Interpolation and Best Approximation for Spherical Radial Basis Function Networks

Abstract

Within the conventional framework of a native space structure, a smooth kernel generates a small native space, and radial basis functions stemming from the smooth kernel are intended to approximate only functions from this small native space. In this paper, we embed the smooth radial basis functions in a larger native space generated by a less smooth kernel and use them to interpolate the samples. Our result shows that there exists a linear combination of spherical radial basis functions that can both exactly interpolate samples generated by functions in the larger native space and near best approximate the target function.