Optimization on class of operator equations in the probabilistic case setting

DOI10.1007/s11425-007-2041-9zbMath1121.65058OpenAlexW2053396739MaRDI QIDQ2372579

Li-Xin Qian, Gen Sun Fang

Publication date: 30 July 2007

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-007-2041-9

zbMATH Keywords

Fredholm integral equationsnormed linear spaceinformation-based complexityoperator equationGauss measuremultivariate Sobolev spaceprobabilistic width

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50) Fredholm integral equations (45B05) Theoretical approximation of solutions to integral equations (45L05)

Related Items

Estimates of probabilistic widths of the diagonal operator of finite-dimensional sets with the Gaussian measure ⋮ The information-based complexity of approximation problem by adaptive Monte Carlo methods

Cites Work

• Probabilistic and average widths of multivariate Sobolev spaces with mixed derivative equipped with the Gaussian measure
• The best quadrature based on given Hermite information for the Sobolev class \(KW^{r}[a, b\)]
• Average-case analysis of numerical problems
• Linear widths of a multivariate function space equipped with a Gaussian measure
• Average optimization of the approximate solution of operator equations and its application
• Linear integral equations
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