Stabilized interpolation using radial basis functions augmented with selected radial polynomials

被引:7
作者
Pooladi, Fatemeh [1 ,2 ]
Larsson, Elisabeth [2 ]
机构
[1] Persian Gulf Univ, Dept Math, Bushehr, Iran
[2] Uppsala Univ, Dept Informat Technol, Uppsala, Sweden
基金
瑞典研究理事会;
关键词
Interpolation; Radial basis function; Radial polynomial; Flat limit; Augmented basis function; OPTIMAL SHAPE-PARAMETERS; MULTIVARIATE INTERPOLATION; STABLE COMPUTATIONS; APPROXIMATION; ALGORITHM; LIMIT;
D O I
10.1016/j.cam.2023.115482
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Infinitely smooth radial basis functions (RBFs) have a shape parameter that controls their shapes. When using these RBFs (e.g., the Gaussian RBF) for interpolation problems, we have ill-conditioning when the shape parameter is very small, while in some cases small shape parameters lead to high accuracy. In this study, we are going to reduce the effect of the ill-conditioning of the infinitely smooth RBFs. We propose a new basis augmenting the infinitely smooth RBFs at different locations with radial polynomials of different even powers. Numerical experiments show that the new basis is stable for all values of the shape parameter.& COPY; 2023 Elsevier B.V. All rights reserved.
引用
收藏
页数:16
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