RBF Approximation of Big Data Sets with Large Span of Data

This contribution presents a new analysis of properties of the Radial Bases Functions (RBF) interpolation and approximation related to data sets with a large data span. The RBF is a convenient method for scattered d-dimensional interpolation and approximation, e.g. for solution of partial differential equations (PDE) etc. The RBF method leads to a solution of linear system of equations and computational complexity of solution is nearly independent of a dimensionality of a problem solved. However, the RBF methods are usually applied for small data sets with a small span of geometric coordinates. In this paper, we show influence of polynomial reproduction mostly used in RBF interpolation and approximation methods in the context of large span data sets. The experiments made proved expected theoretical results.