Radial basis function approximations: comparison and applications

Abstract

• We propose the radial basis function (RBF) approximation of scattered data. • Approximation is based on the distance between a given point and a reference point. • The set of reference points is specified by a user. • Method returns the approximating function which is represented as a sum of M RBFs. • Experimental results show that proposed RBF approximation gives the best results. Approximation of scattered data is often a task in many engineering problems. The radial basis function (RBF) approximation is appropriate for large scattered (unordered) datasets in d -dimensional space. This approach is useful for a higher dimension d > 2, because the other methods require the conversion of a scattered dataset to an ordered dataset (i.e. a semi-regular mesh is obtained by using some tessellation techniques), which is computationally expensive. The RBF approximation is non-separable, as it is based on the distance between two points. This method leads to a solution of linear system of equations (LSE) Ac = h . In this paper several RBF approximation methods are briefly introduced and a comparison of those is made with respect to the stability and accuracy of computation. The proposed RBF approximation offers lower memory requirements and better quality of approximation.