Equidistribution Properties of Generalized Nets and Sequences

Josef Dick () and Jan Baldeaux ()
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Josef Dick: The University of New South Wales, School of Mathematics and Statistics

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, pp 305-322 from Springer

Abstract: Abstract Generalized digital nets and sequences have been introduced for the numerical integration of smooth functions using quasi-Monte Carlo rules. In this paper we study geometrical properties of such nets and sequences. The definition of these nets and sequences does not depend on linear algebra over finite fields, it only requires that the point set or sequence satisfies certain distributional properties. Generalized digital nets and sequences appear as special cases. We prove some propagation rules and give bounds on the quality parameter t.

Keywords: Finite Field; Prime Power; Integration Error; Prime Power Order; Digital Sequence (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04107-5_19

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DOI: 10.1007/978-3-642-04107-5_19

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