Sparse approximate inverses for preconditioning, smoothing, and regularization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
2012
|
| Subjects: | |
| Online Access: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20121002-1107998-1-2 Inhaltsverzeichnis |
| Physical Description: | X, 237 S. Ill., graph. Darst. |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV040709275 | ||
| 003 | DE-604 | ||
| 005 | 20130413 | ||
| 007 | t | ||
| 008 | 130130s2012 ad|| m||| 00||| eng d | ||
| 035 | |a (OCoLC)826628116 | ||
| 035 | |a (DE-599)BVBBV040709275 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-473 |a DE-703 |a DE-1051 |a DE-824 |a DE-29 |a DE-12 |a DE-91 |a DE-19 |a DE-1049 |a DE-92 |a DE-739 |a DE-898 |a DE-355 |a DE-706 |a DE-20 |a DE-1102 |a DE-91G | ||
| 084 | |a MAT 659d |2 stub | ||
| 100 | 1 | |a Sedlacek, Matous |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Sparse approximate inverses for preconditioning, smoothing, and regularization |c Matous Sedlacek |
| 264 | 1 | |c 2012 | |
| 300 | |a X, 237 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a München, Techn. Univ., Diss., 2012 | ||
| 650 | 0 | 7 | |a Schwach besetzte Matrix |0 (DE-588)4056053-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Iteration |0 (DE-588)4123457-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineares Gleichungssystem |0 (DE-588)4035826-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hochdimensionales System |0 (DE-588)4202326-9 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Lineares Gleichungssystem |0 (DE-588)4035826-4 |D s |
| 689 | 0 | 1 | |a Schwach besetzte Matrix |0 (DE-588)4056053-3 |D s |
| 689 | 0 | 2 | |a Hochdimensionales System |0 (DE-588)4202326-9 |D s |
| 689 | 0 | 3 | |a Iteration |0 (DE-588)4123457-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |o urn:nbn:de:bvb:91-diss-20121002-1107998-1-2 |
| 856 | 4 | 1 | |u http://mediatum.ub.tum.de/node?id=1107998 |x Verlag |z kostenfrei |3 Volltext |
| 856 | 4 | |u https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20121002-1107998-1-2 |x Resolving-System | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025689639&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 912 | |a ebook | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025689639 | ||
Record in the Search Index
| _version_ | 1804150015413714944 |
|---|---|
| adam_text | IMAGE 1
VII
CONTENTS
1. INTRODUCTION 1
1.1. SCIENTIFIC ENVIRONMENT OF THE THESIS 1
1.1.1. SPARSE APPROXIMATE INVERSES FOR PRECONDITIONING, 2
1.1.2. ... SMOOTHING, AND REGULARIZATION 2
1.2. OUTLINE OF THE THESIS 3
1.3. NOMENCLATURE 6
2. SOLUTION O F LINEAR SYSTEMS AND DISCRETE INVERSE PROBLEMS 11
2.1. DIRECT METHODS FOR DENSE LINEAR SYSTEMS 12
2.1.1. LU FACTORIZATION 12
2.1.2. CHOLESKY FACTORIZATION 14
2.1.3. LEAST SQUARES AND QR FACTORIZATION 14
2.2. ITERATIVE METHODS FOR SPARSE LINEAR SYSTEMS 16
2.2.1. SPARSE STORAGE SCHEMES AND GRAPH THEORY 17
2.2.2. CLASSICAL ITERATIVE METHODS 19
2.2.3. NONSTATIONARY METHODS: KRYLOV SUBSPACE METHODS 21 2.3.
SENSITIVITY OF LINEAR SYSTEMS AND PRECONDITIONING 26
2.3.1. PERTURBATION ANALYSIS 27
2.3.2. CONVERGENCE ANALYSIS OF THE (PRECONDITIONED) CONJUGATE GRADIENT
METHOD 28
2.3.3. PRECONDITIONING AND PARALLEL PRECONDITIONING 29
2.4. MULTIGRID 35
2.5. DISCRETE INVERSE PROBLEMS 38
2.5.1. THE RELATIONSHIP BETWEEN THE SINGULAR SPECTRUM AND THE MEANINGFUL
EXISTENCE OF A SOLUTION 39
2.5.2. DIRECT REGULARIZATION METHODS 40
2.5.3. ITERATIVE REGULARIZATION METHODS 42
2.5.4. ESTIMATING THE REGULARIZATION PARAMETER 45
2.5.5. AVAILABLE SOFTWARE FOR DISCRETE ILL-POSED PROBLEMS 48
3. SPARSE APPROXIMATE INVERSES 4 9
3.1. FROBENIUS NORM MINIMIZATION FOR THE GENERAL CASE 50
3.1.1. COMPUTATION FOR A FIXED SPARSITY PATTERN J : SAI 50
3.1.2. A PRIORI CHOICES OF J 51
3.1.3. UPDATING THE SPARSITY PATTERN J SPAI 54
3.1.4. MODIFIED SPAI: MSPAI 62
3.1.5. MULTISTEP SUCCESSIVE PRECONDITIONER: MSP 68
3.1.6. MULTISTEP MSPAI: MMSPAI 69
3.2. /^-CONDITION NUMBER MINIMIZATION FOR THE SYMMETRIC POSITIVE
DEFINITE CASE . 78 3.2.1. COMPUTATION FOR A FIXED SPARSITY PATTERN J
FSAI 79
HTTP://D-NB.INFO/1034654454
IMAGE 2
VIII CONTENTS
3.2.2. A PRIORI CHOICES OF J 81
3.2.3. UPDATING THE SPARSITY PATTERN J : FSPAI 81
3.2.4. THEORETICAL PROPERTIES OF FS(P)AI 86
3.2.5. EXACT FSPAI: EFSPAI 87
3.2.6. NOTES ON IMPLEMENTING EFSPAI 90
4. BLOCK FACTORIZED SPARSE APPROXIMATE INVERSES BASED ON X-CONDITION
NUMBER MINIMIZATION 9 7
4.1. THE GENERAL CASE: BLOCK SPAI 98
4.2. COMPUTATION FOR A FIXED BLOCK SPARSITY PATTERN J BFSAI 99
4.3. UPDATING THE BLOCK SPARSITY PATTERN J BFSPAI 101
4.4. NUMERICAL EXPERIMENTS 102
5. SMOOTHING WITH MODIFIED SPARSE APPROXIMATE INVERSES 109
5.1. ID MODEL PROBLEMS 110
5.1.1. ANALYTICAL DERIVATION OF THE OPTIMAL SMOOTHER 110
5.1.2. INDIVIDUAL PROBING MASKS I L L
5.1.3. GLOBAL PROBING VECTORS 112
5.1.4. GLOBAL PROBING VECTORS WITH ACTION ON GENERAL A 113
5.2. 2D MODEL PROBLEMS 113
5.2.1. ANALYTICAL DERIVATION OF THE OPTIMAL SMOOTHER 115
5.2.2. INDIVIDUAL PROBING MASKS 115
5.2.3. GLOBAL PROBING VECTORS AND GLOBAL PROBING VECTORS WITH ACTION ON
A 116 5.2.4. 9-POINT STENCIL DERIVATIONS 117
5.3. INTERPRETATION OF THE RESULTS 119
6. IMPROVING T H E SOLUTION O F DISCRETE ILL-POSED INVERSE PROBLEMS 121
6.1. REGULARIZATION WITH MODIFIED SPARSE APPROXIMATE INVERSES 122 6.1.1.
ID MODEL PROBLEMS 122
6.1.2. HANDLING DISCONTINUITIES AND BOUNDARIES 124
6.1.3. 2D MODEL PROBLEMS 128
6.2. ESTIMATING THE REGULARIZATION PARAMETER FOR CGLS 131
6.3. DATA BASED REGULARIZATION FOR DISCRETE DECONVOLUTION PROBLEMS 135
6.3.1. MOTIVATION FOR INCORPORATING THE SIGNAL DATA 135
6.3.2. DATA BASED REGULARIZATION METHODS 139
6.3.3. IMPROVEMENT BY OUTER ITERATIONS 140
6.3.4. NUMERICAL EXPERIMENTS 140
6.4. PARTITIONED REGULARIZATION 150
6.5. TIKHONOV-PHILLIPS REGULARIZATION WITH OPERATOR DEPENDENT SEMINORMS
. . . 154 6.5.1. SEMINORM FOR GENERAL OPERATORS 155
6.5.2. SEMINORM FOR SYMMETRIC INDEFINITE OPERATORS 157
6.5.3. SEMINORM LH , IC , TX LB FOR GENERAL NONSYMMETRIC OPERATORS
158 6.5.4. NUMERICAL EXPERIMENTS 158
6.6. DATA BASED REGULARIZATION MATRICES FOR THE TIKHONOV-PHILLIPS
REGULARIZATION 168
7. PARALLEL IMPLEMENTATIONS O F SPARSE APPROXIMATE INVERSES 171
7.1. PARALLELIZATION CONCEPT 172
7.1.1. DATA DISTRIBUTION 172
7.1.2. ONE-SIDED COMMUNICATION 172
7.1.3. LATENCY HIDING 173
IMAGE 3
CONTENTS IX
7.1.4. LOAD BALANCING 174
7.2. MSPAI IMPLEMENTATION MSPAI-1.2 174
7.2.1. AVOIDING REDUNDANT QR FACTORIZATIONS 175
7.2.2. MEMORY OPTIMIZATIONS 180
7.2.3. STRONG SCALABILITY 182
7.2.4. REMARKS 184
7.3. FSPAI IMPLEMENTATION FSPAI-1.1 186
7.3.1. GENERAL NOTES 186
7.3.2. AVOIDING REDUNDANT CHOLESKY FACTORIZATIONS 191
7.3.3. SPARSE CHOLESKY FACTORIZATIONS 192
7.3.4. QUALITY AND PERFORMANCE ANALYSIS 196
7.3.5. STRONG SCALABILITY 199
8. CONCLUSIONS AND PERSPECTIVES 203
8.1. VARIANTS OF SPARSE APPROXIMATE INVERSES 203
8.2. IMPLEMENTATIONS OF SPARSE APPROXIMATE INVERSES 204
8.3. SMOOTHING WITH SPARSE APPROXIMATE INVERSES 206
8.4. IMPROVING THE RECONSTRUCTION OF DISCRETE ILL-POSED PROBLEMS 206
8.5. CLOSING REMARK 208
A. MATHEMATICAL DETAILS 211
B. THEORETICAL PROPERTIES O F BFS(P)AI 215
C. EXACT BLOCK FSPAI: EBFSPAI 217
D. EXPERIMENTAL ENVIRONMENTS 221
BIBLIOGRAPHY 225
INDEX 235
|
| any_adam_object | 1 |
| author | Sedlacek, Matous |
| author_facet | Sedlacek, Matous |
| author_role | aut |
| author_sort | Sedlacek, Matous |
| author_variant | m s ms |
| building | Verbundindex |
| bvnumber | BV040709275 |
| classification_tum | MAT 659d |
| collection | ebook |
| ctrlnum | (OCoLC)826628116 (DE-599)BVBBV040709275 |
| discipline | Mathematik |
| format | Thesis Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02069nam a2200445 c 4500</leader><controlfield tag="001">BV040709275</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20130413 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">130130s2012 ad|| m||| 00||| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)826628116</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV040709275</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-473</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-1051</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-1049</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-898</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-1102</subfield><subfield code="a">DE-91G</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 659d</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Sedlacek, Matous</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Sparse approximate inverses for preconditioning, smoothing, and regularization</subfield><subfield code="c">Matous Sedlacek</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 237 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="502" ind1=" " ind2=" "><subfield code="a">München, Techn. Univ., Diss., 2012</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Schwach besetzte Matrix</subfield><subfield code="0">(DE-588)4056053-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Iteration</subfield><subfield code="0">(DE-588)4123457-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lineares Gleichungssystem</subfield><subfield code="0">(DE-588)4035826-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hochdimensionales System</subfield><subfield code="0">(DE-588)4202326-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4113937-9</subfield><subfield code="a">Hochschulschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Lineares Gleichungssystem</subfield><subfield code="0">(DE-588)4035826-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Schwach besetzte Matrix</subfield><subfield code="0">(DE-588)4056053-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Hochdimensionales System</subfield><subfield code="0">(DE-588)4202326-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Iteration</subfield><subfield code="0">(DE-588)4123457-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="o">urn:nbn:de:bvb:91-diss-20121002-1107998-1-2</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">http://mediatum.ub.tum.de/node?id=1107998</subfield><subfield code="x">Verlag</subfield><subfield code="z">kostenfrei</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20121002-1107998-1-2</subfield><subfield code="x">Resolving-System</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025689639&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ebook</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-025689639</subfield></datafield></record></collection> |
| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV040709275 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:32:12Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025689639 |
| oclc_num | 826628116 |
| open_access_boolean | 1 |
| owner | DE-384 DE-473 DE-BY-UBG DE-703 DE-1051 DE-824 DE-29 DE-12 DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-1049 DE-92 DE-739 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-706 DE-20 DE-1102 DE-91G DE-BY-TUM |
| owner_facet | DE-384 DE-473 DE-BY-UBG DE-703 DE-1051 DE-824 DE-29 DE-12 DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-1049 DE-92 DE-739 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-706 DE-20 DE-1102 DE-91G DE-BY-TUM |
| physical | X, 237 S. Ill., graph. Darst. |
| psigel | ebook |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| record_format | marc |
| spelling | Sedlacek, Matous Verfasser aut Sparse approximate inverses for preconditioning, smoothing, and regularization Matous Sedlacek 2012 X, 237 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2012 Schwach besetzte Matrix (DE-588)4056053-3 gnd rswk-swf Iteration (DE-588)4123457-1 gnd rswk-swf Lineares Gleichungssystem (DE-588)4035826-4 gnd rswk-swf Hochdimensionales System (DE-588)4202326-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Lineares Gleichungssystem (DE-588)4035826-4 s Schwach besetzte Matrix (DE-588)4056053-3 s Hochdimensionales System (DE-588)4202326-9 s Iteration (DE-588)4123457-1 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20121002-1107998-1-2 http://mediatum.ub.tum.de/node?id=1107998 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20121002-1107998-1-2 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025689639&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sedlacek, Matous Sparse approximate inverses for preconditioning, smoothing, and regularization Schwach besetzte Matrix (DE-588)4056053-3 gnd Iteration (DE-588)4123457-1 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Hochdimensionales System (DE-588)4202326-9 gnd |
| subject_GND | (DE-588)4056053-3 (DE-588)4123457-1 (DE-588)4035826-4 (DE-588)4202326-9 (DE-588)4113937-9 |
| title | Sparse approximate inverses for preconditioning, smoothing, and regularization |
| title_auth | Sparse approximate inverses for preconditioning, smoothing, and regularization |
| title_exact_search | Sparse approximate inverses for preconditioning, smoothing, and regularization |
| title_full | Sparse approximate inverses for preconditioning, smoothing, and regularization Matous Sedlacek |
| title_fullStr | Sparse approximate inverses for preconditioning, smoothing, and regularization Matous Sedlacek |
| title_full_unstemmed | Sparse approximate inverses for preconditioning, smoothing, and regularization Matous Sedlacek |
| title_short | Sparse approximate inverses for preconditioning, smoothing, and regularization |
| title_sort | sparse approximate inverses for preconditioning smoothing and regularization |
| topic | Schwach besetzte Matrix (DE-588)4056053-3 gnd Iteration (DE-588)4123457-1 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Hochdimensionales System (DE-588)4202326-9 gnd |
| topic_facet | Schwach besetzte Matrix Iteration Lineares Gleichungssystem Hochdimensionales System Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1107998 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20121002-1107998-1-2 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025689639&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sedlacekmatous sparseapproximateinversesforpreconditioningsmoothingandregularization |