Title

Effective Condition Number For the Selection of the RBF Shape Parameter With the Fictitious Point Method

Document Type

Article

Publication Date

8-1-2022

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

Based on the Uncertainty Principle of radial basis functions (RBFs), it is known that the condition number and the error cannot be both kept small at the same time. In contrast to the traditional condition number, the effective condition number provides a much better estimation of the actual condition number of the resultant matrix system. In this paper, motivated by the Uncertainty Principle of RBFs, we propose to apply the effective condition number as a numerical tool to determine a reasonably good shape parameter value in the context of the Kansa method coupled with the fictitious point method. Six examples for second and fourth order partial differential equations in 2D and 3D are presented to demonstrate the effectiveness of the proposed method.

Publication Title

Applied Numerical Mathematics

Volume

178

First Page

280

Last Page

295

Find in your library

Share

COinS