Convergence rates of derivatives of Floater-Hormann interpolants for well-spaced nodes

Floater-Hormann interpolants constitute a family of barycentric rational interpolants which are based on blending local polynomial interpolants of degree d. Recent results suggest that the k-th derivatives of these interpolants converge at the rate of 0 (h(d+l-k)) for k <= d as the mesh size h converges to zero. So far, this convergence rate has been proven for k = 1,2 and for k >= 3 under the assumption of equidistant or quasi-equidistant interpolation nodes. In this paper we extend these results and prove that Floater-Hormann interpolants and their derivatives converge at the rate of 0 (h(j)(d+1-k)), where h(j) is the local mesh size, for any k >= 0 and any set of well-spaced nodes. (C) 2016 IMACS. Published by Elsevier B.V. All rights reserved.