SIAM journal on numerical analysis vol:30 issue:2 pages:583-594
Homotopy methods have become a standard tool for the computation of all solutions of a polynomial system. This paper concerns the solution of deficient polynomial systems which appear to be typical in many engineering applications. The GBQ-algorithm presented consists of two parts: the computation of a generalized Bezout number GB and the construction of a multi-homogeneous start system Q. The approach generalizes m-homogenization into multi-homogenization. It can also be regarded as a generalization ''towards'' the random product homotopy, however, without making assumptions on the coefficients of the polynomials in the system. As is illustrated in the examples, symmetric polynomial systems also can be solved more efficiently.