Some Improvements on Good Lattice Point Sets.

IF 2.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Entropy Pub Date : 2024-10-27 DOI:10.3390/e26110910
Yu-Xuan Lin, Tian-Yu Yan, Kai-Tai Fang
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Abstract

Good lattice point (GLP) sets are a type of number-theoretic method widely utilized across various fields. Their space-filling property can be further improved, especially with large numbers of runs and factors. In this paper, Kullback-Leibler (KL) divergence is used to measure GLP sets. The generalized good lattice point (GGLP) sets obtained from linear-level permutations of GLP sets have demonstrated that the permutation does not reduce the criterion maximin distance. This paper confirms that linear-level permutation may lead to greater mixture discrepancy. Nevertheless, GGLP sets can still enhance the space-filling property of GLP sets under various criteria. For small-sized cases, the KL divergence from the uniform distribution of GGLP sets is lower than that of the initial GLP sets, and there is nearly no difference for large-sized points, indicating the similarity of their distributions. This paper incorporates a threshold-accepting algorithm in the construction of GGLP sets and adopts Frobenius distance as the space-filling criterion for large-sized cases. The initial GLP sets have been included in many monographs and are widely utilized. The corresponding GGLP sets are partially included in this paper and will be further calculated and posted online in the future. The performance of GGLP sets is evaluated in two applications: computer experiments and representative points, compared to the initial GLP sets. It shows that GGLP sets perform better in many cases.

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良好网格点集的一些改进
良好格点集(GLP)是一种广泛应用于各个领域的数论方法。它们的空间填充特性可以得到进一步改善,尤其是在有大量运行和因子的情况下。本文采用库尔贝-莱布勒(KL)发散来衡量 GLP 集。由 GLP 集的线性级数排列得到的广义好格点(GGLP)集证明,排列不会减少准则最大距离。本文证实,线性水平排列可能会导致更大的混合差异。尽管如此,GGLP 集仍能在各种准则下增强 GLP 集的空间填充特性。对于小尺寸情况,GGLP 集均匀分布的 KL 发散低于初始 GLP 集的 KL 发散,而对于大尺寸点几乎没有差异,这表明它们的分布具有相似性。本文在构建 GGLP 集时加入了阈值接受算法,并采用 Frobenius 距离作为大尺寸情况下的空间填充准则。最初的 GLP 集已收录在许多专著中,并被广泛使用。本文部分收录了相应的 GGLP 集,今后将进一步计算并发布到网上。与初始 GLP 集相比,GGLP 集的性能在两个应用领域进行了评估:计算机实验和代表性点。结果表明,GGLP 集在很多情况下表现更好。
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
Entropy
Entropy PHYSICS, MULTIDISCIPLINARY-
CiteScore
4.90
自引率
11.10%
发文量
1580
审稿时长
21.05 days
期刊介绍: Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish as much as possible their theoretical and experimental details. There is no restriction on the length of the papers. If there are computation and the experiment, the details must be provided so that the results can be reproduced.
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