Convergence rates of derivatives of a family of barycentric rational interpolants

In polynomial and spline interpolation the k-th derivative of the interpolant, as a function of the mesh size h, typically converges at the rate of O(h(d+1-k)) as h -> 0, where d is the degree of the polynomial or spline. In this paper we establish, in the important cases k = 1,2, the same convergence rate for a recently proposed family of barycentric rational interpolants based on blending polynomial interpolants of degree d. (C) 2011 IMACS. Published by Elsevier B.V. All rights reserved.