An alternative procedure for selecting a good value for the parameter c in RBF-interpolation

Authors:
Michael Scheuerer
Affiliations:
Institut für Mathematische Stochastik, Georg-August-Universität Göttingen, Göttingen, Germany 37077
Venue:
Advances in Computational Mathematics
Year:
2011

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Abstract

The impact of the scaling parameter c on the accuracy of interpolation schemes using radial basis functions (RBFs) has been pointed out by several authors. Rippa (Adv Comput Math 11:193---210, 1999) proposes an algorithm based on the idea of cross validation for selecting a good such parameter value. In this paper we present an alternative procedure, that can be interpreted as a refinement of Rippa's algorithm for a cost function based on the euclidean norm. We point out how this method is related to the procedure of maximum likelihood estimation, which is used for identifying covariance parameters of stochastic processes in spatial statistics. Using the same test functions as Rippa we show that our algorithm compares favorably with cross validation in many cases and discuss its limitations. Finally we present some computational aspects of our algorithm.