QR algorithm for a real Hessenberg matrix . . 115
14 Generalized eigenvalue problems
14.1 Introduction 120
14.2 Parameterized matrices 122
14.3 The eigenvalue problem Ax = XBx . . ¦ .122
14.4 The eigenvalue problem ABx — Ax .... 126
15 Available implementations
15.1 Introduction 128
15.2 Library routines 128
References 130
Index 131
|
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| author | Gourlay, Alexander R. Watson, George A. 1942- |
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| ctrlnum | (OCoLC)441782334 (DE-599)BVBBV001953495 |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| genre | Matrix-Eigenproblem gnd |
| genre_facet | Matrix-Eigenproblem |
| id | DE-604.BV001953495 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:37:49Z |
| institution | BVB |
| isbn | 0471319155 0471275867 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001273463 |
| oclc_num | 441782334 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-20 DE-19 DE-BY-UBM DE-706 DE-83 DE-188 |
| owner_facet | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-20 DE-19 DE-BY-UBM DE-706 DE-83 DE-188 |
| physical | XI, 132 S. |
| publishDate | 1973 |
| publishDateSearch | 1973 |
| publishDateSort | 1973 |
| publisher | Wiley |
| record_format | marc |
| spelling | Gourlay, Alexander R. Verfasser aut Computational methods for matrix eigenproblems Alexander R. Gourlay ; George A. Watson London Wiley 1973 XI, 132 S. txt rdacontent n rdamedia nc rdacarrier Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Eigenwertproblem (DE-588)4013802-1 gnd rswk-swf Eigenwert (DE-588)4151200-5 gnd rswk-swf Matrix-Eigenproblem gnd rswk-swf Eigenwertproblem (DE-588)4013802-1 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Matrix Mathematik (DE-588)4037968-1 s Eigenwert (DE-588)4151200-5 s Matrix-Eigenproblem f Numerische Mathematik (DE-588)4042805-9 s Watson, George A. 1942- Verfasser (DE-588)120915499 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001273463&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gourlay, Alexander R. Watson, George A. 1942- Computational methods for matrix eigenproblems Matrix Mathematik (DE-588)4037968-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Eigenwertproblem (DE-588)4013802-1 gnd Eigenwert (DE-588)4151200-5 gnd |
| subject_GND | (DE-588)4037968-1 (DE-588)4042805-9 (DE-588)4128130-5 (DE-588)4013802-1 (DE-588)4151200-5 |
| title | Computational methods for matrix eigenproblems |
| title_auth | Computational methods for matrix eigenproblems |
| title_exact_search | Computational methods for matrix eigenproblems |
| title_full | Computational methods for matrix eigenproblems Alexander R. Gourlay ; George A. Watson |
| title_fullStr | Computational methods for matrix eigenproblems Alexander R. Gourlay ; George A. Watson |
| title_full_unstemmed | Computational methods for matrix eigenproblems Alexander R. Gourlay ; George A. Watson |
| title_short | Computational methods for matrix eigenproblems |
| title_sort | computational methods for matrix eigenproblems |
| topic | Matrix Mathematik (DE-588)4037968-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Eigenwertproblem (DE-588)4013802-1 gnd Eigenwert (DE-588)4151200-5 gnd |
| topic_facet | Matrix Mathematik Numerische Mathematik Numerisches Verfahren Eigenwertproblem Eigenwert Matrix-Eigenproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001273463&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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