Gauss elimination algorithms for mimd computers

  • M. Cosnard
  • M. Marrakchi
  • Y. Robert
  • D. Trystram
Namerical Algorithms (Session 3.2)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 237)


This paper uses a graph-theoretic approach to analyse the performances of several parallel variations of the Gaussian triangularization algorithm on an MIMD computer. Dongarra et al. [DGK] have studied various parallel implementations of this method for a vector pipeline machine. We obtain complexity results permitting to select among these parallel algorithms.


Execution Time Greedy Algorithm Parallel Algorithm Arithmetic Operation Parallel Implementation 
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.


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  1. [CRT1]
    M. COSNARD, Y. ROBERT, D. TRYSTRAM, Résolution parallèle de systèmes linéaires denses par diagonalisation, Bulletin EDF série C, no 2, 1986Google Scholar
  2. [CRT2]
    M. COSNARD, Y. ROBERT, D. TRYSTRAM, Comparaison des méthodes parallèles de diagonalisation pour la résolution de systèmes linéaires denses, C. R. A. S. Paris 301, I, 16, 1985, 781–784Google Scholar
  3. [CMRT]
    M. COSNARD, J.M. MULLER, Y. ROBERT, D. TRYSTRAM, Communication costs versus computation costs in parallel Gaussian elimination, Proc. of Conf. Parallel Algorithms and Architectures, M. Cosnard et al. eds, North Holland, to appearGoogle Scholar
  4. [DGK]
    J.J. DONGARRA, F.G. GUSTAVSON, A. KARP, Implementing linear algebra algorithms for dense matrices on a vector pipeline machine, SIAM Review 26, 1, 1984, 91–112CrossRefGoogle Scholar
  5. [Fei]
    M. FEILMEIER, Parallel computers — Parallel mathematics, IMACS North Holland, 1977Google Scholar
  6. [Fly]
    M.J. FLYNN, Very high-speed computing systems, Proc. IEEE 54, 1966, 1901–1909Google Scholar
  7. [GP]
    D.D. GAJSKI, J.K. PEIR, Essential issues in multiprocessors systems, IEEE Computer, June 1985, 9–27Google Scholar
  8. [GV]
    G. H. GOLUB, C. F. VAN LOAN, Matrix computation, The Johns Hopkins University Press, 1983Google Scholar
  9. [Hel]
    D. HELLER, A survey of parallel algorithms in numerical linear algebra, SIAM Review 20, 1978, 740–777CrossRefGoogle Scholar
  10. [HJ]
    R.W. HOCKNEY, C.R. JESSHOPE, Parallel computers: architectures, programming and algorithms, Adam Helger, Bristol, 1981Google Scholar
  11. [HB]
    K. HWANG, F. BRIGGS, Parallel processing and computer architecture, MC Graw Hill, 1984Google Scholar
  12. [Kum]
    S.P. KUMAR, Parallel algorithms for solving linear equations on MIMD computers, PhD. Thesis, Washington State University, 1982Google Scholar
  13. [KK]
    S.P. KUMAR, J.S. KOWALIK, Parallel factorization of a positive definite matrix on an MIMD computer, Proc. ICCD 84, 410–416Google Scholar
  14. [LKK]
    R.E. LORD, J.S. KOWALIK, S.P. KUMAR, Solving linear algebraic equations on an MIMD computer, J. ACM 30, 1, 1983, 103–117CrossRefGoogle Scholar
  15. [Rot]
    G. ROTE, Personnal CommunicationGoogle Scholar
  16. [Saa]
    Y. SAAD, Communication complexity of the Gaussian elimination algorithm on multiprocessors, Report DCS/348, Yale University, 1985Google Scholar
  17. [Sam]
    A. SAMEH, An overview of parallel algorithms, Bulletin EDF, 1983, 129–134Google Scholar
  18. [Sch]
    U. SCHENDEL, Introduction to Numerical Methods for Parallel Computers, Ellis Horwood Series, J. Wiley & Sons, New York, 1984Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • M. Cosnard
    • 1
  • M. Marrakchi
    • 1
  • Y. Robert
    • 1
  • D. Trystram
    • 2
  1. 1.CNRS, Laboratoire TIM3St Martin d'Hères CedexFrance
  2. 2.Ecole Centrale PARISChatenay Malabry CedexFrance

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