Holdings: New parallel algorithms for direct solution of linear equations

New parallel algorithms for direct solution of linear equations:

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Bibliographic Details
Main Authors:	Murthy, C. Siva Ram (Author), Murthy, K. N. Balasubramanya (Author), Aluru, Srinivas (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Wiley 2001
Series:	Wiley series on parallel and distributed computing A Wiley-Interscience publication
Subjects:	Datenverarbeitung Computer algorithms Differential equations, Linear > Data processing Parallel processing (Electronic computers) Direkte Methode Paralleler Algorithmus Lineares Gleichungssystem
Online Access:	Inhaltsverzeichnis
Physical Description:	X, 167 S. graph. Darst.
ISBN:	0471361658

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MARC


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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
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author	Murthy, C. Siva Ram Murthy, K. N. Balasubramanya Aluru, Srinivas
author_facet	Murthy, C. Siva Ram Murthy, K. N. Balasubramanya Aluru, Srinivas
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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
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