On the Lebesgue constant of barycentric rational interpolation at equidistant nodes
Recent results reveal that the family of barycentric rational interpolants introduced by Floater and Hormann is very well-suited for the approximation of functions as well as their derivatives, integrals and primitives. Especially in the case of equidistant interpolation nodes, these infinitely smooth interpolants offer a much better choice than their polynomial analogue. A natural and important question concerns the condition of this rational approximation method. In this paper we extend a recent study of the Lebesgue function and constant associated with Berrut’s rational interpolant at equidistant nodes to the family of Floater–Hormann interpolants, which includes the former as a special case.
Mathematics Subject Classification (2000)65D05 65F35 41A05 41A20
Unable to display preview. Download preview PDF.
- 11.Klein, G., Berrut, J.P.: Linear barycentric rational quadrature. BIT (2011). doi:10.1007/s10543-011-0357-x
- 12.Klein, G., Berrut, J.P.: Linear rational finite differences from derivatives of barycentric rational interpolants. Tech. Rep. 2011-1, Department of Mathematics, University of Fribourg (2011)Google Scholar
- 15.Rivlin, T.J.: The Lebesgue constants for polynomial interpolation. In: Garnir, H.G., Unni, K.R., Williamson, J.H. (eds.) Functional Analysis and its Applications, Lecture Notes in Mathematics, vol. 399, pp. 442–437. Springer, Berlin (1974)Google Scholar