A NUMERICAL INVESTIGATION OF THE SIMPLEX METHOD
STANFORD UNIV CA DEPT OF COMPUTER SCIENCE
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The report analyzes the behavior of the round-off errors associated with three different computer implementations of the simplex method of linear programming. One of the three is representative of computer implementations in common use, and it is shown that the standard method of updating the basic- matrix inverse is numerically unstable. The remaining two implementations are suggested by the author and use triangular decompositions of the basic matrix as substitutes for its inverse. The implementations are shown to be stable, and one of them is shown to be competitive in speed with the standard simplex-method computer implementations. Error bounds which may be calculated from intermediate results are developed for each of the three implementations, and their use during computation for error monitoring and control is discussed.
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