Abstract
Several serial and parallel algorithms for computing the LU-factorization of a dense matrix are investigated. Numerical experiments and programming considerations to reduce bank conflicts on the Cray X-MP4 parallel computer are presented. Speedup factors are given for the parallel algorithms.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
D.A. Calahan. “Task Granularity Studies on a Many-Processor Cray X-MP.” Parallel Computing, Vol. 2, 1985, pp. 109–118.
D.A. Calahan, W.N. Joy, and D.A. Orbits, “Preliminary Report on Results of Matrix Benchmarks on Vector Processors.” U. of Michigan report SEL 94, May 1976.
Steven S. Chen, Jack J. Dongarra, and Christopher C. Hsiung. “Multiprocessing Linear Algebra Algorithms on the Cray X-MP2: Experiences with Small Granularity.” Journal of Parallel and Distributed Computing, Vol. 1, No. 1, August 1984.
J.J. Dongarra, J.R. Bunch, C.B. Moler, and G.W. Stewart. LINPACK User's Guide, Society for Industrial and Applied Mathematics, Philadelphia, 1979.
J.J. Dongarra and S.C. Eisenstat. “Squeezing the most out of an algorithm in CRAY Fortran.” ACM Transactions on Mathematical Software, Vol. 10, No. 3, September 1984, pp. 219–230.
J.J. Dongarra, F.G. Gustavson, and A. Karp. “Implementing Linear Algebra Algorithms for Dense Matrices on a Vector Pipeline Machine.” SIAM Review, Vol. 26, No. 1, January 1984, pp. 91–112.
Jack J. Dongarra and Tom Hewitt. “Implementing Dense Linear Algebra Algorithms Using Multitasking on the Cray X-MP4 (or Approaching the Gigaflop).” SIAM Journal of Scientific and Statistical Computing, Vol. 7, No. 1, January 1986, pp. 347–350.
Jack J. Dongarra and Robert Hiromoto. “A Collection of Parallel Linear Equations Routines for the Denelcor HEP.” Parallel Computing, Vol. 1, No. 2, 1984.
K.W. Fong and T.L. Jordan. “Some Linear Algebraic Algorithms and Their Performance on CRAY-1.” Los Alamos National Laboratory report LA-6774, June 1977.
T.L. Jordan. “A Performance Evaluation of Linear Algebra Software in Parallel Architectures.” Los Alamos National Laboratory report LA-8078-MS, October 1979.
David R. Kincaid and Thomas C. Oppe. “A Parallel Algorithm for the General LU-Factorization.” Center for Numerical Analysis report CNA-208, The University of Texas at Austin, April 1987.
C.L. Lawson, R.J. Hanson, D.R. Kincaid, and F.T. Krogh. “Basic Linear Algebra Subprograms for Fortran Usage.” ACM Transactions on Mathematical Software, Vol. 5, No. 3, September 1979, pp. 308–323.
Cleve B. Moler. “Matrix Computations with Fortran and Paging.” Communications of the ACM, Vol. 15, April 1972, pp. 268–270.
Multitasking User Guide. Cray Computer Systems Technical Note. Publication SN-0222, Revision B, March 1986.
G.W. Stewart. Introduction to Matrix Computation, Academic Press, New York, 1973.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Oppe, T.C., Kincaid, D.R. (1988). Parallel LU-factorization algorithms for dense matrices. In: Houstis, E.N., Papatheodorou, T.S., Polychronopoulos, C.D. (eds) Supercomputing. ICS 1987. Lecture Notes in Computer Science, vol 297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18991-2_34
Download citation
DOI: https://doi.org/10.1007/3-540-18991-2_34
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18991-6
Online ISBN: 978-3-540-38888-3
eBook Packages: Springer Book Archive