Convergence rates of derivatives of a family of barycentric rational interpolants

摘要

In polynomial and spline interpolation the κ-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 κ = 1,2, the same convergence rate for a recently proposed family of barycentric rational interpolants based on blending polynomial interpolants of degree d.