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Minimum-energy measures for singular kernels

Pronzato, Luc and Zhigljavsky, Anatoly 2021. Minimum-energy measures for singular kernels. Journal of Computational and Applied Mathematics 382 , 113089. 10.1016/j.cam.2020.113089

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Elsevier
ISSN: 0377-0427
Date of First Compliant Deposit: 23 August 2020
Date of Acceptance: 9 July 2020
Last Modified: 21 Oct 2021 17:55
URI: http://orca.cardiff.ac.uk/id/eprint/134339

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