On the convergence of Kergin and Hakopian interpolants at Leja sequences for the disk

Abstract

We prove that Kergin interpolation polynomials and Hakopian interpolation polynomials at the points of a Leja sequence for the unit disk D of a sufficiently smooth function f in a neighbourhood of D converge uniformly to f on D. Moreover, when f∈C∞(D), all the derivatives of the interpolation polynomials converge uniformly to the corresponding derivatives of f.