Numerical methods for eigenvalue problems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
de Gruyter
2012
|
| Schriftenreihe: | De Gruyter graduate lectures
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 208 S. graph. Darst. |
| ISBN: | 9783110250336 |
Internformat
MARC
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| 008 | 110901s2012 d||| |||| 00||| eng d | ||
| 020 | |a 9783110250336 |9 978-3-11-025033-6 | ||
| 035 | |a (OCoLC)751006701 | ||
| 035 | |a (DE-599)GBV65616056X | ||
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| 245 | 1 | 0 | |a Numerical methods for eigenvalue problems |c Steffen Börm ; Christian Mehl |
| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 2012 | |
| 300 | |a VIII, 208 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter graduate lectures | |
| 650 | 0 | 7 | |a Eigenwertproblem |0 (DE-588)4013802-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Mehl, Christian |d 1968- |e Verfasser |0 (DE-588)120839148 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-11-025037-4 |
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Datensatz im Suchindex
| _version_ | 1804148380728819712 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
PREFACE V
1 INTRODUCTION 1
1.1 EXAMPLE: STRUCTURAL MECHANICS 1
1.2 EXAMPLE: STOCHASTIC PROCESSES 4
1.3 EXAMPLE: SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS 5
2 EXISTENCE AND PROPERTIES O F EIGENVALUES AND EIGENVECTORS 8
2.1 EIGENVALUES AND EIGENVECTORS 8
2.2 CHARACTERISTIC POLYNOMIALS 12
2.3 SIMILARITY TRANSFORMATIONS 15
2.4 SOME PROPERTIES OF HILBERT SPACES 19
2.5 INVARIANT SUBSPACES 24
2.6 SCHUR DECOMPOSITION 26
2.7 NON-UNITARY TRANSFORMATIONS * 33
3 JACOBI ITERATION 39
3.1 ITERATED SIMILARITY TRANSFORMATIONS 39
3.2 TWO-DIMENSIONAL SCHUR DECOMPOSITION 40
3.3 ONE STEP O F THE ITERATION 43
3.4 ERROR ESTIMATES 47
3.5 QUADRATIC CONVERGENCE * 53
4 POWER METHODS 61
4.1 POWER ITERATION 61
4.2 RAYLEIGH QUOTIENT 66
4.3 RESIDUAL-BASED ERROR CONTROL 70
4.4 INVERSE ITERATION 73
4.5 RAYLEIGH ITERATION 77
4.6 CONVERGENCE TO INVARIANT SUBSPACE 79
HTTP://D-NB.INFO/1018440720
IMAGE 2
VIII CONTENTS
4.7 SIMULTANEOUS ITERATION 83
4.8 CONVERGENCE FOR GENERAL MATRICES * 91
5 QR ITERATION 100
5.1 BASIC QR STEP 100
5.2 HESSENBERG FORM 104
5.3 SHIFTING 113
5.4 DEFLATION 116
5.5 IMPLICIT ITERATION 118
5.6 MULTIPLE-SHIFT STRATEGIES * 126
6 BISECTION METHODS * 132
6.1 STURM CHAINS 134
6.2 GERSHGORIN DISCS 141
7 KRYLOV SUBSPACE METHODS FOR LARGE SPARSE EIGENVALUE PROBLEMS 145
7.1 SPARSE MATRICES AND PROJECTION METHODS 145
7.2 KRYLOV SUBSPACES 149
7.3 GRAM-SCHMIDT PROCESS 152
7.4 ARNOLDI ITERATION 159
7.5 SYMMETRIC LANCZOS ALGORITHM 164
7.6 CHEBYSHEV POLYNOMIALS 165
7.7 CONVERGENCE O F KRYLOV SUBSPACE METHODS 172
8 GENERALIZED AND POLYNOMIAL EIGENVALUE PROBLEMS * 1 82
8.1 POLYNOMIAL EIGENVALUE PROBLEMS AND LINEARIZATION 182
8.2 MATRIX PENCILS 185
8.3 DEFLATING SUBSPACES AND THE GENERALIZED SCHUR DECOMPOSITION 189
8.4 HESSENBERG-TRIANGULAR FORM 192
8.5 DEFLATION 196
8.6 THE Q Z STEP 198
BIBLIOGRAPHY 203
INDEX 206
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:06:13Z |
| institution | BVB |
| isbn | 9783110250336 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024409379 |
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| physical | VIII, 208 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | de Gruyter |
| record_format | marc |
| series2 | De Gruyter graduate lectures |
| spelling | Börm, Steffen 1972- Verfasser (DE-588)121838838 aut Numerical methods for eigenvalue problems Steffen Börm ; Christian Mehl Berlin [u.a.] de Gruyter 2012 VIII, 208 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter graduate lectures Eigenwertproblem (DE-588)4013802-1 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Eigenwertproblem (DE-588)4013802-1 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Mehl, Christian 1968- Verfasser (DE-588)120839148 aut Erscheint auch als Online-Ausgabe 978-3-11-025037-4 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024409379&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Börm, Steffen 1972- Mehl, Christian 1968- Numerical methods for eigenvalue problems Eigenwertproblem (DE-588)4013802-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4013802-1 (DE-588)4128130-5 (DE-588)4123623-3 |
| title | Numerical methods for eigenvalue problems |
| title_auth | Numerical methods for eigenvalue problems |
| title_exact_search | Numerical methods for eigenvalue problems |
| title_full | Numerical methods for eigenvalue problems Steffen Börm ; Christian Mehl |
| title_fullStr | Numerical methods for eigenvalue problems Steffen Börm ; Christian Mehl |
| title_full_unstemmed | Numerical methods for eigenvalue problems Steffen Börm ; Christian Mehl |
| title_short | Numerical methods for eigenvalue problems |
| title_sort | numerical methods for eigenvalue problems |
| topic | Eigenwertproblem (DE-588)4013802-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Eigenwertproblem Numerisches Verfahren Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024409379&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bormsteffen numericalmethodsforeigenvalueproblems AT mehlchristian numericalmethodsforeigenvalueproblems |