Abstract

In this paper, we study the spectral properties of the periodized Radial Basis Function interpolation matrix as well as the related harmonic operators discretized using Radial Basis Functions. For Gaussian RBF, this procedure could be easily extended to an arbitrarily high dimensional space on a tensor-product grid as presented in the later parts of the paper. The experimental result of Boyd’s condition number [1] is analytically well predicted in the context of periodized RBF.

中文翻译：

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径向基函数插值Ⅰ：插值矩阵及相关算子的谱分析

摘要

在本文中，我们研究了周期径向基函数插值矩阵的谱特性以及使用径向基函数离散化的相关谐波算子。对于高斯 RBF，这个过程可以很容易地扩展到张量积网格上的任意高维空间，如本文后面部分所示。Boyd 条件数 ​​[1] 的实验结果在周期性 RBF 的背景下得到了很好的分析预测。