RBF-PU Interpolation with Variable Subdomain Sizes and Shape Parameters

TL;DR

This paper introduces an improved RBF-PU interpolation method that adaptively selects local subdomain sizes and shape parameters to enhance accuracy when interpolating large, non-uniform data sets.

Contribution

It proposes a novel technique that optimally chooses variable subdomain sizes and shape parameters based on an a priori error estimate, improving interpolation accuracy.

Findings

Enhanced interpolation accuracy demonstrated through numerical experiments.

Effective handling of large, non-homogeneous data sets.

Performance improvements over traditional fixed-parameter methods.

Abstract

In this paper, we deal with the challenging computational issue of interpolating large data sets, with eventually non-homogeneous densities. To such scope, the Radial Basis Function Partition of Unity (RBF-PU) method has been proved to be a reliable numerical tool. However, there are not available techniques enabling us to efficiently select the sizes of the local PU subdomains which, together with the value of the RBF shape parameter, greatly influence the accuracy of the final fit. Thus here, by minimizing an \emph{a priori} error estimate, we propose a RBF-PU method by suitably selecting variable shape parameters and subdomain sizes. Numerical results and applications show performaces of the interpolation technique.