Haar function based estimates of the star-discrepancy of plane digital nets

被引：2

作者：

Entacher, K ^{[1
]}

机构：

[1] Salzburg Univ, Inst Math, A-5020 Salzburg, Austria

来源：

MONATSHEFTE FUR MATHEMATIK | 2000年 / 130卷 / 02期

关键词：

Haar functions; uniform distribution module one; discrepancy; Hammersley point set; (t; m; s)-nets;

D O I：

10.1007/s006050070040

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We apply the Haar function system to estimate the star-discrepancy of special digital (t, m, s)-nets in dimension s = 2. We use a basic technique based on discretization combined with an exact calculation of the discrete star-discrepancy. 2000 Mathematics Subject Classification: 11K06, 11K38, 42C10, 42C40.

引用

页码：99 / 108

页数：10

共 16 条

[1] Haar Function Based Estimates of the Star-Discrepancy of Plane Digital Nets
Karl Entacher
[J]. Monatshefte für Mathematik, 2000, 130 : 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
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Pillichshammer, F
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[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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