Strong tractability of integration using scrambled Niederreiter points |
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Authors: | Rong-Xian Yue Fred J Hickernell |
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Institution: | Division of Scientific Computation, E-Institute of Shanghai Universities, 100 Guilin Road, Shanghai 200234, People's Republic of China ; Department of Applied Mathematics, Shanghai Normal University, Shanghai, People's Republic of China |
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Abstract: | We study the randomized worst-case error and the randomized error of scrambled quasi-Monte Carlo (QMC) quadrature as proposed by Owen. The function spaces considered in this article are the weighted Hilbert spaces generated by Haar-like wavelets and the weighted Sobolev-Hilbert spaces. Conditions are found under which multivariate integration is strongly tractable in the randomized worst-case setting and the randomized setting, respectively. The -exponents of strong tractability are found for the scrambled Niederreiter nets and sequences. The sufficient conditions for strong tractability for Sobolev spaces are more lenient for scrambled QMC quadratures than those for deterministic QMC net quadratures. |
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Keywords: | Multivariate integration quasi--Monte Carlo methods nets and sequences scrambling |
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