Uniformly bounded Lebesgue constants for scaled cardinal interpolation with Matérn kernels

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 hZd via the Matérn kernel Φm,d—the fundamental solution of (1−Δ)m in Rd. We prove that the Lebesgue constants of the corresponding interpolation operators are uniformly b...

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Veröffentlicht in:Journal of approximation theory Jg. 278; S. 105740
1. Verfasser: Bejancu, Aurelian
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.06.2022
Schlagworte:
Approximation order
Cardinal interpolation
Compactly supported RBF
Lebesgue constant
Matérn kernel
Non-stationary ladder
Lebesgue constant
41A25
Matérn kernel
41A63
Approximation order
Non-stationary ladder
Cardinal interpolation
41A05
Compactly supported RBF
ISSN:0021-9045, 1096-0430
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Beschreibung
Zusammenfassung: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 hZd via the Matérn kernel Φm,d—the fundamental solution of (1−Δ)m in Rd. We prove that the Lebesgue constants of the corresponding interpolation operators are uniformly bounded as h→0 and deduce the optimal L∞-convergence rate O(h2m) for the scaled interpolation scheme. We also provide convergence results for approximation with Matérn and related compactly supported polyharmonic kernels.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2022.105740