Theoretical aspects of mixed volume computation via mixed subdivision
Tianran Chen, Tien-Yien Li, Xiaoshen Wang · Communications in Information and Systems · 2014
We analyze the computation of mixed volume of tuples of polytopes via fine mixed subdivisions.This method expresses the mixed volume as a sum of easily computable standard volumes of polytopes called mixed cells.Mixed cells play a critically important role in polyhedral homotopy continuation methods, which in turn are a particularly efficient numerical method for the solution of systems of polynomial equations.We provide a complete and selfcontained account of the underlying computational convexity techniques, assuming no background in algebraic geometry.