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.