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Robust certified numerical homotopy tracking

Abstract: Abstract We describe, for the first time, a completely rigorous homotopy (pathfollowing) algorithm (in the Turing machine model) to find approximate zeros of systems of polynomial equations. If the coordinates of the input systems and the initial zero are rational our algorithm involves only rational computations, and if the homotopy is well posed an approximate zero with integer coordinates of the target system is obtained. The total bit complexity is linear in the length of the path in the condition metric, and polynomial in the logarithm of the maximum of the condition number along the path, and in the size of the input.

 Autoría: Beltrán C., Leykin A.,

 Fuente: Foundations of Computational Mathematics 13, 253-295 (2013)

 Editorial: Springer New York LLC

 Año de publicación: 2013

 Nº de páginas: 43

 Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s10208-013-9143-2

 ISSN: 1615-3375,1615-3383

 Proyecto español: MTM2010-16051

 Url de la publicación: https://doi.org/10.1007/s10208-013-9143-2