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 |
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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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