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M. Saunders, “A Fast and Stable Implementation of the Simplex Method Using Bartels-Golub Updating,” In: J. Bunch and S. T. Rachev, Eds., Sparse Matrix Computation, Academic Press, New York, 1976, pp. 213-226.

has been cited by the following article:

• TITLE: A Computational Comparison of Basis Updating Schemes for the Simplex Algorithm on a CPU-GPU System

  AUTHORS: Nikolaos Ploskas, Nikolaos Samaras

  KEYWORDS: Simplex Algorithm; Basis Inverse; Graphics Processing Unit; MATLAB; Compute Unified Device Architecture

  JOURNAL NAME: American Journal of Operations Research, Vol.3 No.6, October 28, 2013

  ABSTRACT: The computation of the basis inverse is the most time-consuming step in simplex type algorithms. This inverse does not have to be computed from scratch at any iteration, but updating schemes can be applied to accelerate this calculation. In this paper, we perform a computational comparison in which the basis inverse is computed with five different updating schemes. Then, we propose a parallel implementation of two updating schemes on a CPU-GPU System using MATLAB and CUDA environment. Finally, a computational study on randomly generated full dense linear programs is preented to establish the practical value of GPU-based implementation.