Convergence rates of derivatives of a family of barycentric rational interpolants

Authors:
Jean-Paul Berrut;Michael S. Floater;Georges Klein
Affiliations:
Department of Mathematics, University of Fribourg, Pérolles, 1700 Fribourg, Switzerland;Centre of Mathematics for Applications, Department of Informatics, University of Oslo, PO Box 1053 Blindern, 0316 Oslo, Norway;Department of Mathematics, University of Fribourg, Pérolles, 1700 Fribourg, Switzerland
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

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.