Parallel Algorithms for Matrix Computations PDF
Preview Parallel Algorithms for Matrix Computations
Parallel Algorithms for Matrix Computations This page intentionally left blank Parallel Algorithms for Matrix Computations K. A. Gallivan Michael T. Heath Esmond Ng James M. Ortega Barry W. Peyton R. J. Plemmons Charles H. Romine A. H. Sameh Robert G. Voigt Philadelphia Philadelphia Society for Industrial and Applied Mathematics Copyright ©1990 by the Society for Industrial and Applied Mathematics. 1 0 9 8 7 6 5 4 All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written per- mission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 University City Science Center, Philadelphia, PA 19104-2688. Library of Congress Cataloging-in-Publication Data Parallel Algorithms for matrix computations / K. A. Gallivan ... [et al.]. p. cm. Includes bibliographical references. ISBN 0-89871-260-2 1. Matrices—Data processing. 2. Algorithms. 3. Parallel processing (Electronic computers) I. Gallivan, K. A. (Kyle A.) QA188.P367 1990 512.9'434—dc20 90-22017 is a registered trademark. List of Authors K. A. Gallivan, Center for Supercomputing Research and Development, University of Illinois, Urbana, IL 61801. Michael T. Heath, Mathematical Sciences Section, Oak Ridge National Laboratory, P.O. Box 2009, Oak Ridge, TN 37831-8083. Esmond Ng, Mathematical Sciences Section, Oak Ridge National Laboratory, P.O. Box 2009, Oak Ridge, TN 37831-8083. James M. Ortega, Applied Mathematics Department, University of Virginia, Charlottesville, VA 22903. Barry W. Peyton, Mathematical Sciences Section, Oak Ridge National Laboratory, P.O. Box 2009, Oak Ridge, TN 37831-8083. R. J. Plemmons, Department of Mathematics and Computer Science, Wake Forest University, Winston-Salem, NC 27109. Charles H. Romine, Mathematical Sciences Section, Oak Ridge National Laboratory, P.O. Box 2009, Oak Ridge, TN 37831-8083. A. H. Sameh, Center for Supercomputing Research and Development, University of Illinois, Urbana, IL 61801. Robert G. Voigt, ICASE, NASA Langley Research Center, Hampton, VA 23665. V This page intentionally left blank Preface This book consists of three papers that collect, describe, or reference an extensive se- lection of important parallel algorithms for matrix computations. Algorithms for matrix computations are among the most widely used computational tools in science and engi- neering. They are usually the first such tools to be implemented in any new computing environment. Due to recent trends in the design of computer architectures, the scien- tific and engineering research community is becoming increasingly dependent upon the development and implementation of efficient parallel algorithms for matrix computa- tions on modern high-performance computers. Architectures considered here include both shared-memory systems and distributed-memory systems, as well as combinations of the two. The volume contains two broad survey papers and an extensive bibliogra- phy. The purpose is to provide an overall perspective on parallel algorithms for both dense and sparse matrix computations in solving systems of linear equations, as well as for dense or structured problems arising in least squares computations, eigenvalue and singular-value computations, and rapid elliptic solvers. Major emphasis is given to com- putational primitives whose efficient execution on parallel and vector computers is es- sential to attaining high-performance algorithms. Short descriptions of the contents of each of the three papers in this book are provided in the following paragraphs. The first paper (by Gallivan, Plemmons, and Sameh) contains a general perspective on modern parallel and vector architectures and the way in which they influence algo- rithm design. The paper also surveys associated algorithms for dense matrix computa- tions. The authors concentrate on approaches to computations that have been used on shared-memory architectures with a modest number of (possibly vector) processors, as well as distributed-memory architectures, such as hypercubes, having a relatively large number of processors. The architectures considered include both commercially available machines and experimental research prototypes. Algorithms for dense or structured matrix computations in direct linear system solvers, direct least squares computations, eigenvalue and singular-value computations, and rapid elliptic solvers are considered. Since the amount of literature in these areas is quite large, an attempt has been made to select representative work. The second paper (by Heath, Ng, and Peyton) is primarily concerned with parallel al- gorithms for solving symmetric positive definite sparse linear systems. The main driving force for the development of vector and parallel computers has been scientific and engi- neering computing, and perhaps the most common problem that arises is that of solving sparse symmetric positive definite linear systems. The authors focus their attention on direct methods of solution, specifically by Cholesky factorization. Parallel algorithms are surveyed for all phases of the solution process for sparse systems, including ordering, symbolic factorization, numeric factorization, and triangular solution. vii The final paper (by Ortega, Voigt, and Romine) consists of an extensive bibliography on parallel and vector numerical algorithms. Over 2,000 references, collected by the au- thors over a period of several years, are provided in this work. Although this is primar- ily a bibliography on numerical methods, also included are a number of references on machine architecture, programming languages, and other topics of interest to computa- tional scientists and engineers. The book may serve as a reference guide on modern computational tools for research- ers in science and engineering. It should be useful to computer scientists, mathemati- cians, and engineers who would like to learn more about parallel and vector computa- tions on high-performance computers. The book may also be useful as a graduate text in scientific computing. For instance, many of the algorithms discussed in the first two pa- pers have been treated in courses on scientific computing that have been offered re- cently at several universities. R. J. Plemmons Wake Forest University Contents 1 Parallel Algorithms for Dense Linear Algebra Computations K.A. Gallivan, R.J.Plemmons, and A.H. Sameh (Reprinted from SIAM Review, March 1990). 83 Parallel Algorithms for Sparse Linear Systems Michael T. Heath, Esmond Ng, and Barry W. Peyton 125 A Bibliography on Parallel and Vector Numerical Algorithms James M. Ortega, Robert G. Voigt, and Charles H. Romine ix
The list of books you might like
