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Orthogonal Decompositions in Hilbertian Subspaces, Error Functions and Optimal Extensions of Interpolation Systems

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Abstract

We address the question of optimal extensions of a fixed set S⊂Ω of measurement points for an interpolation system in a reproducing kernel Hilbert space of R Ω. By considering the interpolation error function obtained from the reproducing kernel, we introduce different criteria of optimal extensions. We highlight the orthogonal decomposition of the space based on the subspace associated with the set S. The connection to the classical Schur decomposition of the Gram matrix of the interpolation problem is established. All the theory extends to conditionally positive functions and for this case, we give a result on the spectrum of the matrix of the interpolation problem.

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  1. Mathématique pour l'Industrie et la Physique, UMR CNRS 5640, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex, France

    L. Amodei

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  1. L. Amodei
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Amodei, L. Orthogonal Decompositions in Hilbertian Subspaces, Error Functions and Optimal Extensions of Interpolation Systems. Numerical Algorithms 30, 157–184 (2002). https://doi.org/10.1023/A:1016003803996

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