Computing nearest Gcd with certification

Authors:
Guillaume Chèze;Jean-Claude Yakoubsohn;André Galligo;Bernard Mourrain
Affiliations:
Université Paul Sabatier, Toulouse, France;Université Paul Sabatier, Toulouse, France;Université de Nice Sophia-Antipolis, Nice, France;INRIA Méditerranée, Sophia Antipolis, France
Venue:
Proceedings of the 2009 conference on Symbolic numeric computation
Year:
2009

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Abstract

A bisection method, based on exclusion and inclusion tests, is used to address the nearest univariate gcd problem formulated as a bivariate real minimization problem of a rational fraction. The paper presents an algorithm, a first implementation and a complexity analysis relying on Smale's α-theory. We report its behavior on an illustrative example.