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An Extension of the Floater-Hormann Family of Barycentric Rational Interpolants


Author: Georges Klein
Journal: Math. Comp. 82 (2013), 2273-2292
MSC (2010): Primary 65D05, 41A05, 41A20, 41A25; Secondary 65L12, 65D32
DOI: https://doi.org/10.1090/S0025-5718-2013-02688-9
Published electronically: March 25, 2013
MathSciNet review: 3073200
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Abstract: The barycentric rational interpolants introduced by Floater and Hormann in $ 2007$ are ``blends'' of polynomial interpolants of fixed degree $ d$. In some cases these rational functions achieve approximation of much higher quality than the classical polynomial interpolants, which, e.g., are ill-conditioned and lead to Runge's phenomenon if the interpolation nodes are equispaced. For such nodes, however, the condition of Floater-Hormann interpolation deteriorates exponentially with increasing $ d$. In this paper, an extension of the Floater-Hormann family with improved condition at equispaced nodes is presented and investigated. The efficiency of its applications such as the approximation of derivatives, integrals and antiderivatives of functions is compared to the corresponding results recently obtained with the original family of rational interpolants.


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Additional Information

Georges Klein
Affiliation: Department of Mathematics, University of Fribourg, Perolles, CH-1700 Fribourg, Switzerland
Email: georges.klein@unifr.ch

DOI: https://doi.org/10.1090/S0025-5718-2013-02688-9
Keywords: Rational interpolation, barycentric form, Lebesgue function, condition
Received by editor(s): May 27, 2011
Received by editor(s) in revised form: February 6, 2012
Published electronically: March 25, 2013
Additional Notes: The authors work was partly supported by the Swiss National Science Foundation under grant No. 200020-124779.
Dedicated: Dedicated to Professor Jean–Paul Berrut on the occasion of his sixtieth birthday.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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