Computation of invariant measures with dimension reduction methods:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Logos Verlag
2010
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | vi, 152 Seiten Diagramme 21 cm |
| ISBN: | 9783832524524 |
Internformat
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| 245 | 1 | 0 | |a Computation of invariant measures with dimension reduction methods |c vorgelegt von Jens Kemper |
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| 653 | |a Invariante Maße | ||
| 653 | |a Dimensionsreduktion | ||
| 653 | |a Partielle Differentialgleichungen | ||
| 653 | |a Mengenwertige Algorithmen | ||
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Datensatz im Suchindex
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CONTENTS INTRODUCTION 1 1 THE ADAPTIVE INVARIANT MEASURE ALGORITHM 7 1.1
DYNAMICAL SYSTEMS 7 1.2 REVIEW OF BASIC CONCEPTS FROM ERGODIC THEORY 13
1.3 ULAM'S METHOD 15 1.4 THE ADAPTIVE INVARIANT MEASURE (AIM) ALGORITHM
17 1.5 CONVERGENCE OF THE AIM ALGORITHM 19 2 MODEL REDUCTION AND
LONG-TIME BEHAVIOR 23 2.1 PROPER ORTHOGONAL DECOMPOSITION (POD) 23 2.1.1
SINGULAR VALUE DECOMPOSITION AND THE RELATION TO POD 24 2.1.2
PERTURBATION THEORY FOR THE SINGULAR VALUE DECOMPOSITION 28 2.2 POD
CONVERGENCE THEORY ON FINITE TIME INTERVALS 31 2.3 LONG-TIME BEHAVIOR OF
POD SOLUTIONS 33 2.3.1 ASYMPTOTICALLY STABLE FIXED POINT 33 2.3.2
ATTRACTING INVARIANT SUBSPACE 35 2.3.3 TWO RATES OF CONVERGENCE 37 2.3.4
DIFFERENT SPEEDS OF CONVERGENCE IN THE DIAGONALIZABLE CASE 39 2.3.5
NUMERICAL EXAMPLES 47 2.3.6 DIFFERENT INITIAL VALUES 53 3 SET-VALUED
ALGORITHMS IN REDUCED SPACE 57 3.1 PODAIM: THE INVARIANT MEASURE
ALGORITHM IN REDUCED SPACE 57 3.2 ADAPTIVE POD ALGORITHM 60 3.3 ANALYSIS
OF THE ALGORITHMS: AN OUTLOOK 62 4 COMPARISON OF DISCRETE MEASURES 63
4.1 DISTANCE NOTIONS FOR DISCRETE MEASURES*THE PROHOROV METRIC 63 4.1.1
THE WEAK METRIC 64 4.1.2 THE CONCEPT OF BLOWING UP BOXES 64 4.1.3
IMPLEMENTATION OF THE PROHOROV METRIC 65 4.1.4 AN ALTERNATIVE DISTANCE
USING NEGATIVE SOBOLEV NORMS 68 4.1.5 PROHOROV METRIC VS. SOBOLEV NORM:
NUMERICAL REALIZATION 70 4. BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/1001628187 DIGITALISIERT DURCH BIBLIOGRAPHY 143 5 ERROR
ESTIMATES FOR DISCRETE AND CONTINUOUS INVARIANT MEASURES 83 5.1 OVERVIEW
OF CONVERGENCE RESULTS FOR THE PODAIM ALGORITHM 83 5.2 RELATIONS BETWEEN
THE CONTINUOUS MEASURES 86 5.2.1 INVARIANCE IN ORIGINAL AND REDUCED
SPACE 86 5.2.2 RELATIONS BETWEEN THE TRANSFER OPERATORS 88 5.3 ERROR
BOUNDS FOR THE DISCRETE MEASURES 89 5.3.1 PERTURBATIONS OI PERRON ROOTS
90 5.3.2 PERRON-PROBENIUS MATRICES OF REDUCED SYSTEMS 92 5.3.3
COMBINATION WITH POD ERROR 102 6 NUMERICAL EXPERIMENTS 105 6.1
REPRESENTING DISCRETE MEASURES IN HIGH DIMENSIONS 105 6.2 EMBEDDED
LORENZ SYSTEM 107 6.2.1 SOLUTION OF THE PODAIM ALGORITHM 108 6.2.2
ANALYSIS OF THE POD COMPUTATION STEP 109 6.3 THE CHAFEE-INFANTE PROBLEM
110 6.3.1 LONG-TIME BEHAVIOR 110 6.3.2 DISCRETIZATION OF THE
CHAFEE-INFANTE PROBLEM 112 6.3.3 MULTIPLE EIGENVALUE 1 OF THE
PERRON-PROBENIUS MATRIX 114 6.3.4 NUMERICAL EXPERIMENTS FOR THE
CHAFEE-INFANTE PROBLEM 116 A APPENDIX 123 A.I NONNEGATIVE MATRICES 123
A.2 PERTURBATION THEORY FOR MATRICES 124 A.3 ASPECTS OF LINEAR
FUNCTIONAL ANALYSIS 128 A.4 TOPICS FROM MEASURE AND INTEGRATION THEORY
129 A.5 TOPICS FROM FOURIER ANALYSIS 137 LIST OF FIGURES 141 |
| any_adam_object | 1 |
| author | Kemper, Jens |
| author_GND | (DE-588)141497483 |
| author_facet | Kemper, Jens |
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| author_sort | Kemper, Jens |
| author_variant | j k jk |
| building | Verbundindex |
| bvnumber | BV043636872 |
| ctrlnum | (OCoLC)953546659 (DE-599)DNB1001628187 |
| dewey-full | 515.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.39 |
| dewey-search | 515.39 |
| dewey-sort | 3515.39 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-08-03T03:02:25Z |
| institution | BVB |
| isbn | 9783832524524 |
| language | English |
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| physical | vi, 152 Seiten Diagramme 21 cm |
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| spelling | Kemper, Jens Verfasser (DE-588)141497483 aut Computation of invariant measures with dimension reduction methods vorgelegt von Jens Kemper Berlin Logos Verlag 2010 vi, 152 Seiten Diagramme 21 cm txt rdacontent n rdamedia nc rdacarrier Dissertation Universität Bielefeld 2010 Dimensionsreduktion (DE-588)4224279-4 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Invariantes Maß (DE-588)4352361-4 gnd rswk-swf Numerische Methoden Invariante Maße Dimensionsreduktion Partielle Differentialgleichungen Mengenwertige Algorithmen (DE-588)4113937-9 Hochschulschrift gnd-content Dynamisches System (DE-588)4013396-5 s Invariantes Maß (DE-588)4352361-4 s Dimensionsreduktion (DE-588)4224279-4 s DE-604 B:DE-101 application/pdf http://d-nb.info/1001628187/04 Inhaltsverzeichnis X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3455837&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029050780&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kemper, Jens Computation of invariant measures with dimension reduction methods Dimensionsreduktion (DE-588)4224279-4 gnd Dynamisches System (DE-588)4013396-5 gnd Invariantes Maß (DE-588)4352361-4 gnd |
| subject_GND | (DE-588)4224279-4 (DE-588)4013396-5 (DE-588)4352361-4 (DE-588)4113937-9 |
| title | Computation of invariant measures with dimension reduction methods |
| title_auth | Computation of invariant measures with dimension reduction methods |
| title_exact_search | Computation of invariant measures with dimension reduction methods |
| title_full | Computation of invariant measures with dimension reduction methods vorgelegt von Jens Kemper |
| title_fullStr | Computation of invariant measures with dimension reduction methods vorgelegt von Jens Kemper |
| title_full_unstemmed | Computation of invariant measures with dimension reduction methods vorgelegt von Jens Kemper |
| title_short | Computation of invariant measures with dimension reduction methods |
| title_sort | computation of invariant measures with dimension reduction methods |
| topic | Dimensionsreduktion (DE-588)4224279-4 gnd Dynamisches System (DE-588)4013396-5 gnd Invariantes Maß (DE-588)4352361-4 gnd |
| topic_facet | Dimensionsreduktion Dynamisches System Invariantes Maß Hochschulschrift |
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| work_keys_str_mv | AT kemperjens computationofinvariantmeasureswithdimensionreductionmethods |
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