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.
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Communicated by Joe Ward.
The author has been supported by the Graduiertenkolleg 1023 “Identification in Mathematical Models: Synergy of Stochastic and Numerical Methods“, Universität Göttingen, in form of a DFG scholarship.
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Scheuerer, M. An alternative procedure for selecting a good value for the parameter c in RBF-interpolation. Adv Comput Math 34, 105–126 (2011). https://doi.org/10.1007/s10444-010-9146-3
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DOI: https://doi.org/10.1007/s10444-010-9146-3