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 $f$ is $C^{\infty }$ on $D$, all the derivatives of the interpolation polynomials converge uniformly to the corresponding derivatives of $f$.

References in corpus (1)

• Lagrange interpolation at real projections of Leja sequences for the unit disk