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W. Auzinger, H.J. Stetter:
"A study of numerical elimination for the solution of multivariate polynomial systems";
Bericht für Technical Report, Institut für Angewandte und Numerische Mathematik; 1989.

In an earlier paper we had motivated and described am algorithm for the computation of the zeros of multivariate polynomial systems by means of multiplication tables and solution of an associated eigenvalue problem. In this paper we give a more transparent description of this approach, including degenerate situations. Both the theoretical results and the algorithmic procedures are applied to examples, and the results are displayed and discussed.

http://www.math.tuwien.ac.at/~winfried/papers/polelim2.pdf