A development of the product form algorithm for the simplex method using reduced transformation vectors

This paper presents a product form version of the reduced basis algorithm for the simplex method. The reduced basis is a sub-matrix of the coefficient matrix formed by the effective constraints and the basic original variables. The product form algorithm using contracted transformation vectors given by Zoutendijk [7], has been extended so as to be able to represent, and update at each iteration, the inverse of the reduced basis as the product of a sequence of transformation matrices.