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W. Auzinger, H.J. Stetter:
"An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations";
in: "ISMN 86 - Proceedings, `International Conference on Numerical Mathematics', Singapore, 1988.", Birkhäuser, 1988, 11 - 30.

A direct numerical method is proposed for the determination of all isolated zeros of a system of multivariate polynomial equations. By "polynomial combination", the system is reduced to a special form which may be interpreted as a multiplication table for power products modulo the system. The zeros are then formed from an ordinary eigenvalue problem for the matrix of the multiplication table. Degenerate situations may be handled by perturbing them into general form and reaching the zeros of the unperturbed system via a homotopy method.

http://www.math.tuwien.ac.at/~winfried/papers/polelim1.pdf