New parallel algorithms for direct solution of linear equations:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
2001
|
| Schriftenreihe: | Wiley series on parallel and distributed computing
A Wiley-Interscience publication |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 167 S. graph. Darst. |
| ISBN: | 0471361658 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV013890940 | ||
| 003 | DE-604 | ||
| 005 | 20031106 | ||
| 007 | t | ||
| 008 | 010904s2001 d||| |||| 00||| eng d | ||
| 020 | |a 0471361658 |9 0-471-36165-8 | ||
| 035 | |a (OCoLC)43167931 | ||
| 035 | |a (DE-599)BVBBV013890940 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-703 | ||
| 050 | 0 | |a QA372 | |
| 082 | 0 | |a 515/.354/0285 |2 21 | |
| 084 | |a SK 915 |0 (DE-625)143271: |2 rvk | ||
| 100 | 1 | |a Murthy, C. Siva Ram |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a New parallel algorithms for direct solution of linear equations |c C. Siva Ram Murthy ; K. N. Balasubramanya Murthy ; Srinivas Aluru |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 2001 | |
| 300 | |a X, 167 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series on parallel and distributed computing | |
| 490 | 0 | |a A Wiley-Interscience publication | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Computer algorithms | |
| 650 | 4 | |a Differential equations, Linear |x Data processing | |
| 650 | 4 | |a Parallel processing (Electronic computers) | |
| 650 | 0 | 7 | |a Direkte Methode |0 (DE-588)4705893-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Paralleler Algorithmus |0 (DE-588)4193615-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineares Gleichungssystem |0 (DE-588)4035826-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineares Gleichungssystem |0 (DE-588)4035826-4 |D s |
| 689 | 0 | 1 | |a Direkte Methode |0 (DE-588)4705893-6 |D s |
| 689 | 0 | 2 | |a Paralleler Algorithmus |0 (DE-588)4193615-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Murthy, K. N. Balasubramanya |e Verfasser |4 aut | |
| 700 | 1 | |a Aluru, Srinivas |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009504217&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009504217 | ||
Datensatz im Suchindex
| _version_ | 1804128731448475648 |
|---|---|
| adam_text | NEW PARALLEL ALGORITHMS FOR DIRECT SOLUTION OF LINEAR EQUATIONS C. SIVA
RAM MURTHY INDIAN INSTITUTE OF TECHNOLOGY, MADRAS K. N. BALASUBRAMANYA
MURTHY MALNAD COLLEGE OF ENGINEERING, INDIA SRINIVAS ALURU IOWA STATE
UNIVERSITY A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. NEW
YORK * CHICHESTER * WEINHEIM * BRISBANE * SINGAPORE * TORONTO CONTENTS
PREFACE IX 1. INTRODUCTION 1 1.1 SOLVING LINEAR EQUATIONS 1 1.2 A BRIEF
SURVEY OF PARALLEL LINEAR SYSTEM SOLVERS 3 1.2.1 DENSE LINEAR SYSTEMS 3
1.2.2 SPARSE LINEAR SYSTEMS 4 1.3 ORGANIZATION OF THE BOOK 5 PROBLEMS 6
2. PARALLEL COMPUTATIONAL MODEL AND ALGORITHM DESIGN ISSUES 8 2.1 THE
NEED FOR PARALLEL COMPUTING 8 2.2 GOALS OF PARALLEL ALGORITHM DESIGN 9
2.3 PARALLEL ARCHITECTURES 11 2.3.1 STATIC INTERCONNECTION NETWORKS 13
2.3.2 DYNAMIC MULTISTAGE INTERCONNECTION NETWORKS 16 2.4 COMMUNICATION
SCHEMES 17 2.5 MODEL OF PARALLEL COMPUTATION 20 2.6 LOGICAL MESH
TOPOLOGY 21 PROBLEMS 22 3. BIDIRECTIONAL GAUSSIAN ELIMINATION 24 3.1
INTRODUCTION 24 3.2 SEQUENTIAL GAUSSIAN ELIMINATION (GE) ALGORITHM 25
3.3 PIVOTING USED IN GE-BASED ALGORITHMS 26 3.3.1 SOME FUNDAMENTAL
CONCEPTS OF PAIRWISE PIVOTING 27 3.3.2 PARALLEL ELIMINATION SCHEMES WITH
PAIRWISE PIVOTING 27 3.4 DIVISION-FREE GE ALGORITHM 27 VI CONTENTS 3.5
PARALLEL BIDIRECTIONAL GAUSSIAN ELIMINATION (BGE) ALGORITHM 29 3.5.1
MEMORY REQUIREMENTS 32 3.5.2 ERROR ANALYSIS 33 3.6 DIVISION-FREE BGE
ALGORITHM 35 3.7 PARALLEL IMPLEMENTATION OF BGE ALGORITHM 36 3.7.1
PARALLEL TIME OF THE BGE ALGORITHM 38 3.7.2 PARALLEL TIME OF THE GE
ALGORITHM 40 3.7.3 COMPARISON OF BGE AND GE ALGORITHMS 45 3.8
CONCLUSIONS 45 BIBLIOGRAPHIC NOTES 48 PROBLEMS 49 4. BIDIRECTIONAL LU
FACTORIZATION 51 4.1 INTRODUCTION 51 4.2 LU FACTORIZATION ALGORITHM 52
4.3 BIDIRECTIONAL LU DECOMPOSITION (BLU) ALGORITHM 54 4.3.1 MULTIPLIER
DUPLICATION PHASE (MDP) 57 4.3.2 MODIFIED BIDIRECTIONAL FORWARD
SUBSTITUTION PHASE (BFSP) 57 4.4 PARALLEL IMPLEMENTATION OF BLU
ALGORITHM 58 4.5 CONCLUSIONS 63 BIBLIOGRAPHIC NOTES 63 PROBLEMS 65 5.
BIDIRECTIONAL HOUSEHOLDER REDUCTIONS AND MODIFIED 66 GRAM-SCHMIDT
ORTHOGONALIZATION 5.1 INTRODUCTION 66 5.2 QR DECOMPOSITION-BASED METHODS
66 5.2.1 HOUSEHOLDER REDUCTIONS METHOD 67 5.2.2 GRAM-SCHMIDT ORTHOGONAL
FACTORIZATION METHOD 68 5.3 BIDIRECTIONAL ALGORITHMS 69 5.3.1
BIDIRECTIONAL HOUSEHOLDER REDUCTIONS (BHR) ALGORITHM 69 5.3.2
BIDIRECTIONAL MGS (BMGS) ORTHOGONALIZATION ALGORITHM 71 5.4 PARALLEL
IMPLEMENTATION OF BHR AND BMGS ALGORITHMS 72 5.4.1 PARALLEL TIME OF THE
BHR ALGORITHM 74 5.4.2 PARALLEL TIME OF THE BMGS ALGORITHM 77 CONTENTS
VII 5.5 CONCLUSIONS 79 BIBLIOGRAPHIC NOTES 80 PROBLEMS 81 6.
BIDIRECTIONAL GIVENS ROTATIONS 83 6.1 INTRODUCTION 83 6.2 SOME
FUNDAMENTAL CONCEPTS OF GIVENS ROTATIONS 84 6.2.1 STANDARD GIVENS 84
6.2.2 BASIC MODIFICATION 84 6.2.3 SQUARE-ROOT-FREE COMPUTATIONS 85 6.2.4
SOLVING LINEAR EQUATIONS USING FAST GIVENS ROTATIONS 85 6.3 PARALLEL
ANNIHILATION SCHEMES 86 6.3.1 TOP-DOWN (TD) SCHEME 86 6.3.2 BOTTOM-UP
(BU) SCHEME 87 6.4 BIDIRECTIONAL GIVENS ROTATIONS (BGR) ALGORITHM 88 6.5
PARALLEL IMPLEMENTATION OF BGR ALGORITHM 89 6.5.1 PARALLEL TIME OF THE
BGR ALGORITHM 92 6.6 CONCLUSIONS 93 BIBLIOGRAPHIC NOTES 94 PROBLEMS 95
7. BIDIRECTIONAL SPARSE CHOLESKY FACTORIZATION 96 7.1 INTRODUCTION 96
7.2 BIDIRECTIONAL SPARSE CHOLESKY FACTORIZATION (BSCF) ALGORITHM 97
7.2.1 THE CONCEPT 97 7.2.2 EXPLOITING THE SPARSITY OF THE COEFFICIENT
MATRIX 98 7.3 PARALLEL IMPLEMENTATION OF BSCF ALGORITHM 99 7.3.1 THE
SUBSTITUTION PHASE 104 7.3.2 ORDERING THE SPARSE SYMMETRIC MATRIX 108
7.3.3 THE SYMBOLIC FACTORIZATION ALGORITHM 112 7.4 CONCLUSIONS 119
BIBLIOGRAPHIC NOTES 119 PROBLEMS 120 8. BIDIRECTIONAL SPARSE
FACTORIZATION 121 8.1 INTRODUCTION 121 VIII CONTENTS 8.2 BIDIRECTIONAL
SPARSE FACTORIZATION (BSF) ALGORITHM 122 8.2.1 THE CONCEPT 122 8.2.2
EXPLOITING THE SPARSITY OF THE COEFFICIENT MATRIX 122 8.3 PARALLEL
IMPLEMENTATION OF BSF ALGORITHM 123 8.3.1 ORDERING THE GENERAL SPARSE
MATRIX FOR BIDIRECTIONAL 126 FACTORIZATION 8.3.2 THE BIDIRECTIONAL
SYMBOLIC FACTORIZATION ALGORITHM 128 8.4 CONCLUSIONS 129 BIBLIOGRAPHIC
NOTES 130 PROBLEMS 130 9. BIDIRECTIONAL ELIMINATION ALGORITHMS REVISITED
131 9.1 CONTROLLING THE INHERENT PARALLELISM IN BIDIRECTIONAL
ELIMINATION 131 ALGORITHMS 9.1.1 VERSION I: PARALLEL BIDIRECTIONAL
ELIMINATION ALGORITHM TO 131 EXISTING SEQUENTIAL ALGORITHM SWITCHOVER
9.1.2 VERSION II: PARALLEL TRIANGULATION ALGORITHM TO PARALLEL 132
BIDIRECTIONAL ALGORITHM SWITCHOVER 9.2 COLUMN PIVOTING AND FULL PIVOTING
X IN BIDIRECTIONAL ELIMINATION 133 ALGORITHMS 9.3 DIRECTIONS FOR FUTURE
WORK 134 A. FAULT-TOLERANT IMPLEMENTATION OF BGE ALGORITHM 137 A.I
FUNDAMENTALS OF FAULT TOLERANCE 137 A.2 TIME REDUNDANCY APPROACH 138 A.3
ABFT APPROACH 139 A.3.1 FUNDAMENTALS OF ABFT 139 A.3.2 ABFT ON A LINEAR
ARRAY 140 A.4 ABFT FOR BGE ALGORITHM 141 B. *- SEMIRINGS ALGORITHM FOR
SOLUTION OF LINEAR EQUATIONS 147 B.I BASICS OF *-SEMIRINGS 147 B.2
SOLUTION OF LINEAR EQUATIONS USING *-SEMIRINGS 148 BIBLIOGRAPHY 152
INDEX 165
|
| any_adam_object | 1 |
| author | Murthy, C. Siva Ram Murthy, K. N. Balasubramanya Aluru, Srinivas |
| author_facet | Murthy, C. Siva Ram Murthy, K. N. Balasubramanya Aluru, Srinivas |
| author_role | aut aut aut |
| author_sort | Murthy, C. Siva Ram |
| author_variant | c s r m csr csrm k n b m knb knbm s a sa |
| building | Verbundindex |
| bvnumber | BV013890940 |
| callnumber-first | Q - Science |
| callnumber-label | QA372 |
| callnumber-raw | QA372 |
| callnumber-search | QA372 |
| callnumber-sort | QA 3372 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 915 |
| ctrlnum | (OCoLC)43167931 (DE-599)BVBBV013890940 |
| dewey-full | 515/.354/0285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.354/0285 |
| dewey-search | 515/.354/0285 |
| dewey-sort | 3515 3354 3285 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01970nam a2200481 c 4500</leader><controlfield tag="001">BV013890940</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20031106 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">010904s2001 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0471361658</subfield><subfield code="9">0-471-36165-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)43167931</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013890940</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-703</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA372</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.354/0285</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 915</subfield><subfield code="0">(DE-625)143271:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Murthy, C. Siva Ram</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">New parallel algorithms for direct solution of linear equations</subfield><subfield code="c">C. Siva Ram Murthy ; K. N. Balasubramanya Murthy ; Srinivas Aluru</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Wiley</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 167 S.</subfield><subfield code="b">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="490" ind1="0" ind2=" "><subfield code="a">Wiley series on parallel and distributed computing</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">A Wiley-Interscience publication</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Datenverarbeitung</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer algorithms</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, Linear</subfield><subfield code="x">Data processing</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Parallel processing (Electronic computers)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Direkte Methode</subfield><subfield code="0">(DE-588)4705893-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Paralleler Algorithmus</subfield><subfield code="0">(DE-588)4193615-2</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="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">Direkte Methode</subfield><subfield code="0">(DE-588)4705893-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Paralleler Algorithmus</subfield><subfield code="0">(DE-588)4193615-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Murthy, K. N. Balasubramanya</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Aluru, Srinivas</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV 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=009504217&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009504217</subfield></datafield></record></collection> |
| id | DE-604.BV013890940 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:53:54Z |
| institution | BVB |
| isbn | 0471361658 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009504217 |
| oclc_num | 43167931 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | X, 167 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series on parallel and distributed computing A Wiley-Interscience publication |
| spelling | Murthy, C. Siva Ram Verfasser aut New parallel algorithms for direct solution of linear equations C. Siva Ram Murthy ; K. N. Balasubramanya Murthy ; Srinivas Aluru New York [u.a.] Wiley 2001 X, 167 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series on parallel and distributed computing A Wiley-Interscience publication Datenverarbeitung Computer algorithms Differential equations, Linear Data processing Parallel processing (Electronic computers) Direkte Methode (DE-588)4705893-6 gnd rswk-swf Paralleler Algorithmus (DE-588)4193615-2 gnd rswk-swf Lineares Gleichungssystem (DE-588)4035826-4 gnd rswk-swf Lineares Gleichungssystem (DE-588)4035826-4 s Direkte Methode (DE-588)4705893-6 s Paralleler Algorithmus (DE-588)4193615-2 s DE-604 Murthy, K. N. Balasubramanya Verfasser aut Aluru, Srinivas Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009504217&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Murthy, C. Siva Ram Murthy, K. N. Balasubramanya Aluru, Srinivas New parallel algorithms for direct solution of linear equations Datenverarbeitung Computer algorithms Differential equations, Linear Data processing Parallel processing (Electronic computers) Direkte Methode (DE-588)4705893-6 gnd Paralleler Algorithmus (DE-588)4193615-2 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd |
| subject_GND | (DE-588)4705893-6 (DE-588)4193615-2 (DE-588)4035826-4 |
| title | New parallel algorithms for direct solution of linear equations |
| title_auth | New parallel algorithms for direct solution of linear equations |
| title_exact_search | New parallel algorithms for direct solution of linear equations |
| title_full | New parallel algorithms for direct solution of linear equations C. Siva Ram Murthy ; K. N. Balasubramanya Murthy ; Srinivas Aluru |
| title_fullStr | New parallel algorithms for direct solution of linear equations C. Siva Ram Murthy ; K. N. Balasubramanya Murthy ; Srinivas Aluru |
| title_full_unstemmed | New parallel algorithms for direct solution of linear equations C. Siva Ram Murthy ; K. N. Balasubramanya Murthy ; Srinivas Aluru |
| title_short | New parallel algorithms for direct solution of linear equations |
| title_sort | new parallel algorithms for direct solution of linear equations |
| topic | Datenverarbeitung Computer algorithms Differential equations, Linear Data processing Parallel processing (Electronic computers) Direkte Methode (DE-588)4705893-6 gnd Paralleler Algorithmus (DE-588)4193615-2 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd |
| topic_facet | Datenverarbeitung Computer algorithms Differential equations, Linear Data processing Parallel processing (Electronic computers) Direkte Methode Paralleler Algorithmus Lineares Gleichungssystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009504217&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT murthycsivaram newparallelalgorithmsfordirectsolutionoflinearequations AT murthyknbalasubramanya newparallelalgorithmsfordirectsolutionoflinearequations AT alurusrinivas newparallelalgorithmsfordirectsolutionoflinearequations |