Methods for updating the LU factors of simplex basis matrices are reviewed. An alternative derivation of the Fletcher and Matthews method is given. This leads to generalizations of their method which avoids problems with both the Bartels and Golub method and the Fletcher and Matthews method. The improvements are to both numerical stability and data access locality. The resulting updating algorithm is preferred to the Reid variant of the Bartels and Golub method for both numerical stability and cost of execution.
Sande and Associates, Halifax, Nova Scotia, June 3, 2013