A new variable shape parameter strategy for Gaussian radial basis function approximation methods

Abstract

In this article, we introduce a new variable shape parameter is called symmetric variable shape parameter (SVSP) for Gaussian radial basis functions (GRBFs). The GRBF has the shape parameter
$c$, which plays an important role in the accuracy of the approximation. In this work, we will use it to  interpolate functions and solve linear boundary value problems (LBVP). Some numerical experiments are presented to show accuracy and robustness of the GRBF with SVSP strategy. These results have the best accuracy for the one- and two-dimensional interpolations and LBVP. Besides, the numerical results show that the SVSP for GRBF often outperforms constant shape parameter strategy.