Parallel systolic LU factorization for simplex updates

  • K. Margaritis
  • D. J. Evans
Session 9A: Algorithms, Architectures And Performance I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 297)


This paper presents systolic designs for modifying an LU factorization of a matrix A when a Simplex update is performed on A. It is assumed that no pivoting is required for the LU updating. Two systolic networks are proposed: one two-dimensional square array and a linear array which can be interconnected with the LU factorization hex-array in [L]. Soft-systolic simulation programs in OCCAM for both designs are given in the Appendix.


Linear Array Simplex Method Systolic Array Diagonal Cell Array Operation 
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5. References

  1. [BJM]
    Bennett, J.M., "Triangular Factors of Modified Matrices", Numer.Math. 7, 217–221 (1965).Google Scholar
  2. [BRH]
    Bartels, R.H., "A Stabilization of the Simplex Method", Numer.Math. 16, 44–434 (1971).Google Scholar
  3. [FM]
    Fletcher R. and Matthews, S.P.J., "Stable Modification of Explicit LU Factors for Simplex Updates", Report NA/64, Dept. of Mathematical Sciences, Univ. of Dundee, June 1983.Google Scholar
  4. [L]
    Leiserson, C.E., "Area-Efficient VLSI Computation", Ph.D. Thesis, Dept. of Computer Studies, CMU, Oct. 1981.Google Scholar
  5. [T]
    Tomlin, J.A., "Modifying Triangular Factors of the Basis in the Simplex Method", 77–85, 'sparse Matrices and Their Applications', edit. Rose, D.J. & Willoughby, R.A., Plenum Press, 1972.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • K. Margaritis
    • 1
  • D. J. Evans
    • 1
  1. 1.Department of Computer StudiesUniversity of TechnologyLoughboroughU.K.

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