Uniformly bounded Lebesgue constants for scaled cardinal interpolation with Matérn kernels

Aurelian Bejancu

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arXiv · 2009.00711

Uniformly bounded Lebesgue constants for scaled cardinal interpolation with Matérn kernels

Aurelian Bejancu

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Abstract

For $h>0$ and positive integers $m$, $d$, such that $m>d/2$, we study non-stationary interpolation at the points of the scaled grid $h\mathbb{Z}^d$ via the Matérn kernel $Φ_{m,d}$---the fundamental solution of $(1-Δ)^m$ in $\mathbb{R}^d$. We prove that the Lebesgue constants of the corresponding interpolation operators are uniformly bounded as $h\to0$ and deduce the convergence rate $O(h^{2m})$ for the scaled interpolation scheme. We also provide convergence results for approximation with Matérn and related compactly supported polyharmonic kernels.

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Aurelian Bejancu. 2020-08-28. Uniformly bounded Lebesgue constants for scaled cardinal interpolation with Matérn kernels. https://arxiv.org/abs/2009.00711

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