Abstract
A renewed algorithm is presented to calculate the mixed volume of the support ${\cal A}=({\cal A}_1,\dots,{\cal A}_n)$ of a polynomial system $P({\bf x})=(p_1({\bf x}),\dots, p_n({\bf x}))$ in $\Bbb C^n$. The key ingredient is a specially tailored application of LP feasibility tests, which allows us to calculate the mixed cells, their volumes constituting the mixed volume, in a mixed subdivision of ${\cal A}$ more efficiently. The problem of finding mixed cells plays a crucial role in polyhedral homotopy methods for finding all isolated zeros of $P({\bf x})$. Our new algorithm advances the speed of mixed volume computation by a considerable margin, illustrated by numerical examples.
Citation
Tangan Gao. T. Y. Li. "MIXED VOLUME COMPUTATION VIA LINEAR PROGRAMMING." Taiwanese J. Math. 4 (4) 599 - 619, 2000. https://doi.org/10.11650/twjm/1500407294
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