On radial basis functions

Abstract

Many sciences and other areas of research and applications from engineering to economics require the approximation of functions that depend on many variables. This can be for a variety of reasons. Sometimes we have a discrete set of data points and we want to find an approximating function that completes this data; another possibility is that precise functions are either not known or it would take too long to compute them explicitly. In this snapshot we want to introduce a particular method of approximation which uses functions called radial basis functions. This method is particularly useful when approximating functions that depend on very many variables. We describe the basic approach to approximation with radial basis functions, including their computation, give several examples of such functions and show some applications.