Holdings: Computation of invariant measures with dimension reduction methods

Computation of invariant measures with dimension reduction methods:

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Bibliographic Details
Main Author:	Kemper, Jens (Author)
Format:	Thesis Book
Language:	English
Published:	Berlin Logos Verlag 2010
Subjects:	Dimensionsreduktion Dynamisches System Invariantes Maß Numerische Methoden Invariante Maße Partielle Differentialgleichungen Mengenwertige Algorithmen Hochschulschrift
Online Access:	Inhaltsverzeichnis Inhaltstext Inhaltsverzeichnis
Physical Description:	vi, 152 Seiten Diagramme 21 cm
ISBN:	9783832524524

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MARC


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adam_text	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
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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
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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
url	http://d-nb.info/1001628187/04 http://deposit.dnb.de/cgi-bin/dokserv?id=3455837&prov=M&dok_var=1&dok_ext=htm 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
work_keys_str_mv	AT kemperjens computationofinvariantmeasureswithdimensionreductionmethods

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