Uniformly bounded Lebesgue constants for scaled cardinal interpolation with Mat\'{e}rn kernels

DOI10.1016/J.JAT.2022.105740arXiv2009.00711WikidataQ114164908 ScholiaQ114164908MaRDI QIDQ6348193

Aurelian Bejancu

Publication date: 28 August 2020

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 $hmathbb{Z}^d$ via the Mat'{e}rn kernel $Ph{i}_{m,d}$---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 $ho0$ 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.

Mathematics Subject Classification ID

Multidimensional problems (41A63) Interpolation in approximation theory (41A05) Rate of convergence, degree of approximation (41A25)

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