Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [20 references]  Display  Hide  Download
Contributor : Luc Pronzato <>
Submitted on : Wednesday, May 20, 2020 - 12:38:48 PM
Last modification on : Wednesday, February 3, 2021 - 3:55:13 PM


Files produced by the author(s)


  • HAL Id : hal-02495643, version 2



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



Record views


Files downloads