6533b85bfe1ef96bd12bbce0

RESEARCH PRODUCT

The Zero-Check for Eliminating Non-Significant Elements

subject

description

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) $${\rm{a}}\, = \,{\rm{2}}\,{\rm{ = }}\,{\rm{.20000000}}\,{\rm{E}}\,{\rm{01}}$$ $${\rm{b}}\, = \,{\rm{6}}\,{\rm{ = }}\,{\rm{.60000000}}\,{\rm{E}}\,{\rm{01}}$$ $${\rm{c}}\, = \,{\rm{1/3}}\,{\rm{ = }}\,{\rm{.33333333}}\,{\rm{E}}\,{\rm{00}}$$