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On rational functions without Froissart doublets. (English) Zbl 1390.41016

Authors’ abstract: 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 determining 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 authors.

MSC:

41A21 Padé approximation
65F22 Ill-posedness and regularization problems in numerical linear algebra
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