Lattice rules with random \(n\) achieve nearly the optimal \(\mathcal{O}(n^{-\alpha-1/2})\) error independently of the dimension
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Publication:666631
DOI10.1016/j.jat.2018.09.011OpenAlexW2625732949MaRDI QIDQ666631
Peter Kritzer, Frances Y. Kuo, Dirk Nuyens, Mario Ullrich
Publication date: 6 March 2019
Published in: Journal of Approximation Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1706.04502
Numerical analysis (65-XX) Harmonic analysis on Euclidean spaces (42-XX) Approximations and expansions (41-XX)
Related Items (6)
High-dimensional sparse FFT based on sampling along multiple rank-1 lattices ⋮ Construction-Free Median Quasi-Monte Carlo Rules for Function Spaces with Unspecified Smoothness and General Weights ⋮ Random-prime-fixed-vector randomised lattice-based algorithm for high-dimensional integration ⋮ Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate ⋮ Polynomial tractability for integration in an unweighted function space with absolutely convergent Fourier series ⋮ Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm
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