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We present an algorithm for multivariate integration over cubes that is unbiased and has optimal order of convergence (in the randomized sense as well as in the worst case setting) for all Sobolev spaces $H^{r, mix}([0,1]^d)$ and $H^s([0,1]^d)$ for $s>d/2$.
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V. N. Temlyakov: Cubature formulas, discrepancy, and nonlinear approximation . Journal of Complexity 19
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E. Novak and H. Woźniakowski: Tractability of Multivariate Problems II: Standard Information for Functionals . European Mathematical Society, 2010
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2014
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2015
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