Minimal dispersion on the cube and the torus

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2024-06-13 DOI:10.1016/j.jco.2024.101883

A. Arman , A.E. Litvak

引用次数: 0

Abstract

We improve some upper bounds for minimal dispersion on the cube and torus. Our new ingredient is an improvement of a probabilistic lemma used to obtain upper bounds for dispersion in several previous works. Our new lemma combines a random and non-random choice of points in the cube. This leads to better upper bounds for the minimal dispersion.

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立方体和环面上的最小色散

我们改进了立方体和环上最小离散度的一些上限。我们的新内容是对之前几部著作中用来获得离散度上限的概率级数的改进。我们的新定理结合了立方体中随机和非随机点的选择。这就为最小离散度带来了更好的上界。

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.