  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.
