On the Radial Basis Function Interpolation I: Spectral Analysis of the Interpolation Matrix and the Related Operators

被引：0

作者：

Xiao, Jianping ^{[1
,2
,3
]}

机构：

[1] China Resources Networks Co Ltd, Shenzhen, Peoples R China

[2] Natl Univ Singapore, Singapore, Singapore

[3] Univ Michigan, Ann Arbor, MI 48109 USA

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2023年 / 63卷 / 05期

基金：

美国国家科学基金会;

关键词：

RBF; interpolation; spectral methods; Neural Network; tensor decomposition; EQUATION;

D O I：

10.1134/S0965542523050172

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：719 / 729

页数：11

共 9 条

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