High-Discrepancy Sequences for High-Dimensional Numerical Integration

Shu Tezuka

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

抄録

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).

本文言語英語
ホスト出版物のタイトルMonte Carlo and Quasi-Monte Carlo Methods 2010
出版社Springer New York LLC
ページ685-694
ページ数10
ISBN(印刷版)9783642274398
DOI
出版ステータス出版済み - 1 1 2012
イベント9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010 - Warsaw, ポーランド
継続期間: 8 15 20108 20 2010

出版物シリーズ

名前Springer Proceedings in Mathematics and Statistics
23
ISSN(印刷版)2194-1009
ISSN(電子版)2194-1017

その他

その他9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010
Countryポーランド
CityWarsaw
Period8/15/108/20/10

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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