Uniformly bounded Lebesgue constants for scaled cardinal interpolation with Matérn kernels

2020/08/28 by Aurelian Bejancu, Bejancu, Aurelian · 1 citation
Computer Science · Mathematics · #41A05 #41A25 #41A63 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.CA #math.NA #msc:41A05 #msc:41A25 #msc:41A63

paper · pdf · doi:10.48550/arxiv.2009.00711

16 pages

arxiv created 2020/08/28 · arxiv updated 2020/09/04

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 hℤ^d via the Matérn kernel Φ_m,d---the fundamental solution of (1-Δ)^m in ℝ^d. We prove that the Lebesgue constants of the corresponding interpolation operators are uniformly bounded as h→0 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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