Holdings: Numerical methods for eigenvalue problems

Numerical methods for eigenvalue problems:

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Bibliographic Details
Main Authors:	Börm, Steffen 1972- (Author), Mehl, Christian 1968- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] de Gruyter 2012
Series:	De Gruyter graduate lectures
Subjects:	Eigenwertproblem Numerisches Verfahren Lehrbuch
Online Access:	Inhaltsverzeichnis
Physical Description:	VIII, 208 S. graph. Darst.
ISBN:	9783110250336

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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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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

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