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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)

Abstract

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.

Keywords

Linear Array Simplex Method Systolic Array Diagonal Cell Array Operation 
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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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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