Minimum-energy measures for singular kernels

Pronzato, Luc and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 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:	22 Nov 2024 17:45
URI:	https://orca.cardiff.ac.uk/id/eprint/134339

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