Mixed Volume Computation and Solving Polynomial Systems (I)
Abstract:
In the last few decades, the homotopy continuation method has been established in the U.S. for finding the full set of isolated zeros to a polynomial system numerically. The method involves first solving a trivial system, and then deforming these solutions along smooth paths to the solutions of the target system. Recently, modeling the sparse structure of a polynomial system by its Newton polytopes leads to a major computational breakthrough. Based on an elegant method for computing the mixed volume, the new polyhedral homotopy can find all isolated zeros of a polynomial system much efficiently. The method has been successfully implemented and proved to be very powerful in many occasions, especially when the systems are sparse. We will elaborate the method in this talk.
Tea Time: 3:30PM R707 (七樓休息室)