Resumen de Convergence rates of derivatives of a family of barycentric rational interpolants

Jean Paul Berrut, Michael S. Floater, Georges Klein

• 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(hd+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.