论文标题
统一边界的Lebesgue常数用于缩放的基本插值与Matérn内核
Uniformly bounded Lebesgue constants for scaled cardinal interpolation with Matérn kernels
论文作者
论文摘要
对于$ h> 0 $和积极的整数$ m $，$ d $，因此，我们通过Matérn内核$φ_{m，d} $ ----------- $（1- $（1- $）$（1- $ $ $（1- $），我们从缩放网格$ h \ mathbb {z}^d $中研究非固定插值。我们证明，相应的插值操作员的Lebesgue常数均匀地限制为$ h \ to0 $，并推断出缩放插值方案的收敛速率$ o（H^{2M}）$。我们还提供了与Matérn和相关紧凑支持的多结核近似值的收敛结果。
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 Matérn kernel $Φ_{m,d}$---the fundamental solution of $(1-Δ)^m$ 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 Matérn and related compactly supported polyharmonic kernels.
