Subresultants, Sylvester sums and the rational interpolation problem

We present a solution for the classical univariate rational interpolation problem by means of (univariate) subresultants. In the case of Cauchy interpolation (interpolation without multiplicities), we give explicit formulas for the solution in terms of symmetric functions of the input data, generali...

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Bibliographic Details
Published in:Journal of symbolic computation 2015-05, Vol.68, p.72-83
Main Authors: D'Andrea, Carlos, Krick, Teresa, Szanto, Agnes
Format: Article
Language:English
Subjects:
Cauchy interpolation
Osculatory interpolation
Rational Hermite interpolation
Rational interpolation
Subresultants
Sylvester sums
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Summary:We present a solution for the classical univariate rational interpolation problem by means of (univariate) subresultants. In the case of Cauchy interpolation (interpolation without multiplicities), we give explicit formulas for the solution in terms of symmetric functions of the input data, generalizing the well-known formulas for Lagrange interpolation. In the case of the osculatory rational interpolation (interpolation with multiplicities), we give determinantal expressions in terms of the input data, making explicit some matrix formulations that can independently be derived from previous results by Beckermann and Labahn.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2014.08.008