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Spectral approach for kernel-based interpolation

Gauthier, Bertrand ORCID: and Bay, Xavier 2012. Spectral approach for kernel-based interpolation. Annales de la faculté des sciences de Toulouse Mathématiques 21 (3) , pp. 439-479. 10.5802/afst.1341

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
ISSN: 0240-2963
Last Modified: 02 Nov 2022 10:13

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