Hierarchical matrices: a means to efficiently solve elliptic boundary value problems ; with 53 tables
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
2008
|
| Schriftenreihe: | Lecture notes in computational science and engineering
63 |
| Schlagworte: | |
| Online-Zugang: | BTU01 TUM01 UBA01 UBT01 UER01 UPA01 Volltext Inhaltsverzeichnis |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783540771470 |
| DOI: | 10.1007/978-3-540-77147-0 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804139040019054592 |
|---|---|
| adam_text | GESCANNT DURCH CONTENTS INTRODUCTION 1 1 LOW-RANK MATRICES AND MATRIX
PARTITIONING 9 1.1 LOW-RANK MATRICES 9 1.1.1 EFFICIENT REPRESENTATION 10
1.1.2 ADDING AND MULTIPLYING LOW-RANK MATRICES 12 1.1.3 APPROXIMATION BY
LOW-RANK MATRICES 13 1.1.4 SINGULAR VALUE DECOMPOSITION OF LOW-RANK
MATRICES 15 1.1.5 APPROXIMATE ADDITION OF LOW-RANK MATRICES 16 1.1.6
AGGLOMERATING LOW-RANK BLOCKS 18 1.2 STRUCTURED LOW-RANK MATRICES 19 1.3
ADMISSIBLE PARTITIONS 21 1.3.1 TENSOR VS. HIERARCHICAL PARTITIONS 25 1.4
CLUSTER TREES 29 1.4.1 CONSTRUCTION OF CLUSTER TREES 33 1.4.2 EXAMPLE:
AN EASILY ANALYZED PARTITION 41 1.5 BLOCK CLUSTER TREES 43 2
HIERARCHICAL MATRICES 49 2.1 THE SET OF HIERARCHICAL MATRICES 50 2.2
MATRIX-VECTOR MULTIPLICATION 52 2.3 PARALLEL MATRIX-VECTOR
MULTIPLICATION 53 2.3.1 PARALLELIZATION FOR USUAL MATRICES 54 2.3.2
NON-UNIFORM BLOCK DISTRIBUTIONS 55 2.3.3 NUMERICAL EXPERIMENTS 60 2.4
BLOCKWISE AND GLOBAL NORMS 63 2.5 ADDING JT-MATRICES 65 2.5.1 PRESERVING
POSITIVITY 66 2.6 COARSENING JF-MATRICES 69 2.7 MULTIPLYING 3V -MATRICES
74 2.7.1 PRODUCT BLOCK CLUSTER TREE 74 XI BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/98738886X DIGITALISIERT DURCH * * * * 289 CONTENTS XIII
4.1.5 APPROXIMATION OF DISCRETE OPERATORS 218 4.1.6 NUMERICAL
EXPERIMENTS 222 4.2 SCHUR COMPLEMENTS 229 4.3 HIERARCHICAL LU
DECOMPOSITION 232 4.3.1 APPROXIMATING SCHUR COMPLEMENTS HIERARCHICALLY
234 4.3.2 CONSTRUCTING THE FACTORS LJG AND UJ? 236 4.4 NUMERICAL
EXPERIMENTS WITH THE J^-MATRIX LU FACTORIZATION 238 4.4.1
TWO-DIMENSIONAL DIFFUSION 239 4.4.2 CONVECTION-DIFFUSION PROBLEMS 244
4.4.3 THREE-DIMENSIONAL DIFFUSION 245 4.5 NESTED DISSECTION LU
FACTORIZATION 248 4.5.1 MATRIX PARTITIONING 249 4.5.2 APPROXIMATION OF
THE FACTORS OF THE LU DECOMPOSITION 250 4.5.3 NUMERICAL RESULTS 253
4.5.4 PARALLEL APPROXIMATE LU FACTORIZATION 253 4.6 SOLVING NONLINEAR
PROBLEMS WITH BROYDEN UPDATES 257 4.6.1 BROYDEN UPDATES 260 4.6.2 AN
UPDATE METHOD FOR THE LU DECOMPOSITION 261 4.6.3 THE INFLUENCE OF
TRUNCATION ERRORS 264 4.6.4 NUMERICAL EXPERIMENTS 265 REFERENCES 269
APPENDIX 281 INDEX
|
| any_adam_object | 1 |
| author | Bebendorf, Mario 1972- |
| author_GND | (DE-588)122575091 |
| author_facet | Bebendorf, Mario 1972- |
| author_role | aut |
| author_sort | Bebendorf, Mario 1972- |
| author_variant | m b mb |
| building | Verbundindex |
| bvnumber | BV023838483 |
| classification_rvk | SK 220 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)1184254231 (DE-599)BVBBV023838483 |
| 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 |
| doi_str_mv | 10.1007/978-3-540-77147-0 |
| format | Electronic eBook |
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| indexdate | 2024-07-09T21:37:45Z |
| institution | BVB |
| isbn | 9783540771470 |
| language | English |
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| series | Lecture notes in computational science and engineering |
| series2 | Lecture notes in computational science and engineering |
| spelling | Bebendorf, Mario 1972- Verfasser (DE-588)122575091 aut Hierarchical matrices a means to efficiently solve elliptic boundary value problems ; with 53 tables Mario Bebendorf Berlin ; Heidelberg Springer 2008 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Lecture notes in computational science and engineering 63 Diskrete Approximation (DE-588)4503166-6 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Integraloperator (DE-588)4131247-8 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Hierarchische Matrix (DE-588)4702093-3 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Elliptisches Randwertproblem (DE-588)4193399-0 s Numerisches Verfahren (DE-588)4128130-5 s Hierarchische Matrix (DE-588)4702093-3 s DE-604 Integraloperator (DE-588)4131247-8 s Diskrete Approximation (DE-588)4503166-6 s Finite-Elemente-Methode (DE-588)4017233-8 s Erscheint auch als Druckausgabe 978-3-540-77146-3 Lecture notes in computational science and engineering 63 (DE-604)BV022396727 63 https://doi.org/10.1007/978-3-540-77147-0 Verlag Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017480587&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bebendorf, Mario 1972- Hierarchical matrices a means to efficiently solve elliptic boundary value problems ; with 53 tables Lecture notes in computational science and engineering Diskrete Approximation (DE-588)4503166-6 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Integraloperator (DE-588)4131247-8 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd Hierarchische Matrix (DE-588)4702093-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4503166-6 (DE-588)4017233-8 (DE-588)4131247-8 (DE-588)4193399-0 (DE-588)4702093-3 (DE-588)4128130-5 (DE-588)4113937-9 |
| title | Hierarchical matrices a means to efficiently solve elliptic boundary value problems ; with 53 tables |
| title_auth | Hierarchical matrices a means to efficiently solve elliptic boundary value problems ; with 53 tables |
| title_exact_search | Hierarchical matrices a means to efficiently solve elliptic boundary value problems ; with 53 tables |
| title_full | Hierarchical matrices a means to efficiently solve elliptic boundary value problems ; with 53 tables Mario Bebendorf |
| title_fullStr | Hierarchical matrices a means to efficiently solve elliptic boundary value problems ; with 53 tables Mario Bebendorf |
| title_full_unstemmed | Hierarchical matrices a means to efficiently solve elliptic boundary value problems ; with 53 tables Mario Bebendorf |
| title_short | Hierarchical matrices |
| title_sort | hierarchical matrices a means to efficiently solve elliptic boundary value problems with 53 tables |
| title_sub | a means to efficiently solve elliptic boundary value problems ; with 53 tables |
| topic | Diskrete Approximation (DE-588)4503166-6 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Integraloperator (DE-588)4131247-8 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd Hierarchische Matrix (DE-588)4702093-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Diskrete Approximation Finite-Elemente-Methode Integraloperator Elliptisches Randwertproblem Hierarchische Matrix Numerisches Verfahren Hochschulschrift |
| url | https://doi.org/10.1007/978-3-540-77147-0 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017480587&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022396727 |
| work_keys_str_mv | AT bebendorfmario hierarchicalmatricesameanstoefficientlysolveellipticboundaryvalueproblemswith53tables |