Fast strategy for PU interpolation: An application for the reconstruction of separatrix manifolds

In this paper, the Partition of Unity (PU) method is performed by blending Radial Basis Functions (RBFs) as local approximants and using locally supported weights. In particular, we present a new multidimensional data structure which makes use of an integer-based scheme. This approach allows to perform an optimized space-partitioning structure. Moreover, because of its flexibility, it turns out to be extremely meaningful in the reconstruction of the attraction basins in dynamical systems.