Communications in Information and Systems
Volume 14 (2014)
Theoretical aspects of mixed volume computation via mixed subdivision
Pages: 213 – 242
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 self-contained account of the underlying computational convexity techniques, assuming no background in algebraic geometry.