Modifying Triangular Factors of the Basis in the Simplex Method

The advantages of using triangular (LU) decomposition in linear programming inversion routines are now becoming widely recognized. The superiority of this form of inverse over the original product form in terms of speed, compactness and accuracy has been clearly demonstrated in practice (see Dantzig, Harvey, McKnight & Smith (1968A)) and it is now becoming the standard method.