On unsymmetric collocation by radial basis functions

被引：216
|
作者：
Hon, YC [1 ]
Schaback, R
机构：
[1] City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China
[2] Univ Gottingen, Inst Numer & Appl Math, D-37083 Gottingen, Germany
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2001年 / 119卷 / 2-3期
关键词：
radial basis functions; Kansa's method; unsymmetric collocation;
D O I：
10.1016/S0096-3003(99)00255-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Solving partial differential equations by collocation with radial basis functions can be efficiently done by a technique first proposed by Kansa in 1990. It rewrites the problem as a generalized interpolation problem, and the solution is obtained by solving a (possibly large) linear system. The method has been used successfully in a variety of applications, but a proof of nonsingularity of the linear system was still missing. This paper shows that a general proof of this fact is impossible. However, numerical evidence shows that cases of singularity are rare and have to be constructed with quite some effort. (C) 2001 Elsevier Science Inc. All rights reserved.
引用
收藏
页码：177 / 186
页数：10
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