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
Recommended Citation
Noorizadegan, A.,
Chen, C.,
Young, D.,
Chen, C.
(2022). Effective Condition Number For the Selection of the RBF Shape Parameter With the Fictitious Point Method. Applied Numerical Mathematics, 178, 280-295.
Available at: https://aquila.usm.edu/fac_pubs/20089