Paper Info
Title
Some interesting behaviors of good lattice point sets
Abstract
Good lattice point (GLP) sets are sets of points that are uniformly distributed over the domain of interest and thus have good space-filling property. GLP sets are an important kind of points for many applications, such as multidimensional quadrature, simulation, computer experiments, quasi-Monte Carlo techniques and design of experiments. It is a significant issue to study the behaviors of GLP sets. For instance, most real-life applications require that the columns of a GLP set are independent, i.e., the GLP set has full rank. If one or more columns are linearly dependent, there will be more confounding among the main effects and interactions in statistical models and also we can not find the least squares estimation of regression coefficients in the linear regression model. The problem of finding the rank of the GLP set remained unsolved since its inception in 1959. It is desirable to put the first stone for solving this significant problem. Through theoretical justifications, this paper gives some interesting behaviors of the generating vector of any GLP set and shows the independence among its rows and columns by presenting some analytic linkages among these rows and columns. The results of this paper are used not only as a benchmark for constructing full rank GLP sets, but also in various applications of GLP sets.
Year
DOI
Venue
2021
10.1080/03610918.2019.1628988
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
Keywords
DocType
Volume
Good lattice points, Generating vector, Confounding, Rank, Euler function, Number theory
Journal
50
Issue
ISSN
Citations 
11
0361-0918
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
A. M. Elsawah182.05
Kai-Tai Fang216523.65
Yu Hui Deng300.68