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The Elimination form of the Inverse and its Application to Linear Programming

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  • Harry M. Markowitz

    (The RAND Corporation)

Abstract

It is common for matrices in industrial applications of linear programming to have a large proportion of zero coefficients. While every item (raw material, intermediate material, end item, equipment item) in, say, a petroleum refinery may be indirectly related to every other, any particular process uses few of these. Thus the matrix describing petroleum technology has a small percentage of non-zeros. If spacial or temporal distinctions are introduced into the model the percentage of non-zeros generally falls further. The present paper discusses a form of inverse which is especially convenient to obtain and use for matrices with a high percentage of zeros. The application of this form of inverse in linear programming is also discussed.

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File URL: http://dx.doi.org/10.1287/mnsc.3.3.255
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 3 (1957)
Issue (Month): 3 (April)
Pages: 255-269

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Handle: RePEc:inm:ormnsc:v:3:y:1957:i:3:p:255-269

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Cited by:
  1. Dobrzyński, Michał & Plata, Jagoda, 2010. "Fill-ins number reducing direct solver designed for FIT-type matrix," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(8), pages 1684-1693.
  2. Miles Lubin & J. Hall & Cosmin Petra & Mihai Anitescu, 2013. "Parallel distributed-memory simplex for large-scale stochastic LP problems," Computational Optimization and Applications, Springer, vol. 55(3), pages 571-596, July.
  3. LOUTE, Etienne, 2003. "Gaussian elimination as a computational paradigm," CORE Discussion Papers 2003059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Gass, Saul I., 1997. "The Washington operations research connection: the rest of the story," Socio-Economic Planning Sciences, Elsevier, vol. 31(4), pages 245-255, December.

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