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

In this paper we propose an enhanced version of the residual sub-sampling method (RSM) in Driscoll and Heryudono (2007) for adaptive interpolation by radial basis functions (RBFs). More precisely, introduce context methods a maximum profile likelihood estimation (MPLE) criterion optimal selection RBF shape parameter. This choice is completely automatic, provides highly reliable accurate results any RBFs, and, unlike original RSM, guarantees that interpolant exists uniquely. The efficacy new method, called MPLE-RSM, tested numerical experiments on some 1D 2D benchmark target functions.