Radial polynomials as alternatives to smooth radial basis functions and their applications

Abstract: Because of the high approximation power and simplicity of computation of smooth radial basis functions (RBFs), in recent decades they have received much attention for function approximation. These RBFs contain a shape parameter that regulates the relation between their accuracy and stability. A difficulty in approximation via smooth RBFs is optimal selection of shape parameter. The aim of this paper is to introduce an alternative for smooth RBFs, which in addition to overcoming this difficulty, its approximation power is almost equal to RBFs....