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 .

The Newton product of polynomial projectors Part 1: Construction and algebraic properties

“…(C) If we substitute the Kergin interpolants by another related projector known as Hakopian interpolants, in the above, see [22,Theorem 4.5], the level will be 28.…”