On the Convergence of Kergin and Hakopian Interpolants at Leja Sequences for the Disk

DOI10.1007/S10474-012-0239-YarXiv1201.0607MaRDI QIDQ6230045

Van Manh Phung

Publication date: 3 January 2012

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

Mathematics Subject Classification ID

Multidimensional problems (41A63) Interpolation in approximation theory (41A05) Spaces of linear operators; topological tensor products; approximation properties (46A32)

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