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Minimum-energy measures for singular kernels

Abstract : 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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https://hal.archives-ouvertes.fr/hal-02495643
Contributor : Luc Pronzato <>
Submitted on : Wednesday, May 20, 2020 - 12:38:48 PM
Last modification on : Monday, June 15, 2020 - 3:17:50 PM

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  • HAL Id : hal-02495643, version 2

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Luc Pronzato, Anatoly Zhigljavsky. Minimum-energy measures for singular kernels. 2020. ⟨hal-02495643v2⟩

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