Duality theory and propagation rules for higher order nets

被引：8

作者：

Baldeaux, Jan ^{[2
]}

Dick, Josef ^{[2
]}

Pillichshammer, Friedrich ^{[1
]}

机构：

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

[2] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

来源：

DISCRETE MATHEMATICS | 2011年 / 311卷 / 05期

基金：

澳大利亚研究理事会;

关键词：

(t; m; s)-net; Propagation rule; Duality theory; Quality parameter; Quasi-Monte Carlo;

D O I：

10.1016/j.disc.2010.11.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Higher order nets and sequences are used in quasi-Monte Carlo rules for the approximation of high dimensional integrals over the unit cube. Hence one wants to have higher order nets and sequences of high quality. In this paper we introduce a duality theory for higher order nets whose construction is not necessarily based on linear algebra over finite fields. We use this duality theory to prove propagation rules for such nets. This way we can obtain new higher order nets (sometimes with improved quality) from existing ones. We also extend our approach to the construction of higher order sequences. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：362 / 386

页数：25

共 15 条

[1] [Anonymous], 1992, RANDOM NUMBER GENERA
[2] Baldeaux J., 2010, UNIF DISTRIB THEORY, V5, P133
[3] Matrix-product codes over Fq
Blackmore, T
Norton, GH
[J]. APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2001, 12 (06) : 477 - 500
[4] Dick J., 2010, Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration
[5] Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high-dimensional periodic functions
Dick, Josef
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (05) : 2141 - 2176
[6] Equidistribution Properties of Generalized Nets and Sequences
Dick, Josef
Baldeaux, Jan
[J]. MONTE CARLO AND QUASI-MONTE CARLO METHODS 2008, 2009, : 305 - 322
[7] On Quasi-Monte Carlo Rules Achieving Higher Order Convergence
Dick, Josef
[J]. MONTE CARLO AND QUASI-MONTE CARLO METHODS 2008, 2009, : 73 - 96
[8] DUALITY THEORY AND PROPAGATION RULES FOR GENERALIZED DIGITAL NETS
Dick, Josef
Kritzer, Peter
[J]. MATHEMATICS OF COMPUTATION, 2010, 79 (270) : 993 - 1017
[9] Walsh spaces containing smooth functions and quasi-Monte Carlo rules of arbitrary high order
Dick, Josef
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2008, 46 (03) : 1519 - 1553
[10] POINT SETS AND SEQUENCES WITH SMALL DISCREPANCY
NIEDERREITER, H
[J]. MONATSHEFTE FUR MATHEMATIK, 1987, 104 (04): : 273 - 337

← 1 2 →