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.
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