Error bounds for quasi-Monte Carlo integration with nets
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- by Christian Lécot PDF
- Math. Comp. 65 (1996), 179-187 Request permission
Abstract:
We analyze the error introduced by approximately calculating the $s$-dimensional Lebesgue measure of a Jordan-measurable subset of $I^s=[0,1)^s$. We give an upper bound for the error of a method using a $(t,m,s)$-net, which is a set with a very regular distribution behavior. When the subset of $I^s$ is defined by some function of bounded variation on ${\bar I}^{s-1}$, the error is estimated by means of the variation of the function and the discrepancy of the point set which is used. A sharper error bound is established when a $(t,m,s)$-net is used. Finally a lower bound of the error is given, for a method using a $(0,m,s)$-net. The special case of the 2-dimensional Hammersley point set is discussed.References
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Additional Information
- Christian Lécot
- Affiliation: address Laboratoire de Mathématiques, Université de Savoie, 73376 Le Bourget du Lac, France
- Email: lecot@univ-savoie.fr
- Received by editor(s): October 10, 1994
- Received by editor(s) in revised form: February 15, 1995
- © Copyright 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 179-187
- MSC (1991): Primary 65C05; Secondary 11K38
- DOI: https://doi.org/10.1090/S0025-5718-96-00690-4
- MathSciNet review: 1325870