On the Numerical Stability of Simplex-Algorithms

Abstract

Stability of update-formulae in linear programming is considered under the assumption that the formula itself is evaluated exactly, i.e. only the effect of an input error in a first step is studied. It is shown that orthogonal decomposition methods but also the revised Simplex-method are stable in that sense. However, this is not true for variants of orthogonal decomposition which do not use the orthogonal factor explicitely.