An extension of the Floater–Hormann family of barycentric rational interpolants
- Klein, Georges Department of Mathematics, University of Fribourg, Switzerland
-
2012
Published in:
- Mathematics of Computation. - 2012, vol. 82, no. 284, p. 2273-2292
English
The barycentric rational interpolants introduced by Floater and Hormann in 2007 are “blends” of polynomial interpolants of fixed degree d. In some cases these ratio- nal functions achieve approximation of much higher quality than the classical poly- nomial 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 equi- spaced nodes is presented and investigated. The efficiency of its applications such as the approximation of derivatives, integrals and primitives of functions is compared to the corresponding results recently obtained with the original family of rational interpolants.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
-
- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
-
- RERO DOC 30491
- DOI 10.1090/S0025-5718-2013-02688-9
- Persistent URL
- https://folia.unifr.ch/unifr/documents/302784
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