“Ill-Conditioned” Vertices

Abstract

The round-off errors tend to increase particularly rapidly after pivoting at “ill-conditioned” vertices. Those vertices where two or more hyperplanes, each representing one constraint, intersect at a very slight angle are considered as “ill-conditioned”. An “ill-conditioned” vertex is for instance given by the intersection of the two constraints:

$$\eqalign{ & 3\,{{\rm{x}}_{\rm{1}}}\, + \,{{\rm{x}}_{\rm{2}}}\, \le \,6 \cr & {{\rm{x}}_{\rm{1}}}\, + \,.354\,{{\rm{x}}_{\rm{2}}}\, \le \,2.001 \cr} $$