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

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 primitives of functions is compared to the corresponding results recently obtained with the original family of rational interpolants. Math Subject Classification: 65D05, 65L12, 65D32, 41A05, 41A20, 41A25