Function values are enough for \(L_2\)-approximation

DOI10.1007/s10208-020-09481-wzbMath1481.41014arXiv1905.02516OpenAlexW3110811957MaRDI QIDQ2231650

David Krieg, Mario Ullrich

Publication date: 30 September 2021

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.02516

zbMATH Keywords

rate of convergencerandom matrices\(L_2\)-approximationsampling numbersSobolev spaces with mixed smoothness

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

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Cites Work

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• On the worst-case error of least squares algorithms for \(L_2\)-approximation with high probability
• 4. On the power of random information
• The power of standard information for multivariate approximation in the randomized setting
• Multivariate Approximation
• Optimal weighted least-squares methods

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