A comparison of radial basis functions

A survey of algorithms for approximation of multivariate functions with radial basis functions (RBF) splines is presented. Algorithms of interpolation, smoothing, selecting the smoothing parameter, and regression with splines are described in detail. These algorithms are based on the properties of conditional positive definiteness of the spline radial basis function. Several families of the radial basis functions generated by means of conditionally complete monotone functions are considered. Recommendations for the selection of the spline basis and on the preparation of the initial data for approximation with the help of the RBF spline are given.