Uniformly bounded Lebesgue constants for scaled cardinal interpolation with Matérn kernels
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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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