Component by Component Construction of Rank-1 Lattice Rules HavingO(n -1(In(n))d) Star Discrepancy

Stephen Joe ()
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Stephen Joe: University of Waikato, Department of Mathematics

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2002, 2004, pp 293-298 from Springer

Abstract: Summary The star discrepancy is a quantity for measuring the uniformity of a set of quadrature points and appears in the Koksma-Hlawka inequality. For integrals over [0, 1]d it is known that there exist d-dimensional rank-1 lattice rules having 0(n -1(ln(n))d) star discrepancy, where n is the number of points. Here we show that for n prime such rules may be obtained by constructing their generating vectors component by component. The rules are constructed to satisfy certain bounds on a quantity known as R. Bounds on the star discrepancy in terms of R then yield the desired O(n -1(In(n))d) star discrepancy.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18743-8_17

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DOI: 10.1007/978-3-642-18743-8_17

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