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Abstract: Given a homotopy connecting two polynomial systems we provide a rigorousalgorithm for tracking a regular homotopy path connecting an approximate zeroof the start system to an approximate zero of the target system. Our methoduses recent results on the complexity of homotopy continuation rooted in thealpha theory of Smale. Experimental results obtained with the implementation inthe numerical algebraic geometry package of Macaulay2 demonstrate thepracticality of the algorithm. In particular, we confirm the theoreticalresults for random linear homotopies and illustrate the plausibility of aconjecture by Shub and Smale on a good initial pair.

Author: Carlos Beltrán, Anton Leykin

Source: https://arxiv.org/

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