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Mathematics of Computation

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Duality theory and propagation rules for generalized digital nets


Authors: Josef Dick and Peter Kritzer
Journal: Math. Comp. 79 (2010), 993-1017
MSC (2000): Primary 11K38, 11K45, 65C05, 94B05
Published electronically: November 17, 2009
MathSciNet review: 2600553
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Abstract: Digital nets are used in quasi-Monte Carlo algorithms for approximating high dimensional integrals over the unit cube. Hence one wants to have explicit constructions of digital nets of high quality. In this paper we consider the so-called propagation rules for digital nets, which state how one can obtain a new digital net of different size from existing digital nets. This way one often can generate digital nets of higher quality than were previously known. Here we generalize existing propagation rules for classical digital nets to generalized digital nets as introduced by Dick.


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Additional Information

Josef Dick
Affiliation: School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia
Email: josef.dick@unsw.edu.au

Peter Kritzer
Affiliation: School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia
Email: peter.kritzer@gmail.com

DOI: https://doi.org/10.1090/S0025-5718-09-02315-1
Keywords: Quasi-Monte Carlo, numerical integration, digital nets, duality theory, propagation rules
Received by editor(s): August 29, 2008
Received by editor(s) in revised form: April 9, 2009
Published electronically: November 17, 2009
Additional Notes: The support of the Australian Research Council under its Centre of Excellence program is gratefully acknowledged.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.