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On rational functions without Froissart doublets

Banff International Research Station for Mathematical Innovation and Discovery

In this talk we consider the problem of working with rational functions in a numeric environment. A particular problem when modelling with such functions is the existence of Froissart doublets, where a zero is close to a pole. We discuss three different parameters which allow one to monitor the absence of Froissart doublets for a given general rational function. These include the euclidean condition number of an underlying Sylvester-type matrix, a parameter for determining coprimeness of two numerical polynomials and bounds on the spherical derivative. We show that our parameters sharpen those found in previous papers (1) and (2) (1) B. Beckermann and G. Labahn, When are two numerical polynomials relatively prime? {\em Journal of Symbolic Computation} {\bf 26} (1998) 677-689. (2) B. Beckermann and A. Matos, Algebraic properties of robust Pad\'e approximants, {\em Journal of Approximation Theory }{\bf 190} (2015) 91-115. This is joint work with B. Beckermann (Lille) and G. Labahn (Waterloo)

Mathematics; Approximations and expansions; Commutative rings and algebras; Classical analysis

video/mp4

Author affiliation: University of Lille France

2017-06-06

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61835

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/