Minimum-energy measures for singular kernels

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:382

Article

Pronzato, Luc¹  Zhigljavsky, Anatoly² 

[1] Univ Cote Azur, CNRS, I3S, Nice, France

[2] Cardiff Univ, Cardiff, Wales

关键词: Energy minimization;    Singular kernels;    Riesz kernel;    Riesz potential;    Space-filling design;   

DOI  :  10.1016/j.cam.2020.113089

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free