The Zero-Check for Eliminating Non-Significant Elements

Abstract

During continued matrix operations like the simplex method a lot of small non-significant elements, the actual value of which is zero,usually augment the working coefficient matrix. These elements are caused by round-off errors. They arise in the following manner in a computation of the type:

$${\rm{d}}\, = \,{\rm{a}}\,{\rm{ - }}\,{\rm{b}}{\rm{.c}}$$

with e.g. the data (in FORTRAN notation)

$${\rm{a}}\, = \,{\rm{2}}\,{\rm{ = }}\,{\rm{.20000000}}\,{\rm{E}}\,{\rm{01}}$$

$${\rm{b}}\, = \,{\rm{6}}\,{\rm{ = }}\,{\rm{.60000000}}\,{\rm{E}}\,{\rm{01}}$$

$${\rm{c}}\, = \,{\rm{1/3}}\,{\rm{ = }}\,{\rm{.33333333}}\,{\rm{E}}\,{\rm{00}}$$