An extension of the Floater–Hormann family of barycentric rational interpolants
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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.References
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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
- 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.
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3073200
Dedicated: Dedicated to Professor Jean–Paul Berrut on the occasion of his sixtieth birthday.