Linear \(n\)-widths of diagonal matrices in the average and probabilistic settings

DOI10.1016/J.JFA.2012.02.010zbMath1254.47019OpenAlexW2088933916MaRDI QIDQ418714

Feng Dai, He Ping Wang

Publication date: 30 May 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2012.02.010

zbMATH Keywords

Gaussian measure\(p\)-average linear \(n\)-widthsdiagonal matricesprobabilistic linear \((n, \delta )\)-widths

Mathematics Subject Classification ID

Gaussian processes (60G15) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37)

Related Items (4)

Approximation of functions on the sphere on a Sobolev space with a Gaussian measure in the probabilistic case setting ⋮ Probabilistic and average widths of Sobolev spaces on compact two-point homogeneous spaces equipped with a Gaussian measure ⋮ Probabilistic and average linear widths of weighted Sobolev spaces on the ball equipped with a Gaussian measure ⋮ Gel'fand-\(N\)-width in probabilistic setting

Cites Work

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• Best approximation of functions on the ball on the weighted Sobolev space equipped with a Gaussian measure
• The approximation characteristic of diagonal matrix in probabilistic setting
• Linear widths of function spaces equipped with the Gaussian measure
• Probabilistic and average linear widths of Sobolev space with Gaussian measure
• Average-case analysis of numerical problems
• Probabilistic and average linear width in \(L_ \infty\)-norm with respect to \(r\)-fold Wiener measure
• On the small balls problem for equivalent Gaussian measures

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