Spectral approach for kernel-based interpolation

Abstract : We describe how the resolution of a kernel-based interpolation problem can be associated with a spectral problem. An integral operator is defined from the embedding of the considered Hilbert subspace into an auxiliary Hilbert space of square-integrable functions. We finally obtain a spectral representation of the interpolating elements which allows their approximation by spectral truncation. As an illustration, we show how this approach can be used to enforce boundary conditions in kernel-based interpolation models and in what it offers an interesting alternative for dimension reduction.
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  • HAL Id : hal-00915529, version 3

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Bertrand Gauthier, Xavier Bay. Spectral approach for kernel-based interpolation. Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc 2012, 21 (3), pp.439-479. ⟨http://afst.cedram.org⟩. ⟨hal-00915529v3⟩

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