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TW 254
B. Huber and J. Verschelde
Polyhedral end games for polynomial continuation
Abstract
Bernshtein's theorem provides a generically exact upper bound on the number of isolated solutions a sparse polynomial system can have in (C*)n, with C* = C - { 0 }. When a sparse polynomial system has fewer than this number of isolated solutions some face system must have isolated solutions in (C*)n. In this paper we address the process of recovering a certificate of deficiency from a diverging solution path. This certificate takes the form of a face system along with a solution to the face system. We apply extrapolation to estimate the cycle number and the face normal. Applications illustrate the practical usefulness of our approach.
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