High-Discrepancy Sequences for High-Dimensional Numerical Integration

Shu Tezuka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we consider a sequence of points in [0, 1]d, which are distributed only on the diagonal line between (0,...,0) and (1,...,1). The sequence is constructed based on a one-dimensional low-discrepancy sequence. We apply such sequences to d-dimensional numerical integration for two classes of integrals. The first class includes isotropic integrals. Under a certain condition, we prove that the integration error for this class is O(√logN/N), where N is the number of points. The second class is called as Kolmogorov superposition integrals for which, under a certain condition, we prove that the integration error for this class is O((logN)/N).

Original languageEnglish
Title of host publicationMonte Carlo and Quasi-Monte Carlo Methods 2010
PublisherSpringer New York LLC
Pages685-694
Number of pages10
ISBN (Print)9783642274398
DOIs
Publication statusPublished - Jan 1 2012
Event9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010 - Warsaw, Poland
Duration: Aug 15 2010Aug 20 2010

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume23
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010
CountryPoland
CityWarsaw
Period8/15/108/20/10

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Tezuka, S. (2012). High-Discrepancy Sequences for High-Dimensional Numerical Integration. In Monte Carlo and Quasi-Monte Carlo Methods 2010 (pp. 685-694). (Springer Proceedings in Mathematics and Statistics; Vol. 23). Springer New York LLC. https://doi.org/10.1007/978-3-642-27440-4_40