Abstract
The main problem in parallel computation is to get a number of computers to cooperate in solving a single problem. The word “single” is necessary here to exclude the case of processors in a system working on unrelated problems. Ideally we should like to take a problem that requires time T to solve on a single processor and solve it in time T/p on a system consisting of p processors. We say that a system is efficient in proportion as it achieves this goal.
This work was supported in part by the Air Force Office of Sponsored Research under grant AFOSR-82–0078.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. S. Almas. Overview of parallel computing. Parallel Compting, 2:191–203, 1985.
M. Annoratone, E. Arnould, T. Gross, H. T. Kung, O. Menzicioglu, and J. A. Webb. The WARP computer: architecture, implementation, and performance. IEEE Transaction on Computers, C-36:1523–1538, 1987.
J. L. Barlow and I. C. F. Ipsen. Scaled Givens rotations for the solution of linear least squares problems on systolic arrays. SIAM Journal on Scientific and Statistical Computing, 8:716–734, 1987.
C. Bischof and C. Van Loan. The WY representation for products of Householder transformations. SIAM Journal on Scientific and Statistical Computing, 8:s2–s13, 1987.
A. Bojanczyk and R. P. Brent. Parallel solution of certain toeplitz least-squares problems. Linear Algebra and Its Applications, 77:43–60, 1986.
A. Brass and G. S. Pawley. Two and three dimensional FFTs on highly parallel compters. Parallel Computing, 3:167–184, 1986.
Jack J. Dongarra, Jeremy Du Croz, , Iain Duff, and Sven Hammarling. A proposal for a set of level 3 basic linear algebra subprograms. SIGNUM Newsletter, 22:2–14, 1987.
M. Flynn. Very high speed computing. Proceedings of the IEEE, 1901–1909, 1966.
G. C. Fox, S. W. Otto, and A. J. G. Hey. Matrix algorithms on a hypercube I: matrix multiplication. Parallel Computing, 4:17–31, 1987.
W. M. Gentleman. Using the Harmony Operating System. Technical Report ERB-966, Natonal Research Council of Canada, 1985.
A. George, M. T. Heath, J. Liu, and E. NG. Sparse cholesky factorization on a local-memory multiprocessor. SIAM Journal on Scientific and Statiscal Computing, 9:327–340, 1988.
Alan George and Eleanor Chu. Gaussian Elimination with Partial Pivoting and Load Balancing on a Multiprocessor. Technical Report ORNL/TM-10323, Mathematical Sciences Section, Oak Ridge National Laboratory, 1987.
Carlo Ghezzi. Concurrency in programming languages: a survey. Parallel Computing, 2:224–241, 1985.
L. Guangye and T. F. Coleman. A parallel triangular solver for a distributed memory multiprocessor. SIAM Journal on Scientific and Statistical Computing, 9:485–502, 1988.
J. L. Gustafson, G. R. Montry, and R. E. Benner. Development of parallel methods for a 1024-processor hypercube. SIAM Journal on Scientific and Statistical Computing, 9:, 1988. To appear in July.
R. W. Hockney. MIMD computing in the USA—1984. Parallel Computing, 3:119–136, 1985.
R. W. Hockney and C. R. Jesshope. Parallel Computers. Adam Hilger Ltd., Bristol, 1981.
K. Hwang and F. A. Briggs. Computer Architecture and Parallel Processing. McGraw-Hill, New York, 1984.
R. Karp and R. Miller. Properties of a model for parallel computation: determinacy, termination, queuing. SIAM Journal on Applied Mathematics, 14:1390–1411, 1966.
H. T. Kung. Why systolic architectures? IEEE Computer, 15:37–46, 1982.
F. T. Luk. A triangular processor array for computing singular values. Linear Algebra and Its Applications, 77:259–274, 1986.
W. Oed and O. Lange. Modelling, measurement, and simulation of memory interference in the CRAY XM-P. Parallel Computing, 3:343–358, 1986.
D. P. O’Leary, Roger Pierson, G. W. Stewart, and Mark Wieser. The Maryland CRAB; A Module for Building Parallel Computers. Technical Report TR-1660, Department of Computer Science, University of Maryland, 1986.
D. P. C’Leary and G. W. Stewart. From determinacy to systaltic arrays. IEEE Transactions on Computers, C-36-.1355–1359, 1987.
D. P. O’Leary, G. W. Stewart, and Robert van de Geijn. DOMINO; A Message Passing Environment for Parallel Computation. TR-1648, University of Maryland, Computer Science, 1986.
J. M. Ortega. Introduction to Parallel and Vector Computing. Plenum Press, New York, 1988.
C. Rieger. Zmob: hardware from a user’s viewpoint. In Proceedings of the IEEE Computer Society Conference on Pettern Recognition and Image Processing, pages 399–408, 1981.
C. Seitz. The cosmic cube. Communications of the Association for Computing Machinery, 28:22–33, 1985.
G. W. Stewart. A Jacobi-like algorithm for computing the Schur decomposition of a non-Hermitian matrix. SIAM Journal on Scientific and Statistical Computing, 28:853–864, 1985.
Robert A. van de Geijn. Implementing the QR-Algorithm on an Array of Processors. Technical Report 1897, Department of Computer Science, University of Maryland, 1987.
Pen-Chung Yew, Niau-Feng Tzeng, and D. H. Lawrie. Distributing hot-spot addressing in large scale multiprocessors. IEEE Transactions on Computers, C-36:338–395, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Physica-Verlag Heidelberg
About this paper
Cite this paper
Stewart, G.W. (1988). Parallel Linear Algebra in Statistical Computations. In: Edwards, D., Raun, N.E. (eds) Compstat. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-46900-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-46900-8_1
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-0411-9
Online ISBN: 978-3-642-46900-8
eBook Packages: Springer Book Archive