A new Parallel algorithm for solving general linear systems of equations

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


A new parallel direct algorithm for solving general linear systems of equations ist proposed in this paper. For sparse systems our algorithm requires less computations than the classical Jordan algorithm. Particularly we have also derived two related algorithms for linear recurrence problems of order 1 and tridiagonal systems. Each of the two algorithms has the same computational complexity as that of the corresponding recursive doubling algorithm or Even/Odd elimination algorithm, but requires half of the processors required by the corresponding algorithm.

The numerical experiments on the vector computer YH-1 indicate that, as the number of equations of a tridiagonal system increases, the speedup of our algorithm over the Even/Odd algorithm increases, and the maximum speedup is more than 3.


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  1. [1]
    Peter M. Kogge and Harold S. Stone, "A parallel algorithm for the efficient solution of a general class of recurrence equations", IEEE Transactions on Computer Vol. C—22, No.8, August 1973.Google Scholar
  2. [2]
    AD-A024792, "A survey of parallel algorithms in numerical linear algebra".Google Scholar
  3. [3]
    UCRL-76993, "A comparison of direct methods for tridiagonal systems on the CDC-STAR-100".Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Liao Qui-wei
    • 1
  1. 1.Chang Sha Computer Co.Hunan ProvinceChina

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