Minimizing multi-homogeneous Bézout numbers by a local search method

Li, Tiejun; Bai, Fengshan

doi:10.1090/S0025-5718-00-01303-X

Minimizing multi-homogeneous Bézout numbers by a local search method
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by Tiejun Li and Fengshan Bai PDF

Math. Comp. 70 (2001), 767-787 Request permission

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.

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