In this paper, we deal with the challenging computational issue ofinterpolating large data sets, with eventually non-homogeneous densities. Tosuch scope, the Radial Basis Function Partition of Unity (RBF-PU) method hasbeen proved to be a reliable numerical tool. However, there are not availabletechniques enabling us to efficiently select the sizes of the local PUsubdomains which, together with the value of the RBF shape parameter, greatlyinfluence the accuracy of the final fit. Thus here, by minimizing an \emph{apriori} error estimate, we propose a RBF-PU method by suitably selectingvariable shape parameters and subdomain sizes. Numerical results andapplications show performaces of the interpolation technique.
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