Tracking how spurious pole-zero pairs move across Padé approximation orders lets an iterative algorithm flag inconsistent data points and reconstruct the underlying function while preserving genuine analytic structures.
On rational functions without Froissart doublets
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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 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.
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Analytically Consistent Reconstruction of Finite Data Using Pad\'e Sequences
Tracking how spurious pole-zero pairs move across Padé approximation orders lets an iterative algorithm flag inconsistent data points and reconstruct the underlying function while preserving genuine analytic structures.