Radial basis function interpolation in the limit of increasingly flat basis functions

We propose a new approach to study Radial Basis Function (RBF) interpolation in the limit of increasingly flat functions. The new approach is based on the semi-analytical computation of the Laurent series of the inverse of the RBF interpolation matrix described in a previous paper [3]. Once the Laurent series is obtained, it can be used to compute the limiting polynomial interpolant, the optimal shape parameter of the RBFs used for interpolation, and the weights of RBF finite difference formulas, among other things.