Institution: | School of Mathematical Sciences, Peking University, Beijing, P. R. China Fengshan Bai ; Department of Mathematics, Tsinghua University, Beijing, 100084, P. R. China |
Abstract: | Consider the multi-homogeneous homotopy continuation method for solving a system of polynomial equations. For any partition of variables, the multi-homogeneous Bézout number bounds the number of isolated solution curves one has to follow in the method. This paper presents a local search method for finding a partition of variables with minimal multi-homogeneous Bézout number. As with any other local search method, it may give a local minimum rather than the minimum over all possible homogenizations. Numerical examples show the efficiency of this local search method. |