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Spectral approach for kernel-based interpolation. (English. French summary) Zbl 1269.47025

Authors’ 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.

MSC:

47B34 Kernel operators
60G15 Gaussian processes
65D05 Numerical interpolation

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References:

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