论文信息 - Heuristic methods for computing the minimal multi-homogeneous Bézout number

Heuristic methods for computing the minimal multi-homogeneous Bézout number

The multi-homogeneous Bezout number of a polynomial system is the number of paths that one has to follow in computing all its isolated solutions with continuation method. Each partition of variables corresponds to a multi-homogeneous Bezout number. It is a challenging problem to find a partition with minimal multi-homogeneous Bezout number. Two heuristic numerical methods for computing the minimal multi-homogeneous Bezout number are presented in this paper. Some analysis of computational complexity are given. Numerical examples show the efficiency of these two methods.

Fengshan Bai | Ting Li | Zhenjiang Lin

[1] Bernd Sturmfels,et al. Bernstein’s theorem in affine space , 1997, Discret. Comput. Geom..

[2] Charles W. Wampler. Bezout number calculations for multi-homogeneous polynomial systems , 1992 .

[3] Mitsuo Gen,et al. Genetic algorithms and engineering optimization , 1999 .

[4] F. Drexler. Eine Methode zur berechnung sämtlicher Lösungen von Polynomgleichungssystemen , 1977 .

[5] Zbigniew Michalewicz,et al. Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[6] C. B. García,et al. Finding all solutions to polynomial systems and other systems of equations , 1979, Math. Program..

[7] A. Morgan,et al. A homotopy for solving general polynomial systems that respects m-homogeneous structures , 1987 .

[8] Xiaoshen Wang,et al. Finding All Isolated Zeros of Polynomial Systems inCnvia Stable Mixed Volumes , 1999, J. Symb. Comput..

[9] Ronald Cools,et al. Mixed-volume computation by dynamic lifting applied to polynomial system solving , 1996, Discret. Comput. Geom..

[10] Bernd Sturmfels,et al. A polyhedral method for solving sparse polynomial systems , 1995 .

[11] Tiejun Li,et al. Minimizing multi-homogeneous Bézout numbers by a local search method , 2001, Math. Comput..

[12] Zbigniew Michalewicz,et al. Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.