Article
Tractability of Multivariate Integration Using Low-Discrepancy Sequences
Authors
Abstract
We propose a notion of (t, e, s)-sequences in multiple bases, which unifies the Halton sequence and (t, s)-sequences under one roof, and obtain an upper bound of their discrepancy consisting only of the leading term. By using this upper bound, we improve the tractability results currently known for the Halton sequence, the Niederreiter sequence, the Sobol’ sequence, and the gener- alized Faure sequence, and also give tractability results for the Xing-Niederreiter sequence and the Hofer-Niederreiter sequence, for which no results have been known so far.
Keywords
discrepancy, low-discrepancy sequences, multivariate integration, tractability.
Citation
Tezuka, S. (2016). Tractability of multivariate integration using low-discrepancy sequences. Uniform Distribution Theory, 11(2), 23–43. https://doi.org/10.1515/udt-2016-0013
S. Tezuka, “Tractability of multivariate integration using low-discrepancy sequences,” Uniform Distribution Theory, vol. 11, no. 2, pp. 23–43, 2016, doi: 10.1515/udt-2016-0013.
Tezuka S. Tractability of multivariate integration using low-discrepancy sequences. Uniform Distribution Theory. 2016;11(2):23–43. doi:10.1515/udt-2016-0013.
Tezuka, S. (2016), ‘Tractability of multivariate integration using low-discrepancy sequences’, Uniform Distribution Theory, 11(2), pp. 23–43. Available at: https://doi.org/10.1515/udt-2016-0013.
Tezuka, Shu. “Tractability of Multivariate Integration Using Low-discrepancy Sequences.” Uniform Distribution Theory, vol. 11, no. 2, 2016, pp. 23–43. https://doi.org/10.1515/udt-2016-0013.
Tezuka, Shu. “Tractability of Multivariate Integration Using Low-discrepancy Sequences.” Uniform Distribution Theory 11, no. 2 (2016): 23–43. https://doi.org/10.1515/udt-2016-0013.
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Published by: Engineering Journals
