Hybrid Divide-and-Conquer Methods for Solving Polynomial Systems
Abstract: In this talk, a brief introduction of some hybrid divide-and-conquer methods for solving polynomial systems will be given. At first, for polynomial systems derived from mixed trigonometric polynomial systems, a hybrid homotopy and its symmetric modified version will be introduced, and the sketch of a hybrid divide-and-conquer method this special class of polynomial systems will be formulated. Then, a framework of a general purposed hybrid divide-and-conquer method for solving deficient polynomial systems will be given. Some numerical results will also be given to show the efficiency of the proposed algorithm.