Some tools for fast and stable Radial Basis Function approximation with Scilab

Gabriele Santin, University of Padova

The theory of Radial Basis Functions (RBF) is of growing importance in the field of approximation thanks to its power and flexibility. This method is particular effective when dealing with data coming from scattered samplings possibly in high space dimension. Nevertheless, in certain conditions this method can be unstable and can suffer from ill-conditioning. We will present a Scilab implementation of some tools which allow a fast and stable computation of RBF approximants in a wide class of problems. These tools come from some recent result about change of basis in the RBF spaces.