Mixed Volume Computation, A Revisit

Abstract

The superiority of the dynamic enumeration of all mixed cells suggested by T. Mizutani et al. for the mixed volume computation over the existing methods was reported in [15]. In this article, we embed the idea of dynamic enumeration into our original algorithm for the mixed volume computation presented in [7], and a new algorithm is developed by employing both primal and dual simplex algorithms. Illustrated by the numerical results, our new algorithm improves the speed of the code in [15] by a substantial margin.