, Volume 107, Issue 2, pp 315-331
Date: 28 Jun 2007

Barycentric rational interpolation with no poles and high rates of approximation

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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.