Parallel LU-factorization algorithms for dense matrices

  • Thomas C. Oppe
  • David R. Kincaid
Session 6B: Parallel Numeric Methods
Part of the Lecture Notes in Computer Science book series (LNCS, volume 297)


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.


Parallel Algorithm Small Problem Size Update Algorithm Serial Algorithm Vector Register 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D.A. Calahan. “Task Granularity Studies on a Many-Processor Cray X-MP.” Parallel Computing, Vol. 2, 1985, pp. 109–118.Google Scholar
  2. [2]
    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.Google Scholar
  3. [3]
    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.Google Scholar
  4. [4]
    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.Google Scholar
  5. [5]
    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.Google Scholar
  6. [6]
    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.Google Scholar
  7. [7]
    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.Google Scholar
  8. [8]
    Jack J. Dongarra and Robert Hiromoto. “A Collection of Parallel Linear Equations Routines for the Denelcor HEP.” Parallel Computing, Vol. 1, No. 2, 1984.Google Scholar
  9. [9]
    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.Google Scholar
  10. [10]
    T.L. Jordan. “A Performance Evaluation of Linear Algebra Software in Parallel Architectures.” Los Alamos National Laboratory report LA-8078-MS, October 1979.Google Scholar
  11. [11]
    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.Google Scholar
  12. [12]
    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.Google Scholar
  13. [13]
    Cleve B. Moler. “Matrix Computations with Fortran and Paging.” Communications of the ACM, Vol. 15, April 1972, pp. 268–270.Google Scholar
  14. [14]
    Multitasking User Guide. Cray Computer Systems Technical Note. Publication SN-0222, Revision B, March 1986.Google Scholar
  15. [15]
    G.W. Stewart. Introduction to Matrix Computation, Academic Press, New York, 1973.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Thomas C. Oppe
    • 1
  • David R. Kincaid
    • 1
  1. 1.Center for Numerical AnalysisThe University of Texas at AustinAustinUSA

Personalised recommendations