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Uniformly bounded Lebesgue constants for scaled cardinal interpolation with Matérn kernels (2009.00711v1)

Published 28 Aug 2020 in math.NA, cs.NA, and math.CA

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 Mat\'{e}rn kernel $\Phi_{m,d}$---the fundamental solution of $(1-\Delta)m$ 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 Mat\'{e}rn and related compactly supported polyharmonic kernels.

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