Radial basis functions under tension |
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Authors: | A. Bouhamidi,A. Le Mé hauté |
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Affiliation: | a LMPA, Université du Littoral Côte d'Opale, 50 rue F. Buisson BP 699, F-62228 Calais Cedex, France b Laboratoire de Mathématiques, CNRS UMR 6629, Université de Nantes, Faculté des Sciences, 2, rue de la Houssinière, F-44072 Nantes Cedex, France |
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Abstract: | We discuss multivariate interpolation with some radial basis function, called radial basis function under tension (RBFT). The RBFT depends on a positive parameter which provides a convenient way of controlling the behavior of the interpolating surface. We show that our RBFT is conditionally positive definite of order at least one and give a construction of the native space, namely a semi-Hilbert space with a semi-norm, minimized by such an interpolant. Error estimates are given in terms of this semi-norm and numerical examples illustrate the behavior of interpolating surfaces. |
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Keywords: | 65D05 65D07 65D15 41A15 |
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