Effective condition number for the selection of the RBF shape parameter with the fictitious point method
Journal
Applied Numerical Mathematics
Journal Volume
178
Pages
280-295
Date Issued
2022
Author(s)
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. © 2022 IMACS
Subjects
Collocation; Effective condition number; Fictitious point method; Kansa method; Multiquadrics; Radial basis functions; Shape parameter
Other Subjects
Functions; Heat conduction; Number theory; Numerical methods; Actual conditions; Collocation; Effective condition number; Fictitious point method; Kansa's method; Multiquadrics; Point methods; Shape parameters; Uncertainty principles; Radial basis function networks
Type
journal article