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Article Dans Une Revue Journal of Computational and Applied Mathematics Année : 2021

Minimum-energy measures for singular kernels

Résumé

We develop algorithms for energy minimization for kernels with singularities. This problem arises in different fields, most notably in the construction of space-filling sequences of points where singularity of kernels guarantees a strong repelling property between these points. Numerical algorithms are based on approximating singular kernels by non-singular ones, subsequent discretization and solving non-singular discrete problems. For approximating singular kernels, we approximate an underlying completely monotone (briefly, CM) function with singularity by a bounded CM function with controlled accuracy. Theoretical properties of the suggested approximation are studied and some numerical results are shown.
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Dates et versions

hal-02495643 , version 1 (02-03-2020)
hal-02495643 , version 2 (20-05-2020)

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  • HAL Id : hal-02495643 , version 2

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Luc Pronzato, Anatoly A. Zhigljavsky. Minimum-energy measures for singular kernels. Journal of Computational and Applied Mathematics, 2021, 382. ⟨hal-02495643v2⟩
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