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arXiv · 1201.0607

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

Phung Van Manh
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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 $f$.

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Phung Van Manh. 2012-01-03. On the Convergence of Kergin and Hakopian Interpolants at Leja Sequences for the Disk. https://arxiv.org/abs/1201.0607

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