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W. Auzinger, W. Herfort:
"An Application of Gröbner Bases to perturbed Polynomial Equations";
in: "ASC Report 01/2015", herausgegeben von: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2015, ISBN: 978-3-902627-08-7, S. 1 - 11.

The interplay of symbolic and numerical calculations in polynomial algebra is featured in the seminal monograph (4) by H.J. Stetter. We present a contribution to this field in form of an ideal-theoretic approach for determining solutions of an a perturbed polynomial system which are close to the zeros of the system subject to perturbation. Algorithmically, identifying these zeros is of special interest if the unperturbed system has a nontrivial solution manifold while the perturbed system admits only isolated zeros.

http://www.asc.tuwien.ac.at/preprint/2015/asc01x2015.pdf