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We study a Monte Carlo algorithm that is based on a specific (randomly shifted and dilated) lattice point set.
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I. H. Sloan, F. Y. Kuo and S. Joe, Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces, SIAM J. Numer. Anal. 40
2002
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V. N. Temlyakov, Cubature formulas, discrepancy, and nonlinear approximation, J. Complexity 19
2003
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S. Heinrich, F. Hickernell, R.-X. Yue, Optimal quadrature for Haar wavelet spaces. Math. Comp. 73
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F. Y. Kuo, G. W. Wasilkowski and B. J. Waterhouse, Randomly shifted lattice rules for unbounded integrands, J. Complexity 22
2006
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J. Johnsen, W. Sickel, A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin-Triebel spaces with mixed norms, J. Funct. Space Appl. 5
2007
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A. Hinrichs, Optimal importance sampling for the approximation of integrals, J. Complexity 26
2010
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2016
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2016
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D. Krieg and E. Novak, A Universal Algorithm for Multivariate Integration, Found. Comput. Math. (2016), DOI:10.1007/s10208-016-9307-y
2016
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E. Novak, Some Results on the Complexity of Numerical Integration, In: Ronald Cools and Dirk Nuyens (Eds): Monte Carlo and Quasi-Monte Carlo Methods , Springer Proceedings in Mathematics & Statistics 163
2016
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M. Ullrich, On “Upper error bounds for quadrature formulas on function classes” by K. K. Frolov. In: Ronald Cools and Dirk Nuyens (Eds): Monte Carlo and Quasi-Monte Carlo Methods , Springer Proceedings in Mathematics & Statistics 163
2016
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M. Ullrich and T. Ullrich, The Role of Frolov’s Cubature Formula for Functions with Bounded Mixed Derivative, SIAM J. Numer. Anal., 54
2016
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