On the Minimax Spherical Designs
Combinatorics
2022-03-21 v2 Numerical Analysis
Metric Geometry
Numerical Analysis
Probability
Abstract
Distributing points on a (possibly high-dimensional) sphere with minimal energy is a long-standing problem in and outside the field of mathematics. This paper considers a novel energy function that arises naturally from statistics and combinatorial optimization, and studies its theoretical properties. Our result solves both the exact optimal spherical point configurations in certain cases and the minimal energy asymptotics under general assumptions. Connections between our results and the L1-Principal Component analysis and Quasi-Monte Carlo methods are also discussed.
Keywords
Cite
@article{arxiv.2102.04599,
title = {On the Minimax Spherical Designs},
author = {Weibo Fu and Guanyang Wang and Jun Yan},
journal= {arXiv preprint arXiv:2102.04599},
year = {2022}
}
Comments
24 pages, 5 figures. To appear in Random Structures & Algorithms