Error bounds for anisotropic RBF interpolation

被引：13

作者：

Beatson, Rick ^{[2
]}

Davydov, Oleg ^{[1
]}

Levesley, Jeremy ^{[3
]}

机构：

[1] Univ Strathclyde, Dept Math, Glasgow G1 1XH, Lanark, Scotland

[2] Univ Canterbury, Dept Math & Stat, Christchurch 1, New Zealand

[3] Univ Leicester, Dept Math, Leicester LE1 7RH, Leics, England

来源：

JOURNAL OF APPROXIMATION THEORY | 2010年 / 162卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Radial basis functions; Anisotropic approximation;

D O I：

10.1016/j.jat.2009.08.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present error bounds for the interpolation with anisotropically transformed radial basis functions for both a function and its partial derivatives. The bounds rely on a growth function and do not contain unknown constants. For polyharmonic basic functions in R-2, we show that the anisotropic estimates predict a significant improvement of the approximation error if both the target function and the placement of the centers are anisotropic, and this improvement is confirmed numerically. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：512 / 527

页数：16

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