A note on generalized Floater–Hormann interpolation at arbitrary distributions of nodes

The paper is concerned with a generalization of Floater–Hormann (briefly FH) rational interpolation recently introduced by the authors. Compared with the original FH interpolants, the generalized ones depend on an additional integer parameter γ>1, that, in the limit case γ=1 returns the classical FH definition. Here we focus on the general case of an arbitrary distribution of nodes and, for any γ>1, we estimate the sup norm of the error in terms of the maximum (h) and minimum (h∗) distance between two consecutive nodes. In the special case of equidistant (h=h∗) or quasi–equidistant (h≈h∗) nodes, the new estimate improves previous results requiring some theoretical restrictions on γ which are not needed as shown by the numerical tests carried out to validate the theory.