Random sections of ellipsoids and the power of random information

DOI10.1090/tran/8502zbMath1501.60008arXiv1901.06639OpenAlexW3180748791MaRDI QIDQ5047902

Mario Ullrich, David Krieg, Aicke Hinrichs, Erich Novak, Joscha Prochno

Publication date: 17 November 2022

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.06639

zbMATH Keywords

least squaresGaussian random matrixrandom informationhigh dimensional convexity\(L_2\) approximationcomparison principles for Gaussian processesrandom intersection

Mathematics Subject Classification ID

Gaussian processes (60G15) Geometric probability and stochastic geometry (60D05) Random matrices (probabilistic aspects) (60B20) Algorithms for approximation of functions (65D15) Complexity and performance of numerical algorithms (65Y20) Random convex sets and integral geometry (aspects of convex geometry) (52A22) Asymptotic theory of convex bodies (52A23)

Related Items

Spectral flatness and the volume of intersections of \(p\)-ellipsoids, Best and random approximation of a convex body by a polytope, Lower bounds for integration and recovery in \(L_2\), Weighted \(p\)-radial distributions on Euclidean and matrix \(p\)-balls with applications to large deviations, A sharp upper bound for sampling numbers in \(L_2\), Optimal recovery and volume estimates, Recovery of Sobolev functions restricted to iid sampling, Random sections of \(\ell_p\)-ellipsoids, optimal recovery and Gelfand numbers of diagonal operators, Norms of structured random matrices, On the power of standard information for tractability for \(L_{\infty}\) approximation of periodic functions in the worst case setting, Exponential tractability of \(L_2\)-approximation with function values, Large deviations for uniform projections of $p$-radial distributions on $\ell_p^n$-balls

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