Partition of unity interpolation using stable kernel-based techniques

TL;DR

This paper introduces a stable, accurate partition of unity interpolation method using kernel-based techniques with local stable bases, improving stability and efficiency for large scattered data sets.

Contribution

It presents a novel stable basis construction for local RBF approximations within the partition of unity framework, enhancing stability and computational efficiency.

Findings

Improved stability for flat kernels in RBF interpolation

Enhanced efficiency through optimized local basis search

Effective handling of large scattered data sets

Abstract

In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs) as local approximants and using locally supported weights. In particular, the approach consists in computing, for each PU subdomain, a stable basis. Such technique, taking advantage of the local scheme, leads to a significant benefit in terms of stability, especially for flat kernels. Furthermore, an optimized searching procedure is applied to build the local stable bases, thus rendering the method more efficient.