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Lattice Rules: How Well Do They Measure Up?

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Book cover Random and Quasi-Random Point Sets

Part of the book series: Lecture Notes in Statistics ((LNS,volume 138))

Abstract

A simple, but often effective, way to approximate an integral over the s-dimensional unit cube is to take the average of the integrand over some set P of N points. Monte Carlo methods choose P randomly and typically obtain an error of 0(N-1/2). Quasi-Monte Carlo methods attempt to decrease the error by choosing P in a deterministic (or quasi-random) way so that the points are more uniformly spread over the integration domain.

This research was supported by an HKBU FRG grant 96–97/II-67.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Fred J. Hickernell

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  1. Fred J. Hickernell
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Editors and Affiliations

  1. Institut für Mathematik, Universität Salzburg, Hellbrunner Str. 34, Salzburg, A-5020, Austria

    Peter Hellekalek  & Gerhard Larcher  & 

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Hickernell, F.J. (1998). Lattice Rules: How Well Do They Measure Up?. In: Hellekalek, P., Larcher, G. (eds) Random and Quasi-Random Point Sets. Lecture Notes in Statistics, vol 138. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1702-2_3

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  • DOI: https://doi.org/10.1007/978-1-4612-1702-2_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98554-1

  • Online ISBN: 978-1-4612-1702-2

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