Low-energy points on the sphere and the real projective plane

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2023-06-01 DOI:10.1016/j.jco.2023.101742

Carlos Beltrán, Ujué Etayo, Pedro R. López-Gómez

引用次数: 3

Abstract

We present a generalization of a family of points on $S^{2}$ , the Diamond ensemble, containing collections of N points on $S^{2}$ with very small logarithmic energy for all $N \in N$ . We extend this construction to the real projective plane ${RP}^{2}$ and we obtain upper and lower bounds with explicit constants for the Green and logarithmic energy on this last space.

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球面和实投影平面上的低能点

我们给出了S2上的点族的推广，即Diamond系综，它包含了S2上N个点的集合，对于所有N∈N，它们的对数能量非常小。我们将这种构造推广到实射影平面RP2上，得到了最后一个空间上Green能量和对数能量的带显式常数的上界和下界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.