Spatially adaptive sparse grids for high-dimensional problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
München
Verl. Dr. Hut
2010
|
| Edition: | 1. Aufl. |
| Series: | Informatik
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 181 S. graph. Darst. 240 mm x 170 mm, 511 g |
| ISBN: | 9783868535556 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804143366965821440 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION 1
2 SPARSE GRIDS 5
2.1 BASICS 6
2.1.1 INTERPOLATION ON A PULL GRID 7
2.1.2 HIERARCHICAL BASIS FUNCTIONS IN ONE DIMENSION 8
2.1.3 HIGHER-DIMENSIONAL INTERPOLATION ON A PULL GRID 8
2.1.4 SPARSE GRIDS 10
2.2 BOUNDARY TREATMENT 12
2.3 VARIANTS OF SPARSE GRIDS 16
2.4 ADAPTIVITY 20
2.5 FURTHER TYPES OF BASIS FUNCTIONS 22
2.6 ALGORITHMS ON SPARSE GRIDS 30
2.6.1 BASIC SCHEME 31
2.6.2 THE ONE-DIMENSIONAL CASE 32
2.6.3 THE D-DIMENSIONAL CASE 36
2.7 PARALLELIZATION 39
3 SPATIALLY ADAPTIVE SPARSE GRID TOOLBOX SG ++ 41
4 EFFICIENT COSMOLOGICAL PARAMETER SAMPLING (INTERPOLATION) 45 4.1 THE
PROBLEM 45
4.2 REMARKS ON THE INTERPOLATION OF GAUSSIANS 48
4.3 INTERPOLATING THE WMAP LOG-LIKELIHOOD SURFACE 55
4.3.1 GENERATION OF TEST SET AND CHOICE OF INTERPOLATION RANGE . . .. 55
4.3.2 CHOICE OF BASIS FUNCTIONS 56
4.3.3 RESULTS FOR REGULAR SPARSE GRIDS 57
4.4 EMPLOYING ADAPTIVITY 63
4.5 SUMMARY 70
5 DECISIONS FROM DATA (CLASSIFICATION) 73
5.1 THE PROBLEM 74
5.1.1 CLASSIFICATION AS A SCATTERED DATA APPROXIMATION PROBLEM . . .. 76
5.1.2 REACHING TO HIGHER DIMENSIONALITIES 78
5.2 CLASSIFICATION EXAMPLES 83
5.2.1 CHECKERBOARD DATA SET 83
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1007275030
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
5.2.2 RIPLEY DATA SET 85
5.2.3 BUPA LIVER DATA SET 87
5.2.4 OPTICAL RECOGNITION OF HANDWRITTEN DIGITS 89
5.2.5 MUSKL DATA SET 91
5.2.6 DISCUSSION 92
5.3 REFINEMENT CRITERION AND ERROR MEASURE 93
5.4 SUMMARY 100
6 LEARNING FUNCTIONS FROM DATA (REGRESSION) 103
6.1 THE PROBLEM 103
6.2 NUMERICAL RESULTS FOR ARTIFICIAL DATA SETS 108
6.3 PHOTOMETRIC ESTIMATION OF COSMOLOGICAL REDSHIFTS 114
6.3.1 THE PROBLEM 114
6.3.2 EXPERIMENTS 116
6.3.3 DISCUSSION 126
6.4 REGRESSION IN OPTION PRICING 127
6.4.1 THE PROBLEM 127
6.4.2 EXPERIMENTS 130
6.4.3 DISCUSSION 136
6.5 SUMMARY 138
7 PARALLELIZATION OF SPARSE GRID ALGORITHMS 139
7.1 SPARSE GRID ALGORITHMS ON SHARED MEMORY SYSTEMS 139
7.2 PARALLELIZATION OF THE BLACK-SCHOLES PDE 145
7.2.1 BLACK-SCHOLES DISCRETIZATION ON SPARSE GRIDS 146
7.2.2 NUMERICAL EXPERIMENTS 147
7.2.3 PARALLEL RESULTS 148
7.3 SUMMARY 152
8 CONCLUSIONS 153
A SPARSE GRIDS 155
B EFFICIENT COSMOLOGICAL PARAMETER SAMPLING 157
B.I NORMAL PARAMETERS 157
B.2 INVERSION OF THE PARAMETER TRANSFORMATION 159
B.3 GRID PROJECTIONS 161
C LEARNING FUNCTIONS FROM DATA 167
VI
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| any_adam_object | 1 |
| author | Pflüger, Dirk |
| author_GND | (DE-588)14255037X |
| author_facet | Pflüger, Dirk |
| author_role | aut |
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| author_variant | d p dp |
| building | Verbundindex |
| bvnumber | BV036719014 |
| classification_tum | MAT 650d |
| ctrlnum | (OCoLC)700066168 (DE-599)DNB1007275030 |
| dewey-full | 518.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.64 |
| dewey-search | 518.64 |
| dewey-sort | 3518.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Geographie |
| edition | 1. Aufl. |
| format | Thesis Book |
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| id | DE-604.BV036719014 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:46:31Z |
| institution | BVB |
| isbn | 9783868535556 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020636929 |
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| owner_facet | DE-12 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-92 |
| physical | VI, 181 S. graph. Darst. 240 mm x 170 mm, 511 g |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Verl. Dr. Hut |
| record_format | marc |
| series2 | Informatik |
| spelling | Pflüger, Dirk Verfasser (DE-588)14255037X aut Spatially adaptive sparse grids for high-dimensional problems Dirk Pflüger 1. Aufl. München Verl. Dr. Hut 2010 VI, 181 S. graph. Darst. 240 mm x 170 mm, 511 g txt rdacontent n rdamedia nc rdacarrier Informatik Zugl.: München, Techn. Univ., Diss., 2010 Hochdimensionales System (DE-588)4202326-9 gnd rswk-swf Adaptives Gitter (DE-588)4333769-7 gnd rswk-swf Dünnes Gitter (DE-588)4411841-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Hochdimensionales System (DE-588)4202326-9 s Dünnes Gitter (DE-588)4411841-7 s Adaptives Gitter (DE-588)4333769-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020636929&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pflüger, Dirk Spatially adaptive sparse grids for high-dimensional problems Hochdimensionales System (DE-588)4202326-9 gnd Adaptives Gitter (DE-588)4333769-7 gnd Dünnes Gitter (DE-588)4411841-7 gnd |
| subject_GND | (DE-588)4202326-9 (DE-588)4333769-7 (DE-588)4411841-7 (DE-588)4113937-9 |
| title | Spatially adaptive sparse grids for high-dimensional problems |
| title_auth | Spatially adaptive sparse grids for high-dimensional problems |
| title_exact_search | Spatially adaptive sparse grids for high-dimensional problems |
| title_full | Spatially adaptive sparse grids for high-dimensional problems Dirk Pflüger |
| title_fullStr | Spatially adaptive sparse grids for high-dimensional problems Dirk Pflüger |
| title_full_unstemmed | Spatially adaptive sparse grids for high-dimensional problems Dirk Pflüger |
| title_short | Spatially adaptive sparse grids for high-dimensional problems |
| title_sort | spatially adaptive sparse grids for high dimensional problems |
| topic | Hochdimensionales System (DE-588)4202326-9 gnd Adaptives Gitter (DE-588)4333769-7 gnd Dünnes Gitter (DE-588)4411841-7 gnd |
| topic_facet | Hochdimensionales System Adaptives Gitter Dünnes Gitter Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020636929&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pflugerdirk spatiallyadaptivesparsegridsforhighdimensionalproblems |