Exponential convergence and tractability of multivariate integration for Korobov spaces
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Publication:3168728
DOI10.1090/S0025-5718-2010-02433-0zbMath1221.65077OpenAlexW2006791985MaRDI QIDQ3168728
Josef Dick, Friedrich Pillichshammer, Henryk Woźniakowski, Gerhard Larcher
Publication date: 19 April 2011
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0025-5718-2010-02433-0
Monte Carlo methods (65C05) Numerical integration (65D30) Pseudo-random numbers; Monte Carlo methods (11K45)
Related Items (36)
On the power of standard information for tractability for \(L_2\)-approximation in the average case setting ⋮ \(\mathbb{L}_\infty\)-approximation in Korobov spaces with exponential weights ⋮ A note on tractability of multivariate analytic problems ⋮ Approximation in Hermite spaces of smooth functions ⋮ Tractability of multivariate approximation defined over Hilbert spaces with exponential weights ⋮ EC-tractability of multivariate approximation in Hermite spaces for the standard information class ⋮ Strong equivalences of approximation numbers and tractability of weighted anisotropic Sobolev embeddings ⋮ (\(s, \ln^\kappa\))-weak tractability of linear problems ⋮ Exponential convergence of an approximation problem for infinitely differentiable multivariate functions ⋮ EC-\((t_1,t_2)\)-tractability of approximation in weighted Korobov spaces in the worst case setting ⋮ Average case tractability of a multivariate approximation problem ⋮ Construction of interlaced polynomial lattice rules for infinitely differentiable functions ⋮ Multivariate integration for analytic functions with Gaussian kernels ⋮ On the power of standard information for \(\mathbb{L}_2\)-approximation in the average case setting ⋮ Some Results on the Complexity of Numerical Integration ⋮ Multivariate approximation for analytic functions with Gaussian kernels ⋮ Approximation of analytic functions in Korobov spaces ⋮ Average case tractability of multivariate approximation with Gaussian kernels ⋮ Simple characterizations of exponential tractability for linear multivariate problems ⋮ A note on \((s,t)\)-weak tractability of the weighted star discrepancy of regular grids ⋮ Multivariate integration of infinitely many times differentiable functions in weighted Korobov spaces ⋮ A note on EC-tractability of multivariate approximation in weighted Korobov spaces for the standard information class ⋮ Tractability properties of the weighted star discrepancy of regular grids ⋮ Super-polynomial convergence and tractability of multivariate integration for infinitely times differentiable functions ⋮ Exponential tractability of linear weighted tensor product problems in the worst-case setting for arbitrary linear functionals ⋮ A note on Korobov lattice rules for integration of analytic functions ⋮ Integration and approximation in cosine spaces of smooth functions ⋮ EC-tractability of \(\mathbb{L}_p\)-approximation in Korobov spaces with exponential weights ⋮ Multivariate integration over \(\mathbb{R}^s\) with exponential rate of convergence ⋮ A note on isotropic discrepancy and spectral test of lattice point sets ⋮ EC-tractability of approximation problems in function spaces defined over products of simplices ⋮ A note about EC-\((s, t)\)-weak tractability of multivariate approximation with analytic Korobov kernels ⋮ EC-\((s, t)\)-weak tractability of multivariate linear problems in the average case setting ⋮ Discrepancy Theory and Quasi-Monte Carlo Integration ⋮ Integration in Hermite spaces of analytic functions ⋮ Exponential convergence-tractability of general linear problems in the average case setting
Cites Work
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