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Article Dans Une Revue SIAM Journal on Matrix Analysis and Applications Année : 2021

Spectral properties of kernel matrices in the flat limit

Résumé

Kernel matrices are of central importance to many applied fields. In this manuscript, we focus on spectral properties of kernel matrices in the so-called "flat limit", which occurs when points are close together relative to the scale of the kernel. We establish asymptotic expressions for the determinants of the kernel matrices, which we then leverage to obtain asymptotic expressions for the main terms of the eigenvalues. Analyticity of the eigenprojectors yields expressions for limiting eigenvectors, which are strongly tied to discrete orthogonal polynomials. Both smooth and finitely smooth kernels are covered, with stronger results available in the finite smoothness case.

Dates et versions

hal-03017947 , version 1 (21-11-2020)

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Simon Barthelme, Konstantin Usevich. Spectral properties of kernel matrices in the flat limit. SIAM Journal on Matrix Analysis and Applications, 2021, 42 (1), pp.17-57. ⟨10.1137/19M129677X⟩. ⟨hal-03017947⟩
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