Haar Function Based Estimates of the Star-Discrepancy of Plane Digital Nets

被引：0

作者：

Karl Entacher

机构：

[1] Universität Salzburg,

[2] Austria,undefined

来源：

Monatshefte für Mathematik | 2000年 / 130卷

关键词：

2000 Mathematics Subject Classification: 11K06; 11K38; 42C10; 42C40; Key words: Haar functions; uniform distribution modulo one; discrepancy; Hammersley point set; (t; m; s)-nets;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We apply the Haar function system to estimate the star-discrepancy of special digital (t,m,s)-nets in dimension \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. We use a basic technique based on discretization combined with an exact calculation of the discrete star-discrepancy.

引用

页码：99 / 108

页数：9

共 16 条

[1] Haar function based estimates of the star-discrepancy of plane digital nets
Entacher, K
[J]. MONATSHEFTE FUR MATHEMATIK, 2000, 130 (02): : 99 - 108
[2] Discrepancy estimates based on Haar functions
Entacher, K
[J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2001, 55 (1-3) : 49 - 57
[3] On the star discrepancy of digital nets and sequences in three dimensions
Kritzer, P
[J]. Monte Carlo and Quasi-Monte Carlo Methods 2004, 2006, : 273 - 287
[4] Weighted star discrepancy of digital nets in prime bases
Dick, J
Niederreiter, H
Pillichshammer, F
[J]. MONTE CARLO AND QUASI-MONTE CARLO METHODS 2004, 2006, : 77 - +
[5] GENERAL DISCREPANCY ESTIMATES .2. THE HAAR FUNCTION SYSTEM
HELLEKALEK, P
[J]. ACTA ARITHMETICA, 1994, 67 (04) : 313 - 322
[6] Construction algorithms for digital nets with low weighted star discrepancy
Dick, J
Leobacher, G
Pillichshammer, F
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2005, 43 (01) : 76 - 95
[7] Walsh series analysis of the star discrepancy of digital nets and sequences
Larcher, G
Pillichshammer, F
[J]. MONTE CARLO AND QUASI-MONTE CARLO METHODS 2002, 2004, : 315 - 327
[8] Star discrepancy estimates for digital (t, m, 2)-nets and digital (t, 2)-sequences over Z2
Dick, J
Kritzer, P
[J]. ACTA MATHEMATICA HUNGARICA, 2005, 109 (03) : 239 - 254
[9] Star discrepancy estimates for digital (t, m, 2)-nets and digital (t, 2) -sequences over Z2
Josef Dick
Peter Kritzer
[J]. Acta Mathematica Hungarica, 2005, 109 : 239 - 254
[10] Improved upper bounds for the star discrepancy of digital nets in dimension 3
Pillichshammer, F
[J]. ACTA ARITHMETICA, 2003, 108 (02) : 167 - 189

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