Abstract
Recent results reveal that the family of barycentric rational interpolants introduced by Floater and Hormann is very well-suited for the approximation of functions as well as their derivatives, integrals and primitives. Especially in the case of equidistant interpolation nodes, these infinitely smooth interpolants offer a much better choice than their polynomial analogue. A natural and important question concerns the condition of this rational approximation method. In this paper we extend a recent study of the Lebesgue function and constant associated with Berrut’s rational interpolant at equidistant nodes to the family of Floater–Hormann interpolants, which includes the former as a special case.
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Bos, L., De Marchi, S., Hormann, K. et al. On the Lebesgue constant of barycentric rational interpolation at equidistant nodes. Numer. Math. 121, 461–471 (2012). https://doi.org/10.1007/s00211-011-0442-8
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DOI: https://doi.org/10.1007/s00211-011-0442-8