International Journal of Numerical Methods and Applications
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Abstract: The mixed volume and stable mixed volume are types of
BKK bound, each of which gives an upper bound of the number of isolated
solutions of polynomial systems in A recent
work by Xing Li applies the linear programming technique to computing the mixed
volume of a polynomial system. However, the technique exhibits a serious
shortcoming which undermines its effectiveness, namely, it ignores some lower
edges that may have contribution in computing the mixed volume; an example of
such a situation is provided in the present paper. The present work improves on
the method of Xing Li, in that it stipulates additional conditions so that the
totality of the conditions renders the method of Xing Li effective. Furthermore,
we present a new version of the improved method which can be used for computing
the stable mixed volume.
Keywords and phrases: polynomial systems, homotopy methods, polyhedral homotopy, mixed volume, stable mixed volume, lower edges, linear programming.
