High Performance Algorithms for Structured Matrix Problems

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Peter Arbenz
Nova Publishers, 1998 - Computers - 203 pages
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The main aim of this volume is to summarise the state of the art in the area of high performance solutions of structured linear systems as well as the area of structured eigenvalue and singular-value problems. The volume highlights research directions perceived to be the most important for computing the structured problems. The topics covered range from parallel solvers for sparse or banded linear systems to parallel computation of eigenvalues and singular values of tridiagonal and bidiagonal matrices. In addition, the volume contains articles on specialised solution techniques for dense Toeplitz and Hankel matrices. The papers also discuss implementation issues on numerous parallel architectures such as vector computers, shared and distributed memory multiprocessors, and clusters of workstations.
 

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Contents

A COMPARISON OF FRONTAL SOFTWARE WITH OTHER HARWELL SUBROUTINE LIBRARY SPARSE DIRECT SOLVERS
1
ALGORITHMS APPLICATIONS AND REAL INDUSTRIAL CASES IN ELECTROMAGNETICS
27
ON THE STABLE PARALLEL SOLUTION OF GENERAL NARROW BANDED LINEAR SYSTEMS
47
EIGENVALUE PROBLEMS
74
EFFICIENT ALGORITHMS FOR REDUCING BANDED MATRICES TO BIDIAGONAL AND TRIDIAGONAL FORM
75
PARALLEL BISECTION ALGORITHMS FOR SOLVING THE SYMMETRIC TRIDIAGONAL EIGENPROBLEM
91
A PARALLEL QR ALGORITHM FOR THE SYMMETRIC TRIDIAGONAL EIGENVALUE PROBLEM
113
MATRICES WITH SPECIAL STRUCTURE
125
A NUMERICAL COMPARISON OF LOOKAHEAD LEVINSON AND SCHUR ALGORITHMS FOR NONHERMITIAN TOEPLITZ SYSTEMS
127
SUPERFAST SOLUTION OF LINEAR EQUATIONS WITH LOW DISPLACEMENT RANK
149
PARALLEL COMPUTATION
162
LOADBALANCE IN PARALLEL FACR
163
PARALLEL CGMETHODS AUTOMATICALLY OPTIMIZED FOR PC AND WORKSTATIONCLUSTERS
181
Index
199
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