Partition of unity interpolation using stable kernel-based techniques
This work addresses the need for stable and efficient interpolation of large scattered data sets, a common problem in scientific computing and data analysis.
The paper proposes a stable and accurate interpolation technique for large scattered data sets by combining Partition of Unity with stable local RBF bases, achieving improved stability for flat kernels and computational efficiency.
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.