New star discrepancy bounds for -nets and -sequences

被引：0

作者：

Faure, Henri ^{[1
]}

Kritzer, Peter ^{[2
]}

机构：

[1] Univ Aix Marseille, Inst Math Luminy CNRS, F-13288 Marseille 09, France

[2] Univ Linz, Inst Finanzmath, A-4040 Linz, Austria

来源：

MONATSHEFTE FUR MATHEMATIK | 2013年 / 172卷 / 01期

基金：

奥地利科学基金会;

关键词：

Discrepancy; (t; m; s)-net; s)-sequence; Uniform distribution modulo one; 2; DIMENSIONS; (T; S)-SEQUENCES; HAMMERSLEY; SETS;

D O I：

10.1007/s00605-012-0470-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we derive new general upper bounds on the star discrepancy of -nets and -sequences. These kinds of point sets are among the most widely used in quasi-Monte Carlo methods for numerical integration. By our new results, we improve on previous discrepancy bounds and prove a conjecture stated by the second author in an earlier paper.

引用

页码：55 / 75

页数：21

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