On rational functions without Froissart doublets

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 abse...

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Bibliographic Details
Published in:Numerische Mathematik 2018-03, Vol.138 (3), p.615-633
Main Authors: Beckermann, Bernhard, Labahn, George, Matos, Ana C.
Format: Article
Language:English
Subjects:
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Rational functions
Simulation
Theoretical
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Summary: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.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-017-0917-3