On rational functions without Froissart doublets
For researchers using rational functions in numerical environments, this work provides sharper tools to detect Froissart doublets, though it is an incremental improvement.
The paper addresses the problem of Froissart doublets in rational function modeling and proposes three parameters to monitor their absence, showing that these parameters improve upon previous work.
In this paper we consider the problem of working with rational functions in a numeric environment. A particular problem when modeling 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 determing coprimeness of two numerical polynomials and bounds on the spherical derivative. We show that our parameters sharpen those found in a previous paper by two of the autours.