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Gauss elimination algorithms for mimd computers

  • Namerical Algorithms (Session 3.2)
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 237))

Abstract

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.

This work has been supported by the CNRS through the GRECOC3.

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References

  1. M. COSNARD, Y. ROBERT, D. TRYSTRAM, Résolution parallèle de systèmes linéaires denses par diagonalisation, Bulletin EDF série C, no 2, 1986

    Google Scholar 

  2. 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, 781–784

    Google Scholar 

  3. 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 appear

    Google Scholar 

  4. 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, 91–112

    Article  Google Scholar 

  5. M. FEILMEIER, Parallel computers — Parallel mathematics, IMACS North Holland, 1977

    Google Scholar 

  6. M.J. FLYNN, Very high-speed computing systems, Proc. IEEE 54, 1966, 1901–1909

    Google Scholar 

  7. D.D. GAJSKI, J.K. PEIR, Essential issues in multiprocessors systems, IEEE Computer, June 1985, 9–27

    Google Scholar 

  8. G. H. GOLUB, C. F. VAN LOAN, Matrix computation, The Johns Hopkins University Press, 1983

    Google Scholar 

  9. D. HELLER, A survey of parallel algorithms in numerical linear algebra, SIAM Review 20, 1978, 740–777

    Article  Google Scholar 

  10. R.W. HOCKNEY, C.R. JESSHOPE, Parallel computers: architectures, programming and algorithms, Adam Helger, Bristol, 1981

    Google Scholar 

  11. K. HWANG, F. BRIGGS, Parallel processing and computer architecture, MC Graw Hill, 1984

    Google Scholar 

  12. S.P. KUMAR, Parallel algorithms for solving linear equations on MIMD computers, PhD. Thesis, Washington State University, 1982

    Google Scholar 

  13. S.P. KUMAR, J.S. KOWALIK, Parallel factorization of a positive definite matrix on an MIMD computer, Proc. ICCD 84, 410–416

    Google Scholar 

  14. R.E. LORD, J.S. KOWALIK, S.P. KUMAR, Solving linear algebraic equations on an MIMD computer, J. ACM 30, 1, 1983, 103–117

    Article  Google Scholar 

  15. G. ROTE, Personnal Communication

    Google Scholar 

  16. Y. SAAD, Communication complexity of the Gaussian elimination algorithm on multiprocessors, Report DCS/348, Yale University, 1985

    Google Scholar 

  17. A. SAMEH, An overview of parallel algorithms, Bulletin EDF, 1983, 129–134

    Google Scholar 

  18. U. SCHENDEL, Introduction to Numerical Methods for Parallel Computers, Ellis Horwood Series, J. Wiley & Sons, New York, 1984

    Google Scholar 

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Authors and Affiliations

Authors

Editor information

Wolfgang Händler Dieter Haupt Rolf Jeltsch Wilfried Juling Otto Lange

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© 1986 Springer-Verlag Berlin Heidelberg

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Cosnard, M., Marrakchi, M., Robert, Y., Trystram, D. (1986). Gauss elimination algorithms for mimd computers. In: Händler, W., Haupt, D., Jeltsch, R., Juling, W., Lange, O. (eds) CONPAR 86. CONPAR 1986. Lecture Notes in Computer Science, vol 237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16811-7_177

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  • DOI: https://doi.org/10.1007/3-540-16811-7_177

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16811-9

  • Online ISBN: 978-3-540-44856-3

  • eBook Packages: Springer Book Archive

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