Proof techniques in quasi-Monte Carlo theory

DOI10.1016/j.jco.2014.09.003zbMath1316.65002arXiv1403.7334OpenAlexW2036624041MaRDI QIDQ2347957

Aicke Hinrichs, Friedrich Pillichshammer, Josef Dick

Publication date: 10 June 2015

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.7334

zbMATH Keywords

exponential sumsnumerical integrationLittlewood-Paley theorydiophantine approximationsurvey paperdiscrepancyempirical processquasi-Monte Carlo methodworst-case errorHoeffding's inequalityRiesz productsaverage-case errorMinkowski's fundamental theorem

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02)

Related Items

Quasi-Monte Carlo integration for twice differentiable functions over a triangle, Construction of interlaced polynomial lattice rules for infinitely differentiable functions, The two-dimensional small ball inequality and binary nets, The Inverse of the Star-Discrepancy Problem and the Generation of Pseudo-Random Numbers, Point sets with optimal order of extreme and periodic discrepancy, Construction-Free Median Quasi-Monte Carlo Rules for Function Spaces with Unspecified Smoothness and General Weights, Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate, Suboptimality of Gauss–Hermite Quadrature and Optimality of the Trapezoidal Rule for Functions with Finite Smoothness, A Universal Median Quasi-Monte Carlo Integration, Extreme and periodic $L_2$ discrepancy of plane point sets, \(L_p\)- and \(S_{p, q}^r B\)-discrepancy of the symmetrized van der Corput sequence and modified Hammersley point sets in arbitrary bases, Creative telescoping on multiple sums, A weighted discrepancy bound of quasi-Monte Carlo importance sampling, \(L_p\)-discrepancy of the symmetrized van der Corput sequence

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