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In this paper we propose an enhanced version of the residual sub-samplingmethod (RSM) in [9] for adaptive interpolation by radial basis functions(RBFs). More precisely, we introduce in the context of sub-sampling methods amaximum profile likelihood estimation (MPLE) criterion for the optimalselection of the RBF shape parameter. This choice is completely automatic,provides highly reliable and accurate results for any RBFs, and, unlike theoriginal RSM, guarantees that the RBF interpolant exists uniquely. The efficacyof this new method, called MPLE-RSM, is tested by numerical experiments on some1D and 2D benchmark target functions.

An adaptive residual sub-sampling algorithm for kernel interpolation based on maximum likelihood estimations