The Zero-Check for Eliminating Non-Significant Elements

  • H. Müller-Merbach
Part of the Lecture Notes in Operations Research and Mathematical Systems book series (LNE, volume 37)


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


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  1. +).
    A special subroutine in the internal programming language of the computer used may accelerate the procedure (19) effectively. E.g., it may be possible simply to compare the exponents of the two elements ait* an ait.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1970

Authors and Affiliations

  • H. Müller-Merbach
    • 1
  1. 1.Lehrstuhl für BetriebswirtschaftslehreJohannes-Gutenberg-UniversitätMainzGermany

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