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We prove upper bounds on the order of convergence of Frolov's cubature formula for numerical integration in function spaces of dominating mixed smoothness on the unit cube with homogeneous boundary condition.
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J. Dick and F. Pillichshammer, Discrepancy theory and quasi-Monte Carlo integration, to appear in: W. W. L. Chen, A. Srivastav, G. Travaglini, Panorama in Discrepancy Theory, Springer Verlag, 2013
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A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces
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2013
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L. Markhasin, Discrepancy of generalized Hammersley type point sets in Besov spaces with dominating mixed smoothness, Unif. Distrib. Theory 8(1), 135–164, 2013
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A. Hinrichs, E. Novak, M. Ullrich, and H. Woźniakowski, The curse of dimensionality for numerical integration of smooth functions, Math. Comp. 83, no. 290, 2853–2863, 2014
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A. Hinrichs, E. Novak, M. Ullrich, and H. Woźniakowski, The curse of dimensionality for numerical integration of smooth functions II, J. Complexity 30, 117-143, 2014
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A. Hinrichs, E. Novak, and M. Ullrich, On weak tractability of the Clenshaw-Curtis Smolyak algorithm, J. Approx. Theory
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2014
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M. Ullrich, On ”Upper error bounds for quadrature formulas on function classes” by K. K. Frolov, ArXiv e-prints 1404.5457, 2014
2014
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T. Ullrich, Optimal cubature in Besov spaces with dominating mixed smoothness on the unit square, J. Complexity 30, 72–94, 2014
2014
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D. Dũng and T. Ullrich, Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square, Math. Nachrichten 288(7), 743–762, 2015
2015
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A. Hinrichs, L. Markhasin, J. Oettershagen, and T. Ullrich, Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions, Numer. Math. DOI 10.1007/s00211-015-0765-y, 2015
2015
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D. Krieg and E. Novak, A Universal Algorithm for Multivariate Integration, arXiv:1507.06853, 2015
2015
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2015
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2015
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