RBF Interpolation with CSRBF of Large Data Sets
For practitioners using RBF interpolation, this work provides insights into numerical stability for large-scale problems, but the analysis is incremental.
The paper analyzes the numerical stability of RBF interpolation for large data sets with large geometric spans, showing that the method remains computationally feasible despite the data size.
This contribution presents a new analysis of properties of the interpolation using Radial Bases Functions (RBF) related to large data sets interpolation. The RBF application is convenient method for scattered d-dimensional interpolation. The RBF methods lead to a solution of linear system of equations and computational complexity of solution is nearly independent of a dimensionality. However, the RBF methods are usually applied for small data sets with a small span geometric coordinates. This contribution explores properties of the RBF interpolation for large data sets and large span of geometric coordinates of the given data sets with regard to expectable numerical stability of computation.