Numerical analysis of symmetric matrices:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Englewood Cliffs, N.J.
Prentice-Hall
1973
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| Series: | Prentice-Hall series in automatic computation
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | EST: Numerik symmetrischer Matrizen <engl.> |
| Physical Description: | 278 S. |
Staff View
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Record in the Search Index
| _version_ | 1804123404968656896 |
|---|---|
| adam_text | CONTENTS
1 EUCLIDIAN VECTOR SPACE: NORMS, QUADRATIC FORMS,
SYMMETRIC DEFINITE SYSTEMS OF EQUATIONS 1
1 1 The Linear Vector Space; Matrices 1
1 2 Norms; Condition of a Matrix 7
1 3 Necessary and Sufficient Conditions for the
Definiteness of a Quadratic Form 15
1 4 Symmetric Triangular Decomposition: Cholesky s
Method 23
2 RELAXATION METHODS 38
2 1 Fundamentals in Relaxation Calculations 38
2 2 The Successive Displacement Method 42
2 3 Gradient Methods 63
2 4 The Method of Conjugate Gradients 68
3 DATA FITTING 76
3 1 Formulation of the Problem 76
3 2 Unconstrained Fitting 81
3 3 Constrained Fitting 86
3 4 The Method of Orthogonalization in Data Fitting 92
3 5 The Method of Conjugate Gradients in
Data Fitting 103
4 SYMMETRIC EIGENVALUE PROBLEMS 111
4 1 Eigenvalue Problems of Physics 111
4 2 Criticism of the Characteristic Polynomial 114
4 3 The Principal Axis Theorem 117
4 4 Transformation to Diagonal Form: Simultaneous
Computation of All Eigenvalues 121
4 5 Transformation to Tridiagonal Form:
Sturm Sequences; Computation of Individual
Eigenvalues 136
vii
Viii CONTENTS
4 6 LR Transformation and QD Algorithm:
Calculation of the Smallest Eigenvalues 158
4 7 Vector Iteration: Largest and Smallest Eigenvalues 187
4 8 The Generalized Symmetric Eigenvalue Problem 199
4 9 Resume of Eigenvalue Methods 203
5 BOUNDARY VALUE PROBLEMS, RELAXATION 205
5 1 Boundary Value Problems 205
5 2 Operator Equations and Relaxation 221
5 3 The Eigenvalue Problem 248
APPENDIX: Fortran Subroutine Counterparts
of Algol Procedures 251
BIBLIOGRAPHY 265
INDEX 271
|
| any_adam_object | 1 |
| author | Schwarz, Hans R. |
| author_facet | Schwarz, Hans R. |
| author_role | aut |
| author_sort | Schwarz, Hans R. |
| author_variant | h r s hr hrs |
| building | Verbundindex |
| bvnumber | BV009049266 |
| callnumber-first | Q - Science |
| callnumber-label | QA263 |
| callnumber-raw | QA263 |
| callnumber-search | QA263 |
| callnumber-sort | QA 3263 |
| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)427512 (DE-599)BVBBV009049266 |
| 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 |
| format | Book |
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| id | DE-604.BV009049266 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:29:14Z |
| institution | BVB |
| language | English German |
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| owner_facet | DE-29T DE-83 |
| physical | 278 S. |
| psigel | TUB-nveb |
| publishDate | 1973 |
| publishDateSearch | 1973 |
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| publisher | Prentice-Hall |
| record_format | marc |
| series2 | Prentice-Hall series in automatic computation |
| spelling | Schwarz, Hans R. Verfasser aut Numerik symmetrischer Matrizen Numerical analysis of symmetric matrices Englewood Cliffs, N.J. Prentice-Hall 1973 278 S. txt rdacontent n rdamedia nc rdacarrier Prentice-Hall series in automatic computation EST: Numerik symmetrischer Matrizen <engl.> Analyse numérique Matrices Matrices symétriques ram Numerical analysis Symmetric matrices Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Symmetrische Matrix (DE-588)4314057-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Eigenwertproblem (DE-588)4013802-1 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf Matrizenrechnung (DE-588)4126963-9 s Numerische Mathematik (DE-588)4042805-9 s DE-604 Lineare Algebra (DE-588)4035811-2 s Matrix Mathematik (DE-588)4037968-1 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Eigenwertproblem (DE-588)4013802-1 s 2\p DE-604 Symmetrische Matrix (DE-588)4314057-9 s 3\p DE-604 4\p DE-604 5\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005989307&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Schwarz, Hans R. Numerical analysis of symmetric matrices Analyse numérique Matrices Matrices symétriques ram Numerical analysis Symmetric matrices Matrix Mathematik (DE-588)4037968-1 gnd Symmetrische Matrix (DE-588)4314057-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Eigenwertproblem (DE-588)4013802-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd Lineare Algebra (DE-588)4035811-2 gnd Matrizenrechnung (DE-588)4126963-9 gnd |
| subject_GND | (DE-588)4037968-1 (DE-588)4314057-9 (DE-588)4128130-5 (DE-588)4013802-1 (DE-588)4042805-9 (DE-588)4035811-2 (DE-588)4126963-9 |
| title | Numerical analysis of symmetric matrices |
| title_alt | Numerik symmetrischer Matrizen |
| title_auth | Numerical analysis of symmetric matrices |
| title_exact_search | Numerical analysis of symmetric matrices |
| title_full | Numerical analysis of symmetric matrices |
| title_fullStr | Numerical analysis of symmetric matrices |
| title_full_unstemmed | Numerical analysis of symmetric matrices |
| title_short | Numerical analysis of symmetric matrices |
| title_sort | numerical analysis of symmetric matrices |
| topic | Analyse numérique Matrices Matrices symétriques ram Numerical analysis Symmetric matrices Matrix Mathematik (DE-588)4037968-1 gnd Symmetrische Matrix (DE-588)4314057-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Eigenwertproblem (DE-588)4013802-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd Lineare Algebra (DE-588)4035811-2 gnd Matrizenrechnung (DE-588)4126963-9 gnd |
| topic_facet | Analyse numérique Matrices Matrices symétriques Numerical analysis Symmetric matrices Matrix Mathematik Symmetrische Matrix Numerisches Verfahren Eigenwertproblem Numerische Mathematik Lineare Algebra Matrizenrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005989307&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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