Scattered Data Interpolation in N-Dimensional Space

Abstract

Radial Basis Functions (RBF) interpolation theory is briefly introduced at the “application level” including some basic principles and computational issues. The RBF interpolation is convenient for un-ordered data sets in n-dimensional space, in general. This approach is convenient especially for a higher dimension N > 2 conversion to ordered data set, e.g. using tessellation, is computationally very expensive. The RBF interpolation is not separable and it is based on distance of two points. The RBF interpolation leads to a solution of a Linear System of Equations (LSE) Ax=b. There are two main groups of interpolating functions: ‘global” and “local”. Application of “local” functions, called Compactly Supporting Functions (CSFBF), can significantly decrease computational cost as they lead to a system of linear equations with a sparse matrix. The RBF interpolation can be used also for image reconstruction, inpainting removal, for solution of Partial Differential Equations (PDE) etc.