Radial Basis Functions Interpolation and Applications: An Incremental Approach

Abstract

Radial Basis Functions (RBF) interpolation is primarily used for interpolation of scattered data in higher dimensions. The RBF interpolation is a non-separable interpolation which offers a smooth interpolation, generally in n-dimensional space. We present a new method for RBF computation using an incremental approach. The proposed method is especially convenient in cases when larger data sets are randomly updated as the proposed method is of O(N2) computational complexity instead of O(N3) for insert / remove operations only and therefore it is much faster than the standard approach. If t-varying data or vector data are to be interpolated, the proposed method offers a significant speed-up as well.