Barycentric rational interpolation with no poles and high rates of approximation

Authors:
Michael S. Floater;Kai Hormann
Affiliations:
University of Oslo, Centre of Mathematics for Applications, Department of Informatics, PO Box 1053, 0316, Blindern, Oslo, Norway;Clausthal University of Technology, Department of Informatics, PO Box 1053, Julius-Albert-Str. 4, 38678, Clausthal-Zellerfeld, Oslo, Germany
Venue:
Numerische Mathematik
Year:
2007

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Abstract

It is well known that rational interpolation sometimes gives better approximations than polynomial interpolation, especially for large sequences of points, but it is difficult to control the occurrence of poles. In this paper we propose and study a family of barycentric rational interpolants that have no real poles and arbitrarily high approximation orders on any real interval, regardless of the distribution of the points. These interpolants depend linearly on the data and include a construction of Berrut as a special case.