In this seminar we present a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and  performed by blending radial basis functions (RBFs) as local approximants and using locally supported weight functions. In particular we propose a new space-partitioning data structure based on a partition of the underlying generic domain in blocks. This approach allows us to examine only a reduced number of blocks in the search process of the nearest neighbour points, leading to an optimized searching routine. Complexity analysis and numerical experiments in two- and three-dimensional interpolation support our findings. Some applications to geometric modelling are also considered.

Roberto Cavoretto is a Research Fellow in Numerical Analysis at the Department of Mathematics "Giuseppe Peano" of the University of Torino; Ph.D. in Mathematics, University of Torino in 2010. He held a post-doc position funded by the "Istituto Nazionale di Alta Matematica" (INdAM, Rome) in 2010-2011. In 2012-13 he was invited as visiting researcher at the Illinois Institute of Technology (Chicago, USA). He was member of organizing committees of some international conferences in Numerical Analysis and Modeling, and published more than 50 referred papers. His research activity is mainly focused on topics of Numerical Analysis and Applied Mathematics, such as kernel-based approximation, RBF methods, spherical interpolation, applications to image registration and biomathematics.