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Certified numerical homotopy tracking

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

 Autoría: Beltrán C., Leykin A.,

 Fuente: Experimental Mathematics, 2012, 21(1), 69-83

 Editorial: Taylor & Francis

 Fecha de publicación: 13/03/2012

 Nº de páginas: 15

 Tipo de publicación: Artículo de Revista

 DOI: 10.1080/10586458.2011.606184

 ISSN: 1058-6458,1944-950X

 Url de la publicación: https://doi.org/10.1080/10586458.2011.606184

Autoría

LEYKIN, ANTON