RBF Interpolation with CSRBF of Large Data Sets

TL;DR

This paper analyzes the properties of Radial Basis Function (RBF) interpolation, especially for large data sets with extensive geometric spans, focusing on numerical stability and applicability beyond small data sets.

Contribution

It provides a new analysis of RBF interpolation properties for large data sets, extending its applicability and examining numerical stability issues.

Findings

RBF methods are effective for large, scattered data sets.

Numerical stability depends on data distribution and span.

Application to large data sets is feasible with proper analysis.

Abstract

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.