The curse of dimensionality for numerical integration on general domains

DOI10.1016/j.jco.2018.08.003OpenAlexW2797465556MaRDI QIDQ1633623

Aicke Hinrichs, Joscha Prochno, Mario Ullrich

Publication date: 20 December 2018

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

Full work available at URL: https://arxiv.org/abs/1804.03957

zbMATH Keywords

numerical integrationtractabilityisotropic convex bodycurse of dimension\(\psi_2\)-conditionthin-shell estimate

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX) Approximations and expansions (41-XX)

Related Items (12)

Spectral flatness and the volume of intersections of \(p\)-ellipsoids ⋮ On norms in some class of exponential type Orlicz spaces of random variables ⋮ Uniform recovery of high-dimensional \(C^r\)-functions ⋮ Weighted \(p\)-radial distributions on Euclidean and matrix \(p\)-balls with applications to large deviations ⋮ Optimal recovery and volume estimates ⋮ Exponential tractability of \(L_2\)-approximation with function values ⋮ Thin-shell concentration for random vectors in Orlicz balls via moderate deviations and Gibbs measures ⋮ Algorithms and complexity for functions on general domains ⋮ Tractability properties of the discrepancy in Orlicz norms ⋮ The radii of sections of origin-symmetric convex bodies and their applications ⋮ The isotropic constant of random polytopes with vertices on convex surfaces ⋮ A new look at random projections of the cube and general product measures

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