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A Parallel Block Cholesky Factorization for Staircase Linear Programming Problems

Author

Listed:
  • LOUTE, Etienne

    (Facultés Universitaires Saint-Louis, Brussels and CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • VIAL, Jean-Philippe

    (Département COMIN, Université de Genève, Switzerland)

Abstract

We present a variant of the Cholesky factorization for block tridiagonal positive definite matrices. We show that a suitable ordering of block pivots makes it possible to parallelize the linear algebra on a multiple instruction multiple data (MIMD) processor achitecture. The technique applies to linear programming problems with a staircase constraint matrix, a structure that is typical of dynamic (multiperiod, multistage) problems. We compute the amount of parallelism that is theoretically achievable and we show that the increase in block fill-in of the Cholesky factor is limited.

Suggested Citation

  • LOUTE, Etienne & VIAL, Jean-Philippe, 1992. "A Parallel Block Cholesky Factorization for Staircase Linear Programming Problems," LIDAM Discussion Papers CORE 1992060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1992060
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1992.html
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