Optimal randomized quadrature for weighted Sobolev and Besov classes with the Jacobi weight on the ball

DOI10.1016/j.jco.2022.101691OpenAlexW4226452349WikidataQ114163579 ScholiaQ114163579MaRDI QIDQ2171950

Jiansong Li, He Ping Wang

Publication date: 12 September 2022

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

Full work available at URL: https://arxiv.org/abs/2201.06709

zbMATH Keywords

weighted Sobolev classesfiltered hyperinterpolationweighted Besov classesdeterministic case settingoptimal quadrature errorrandomized case setting

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical integration (65D30)

Cites Work

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• Filtered hyperinterpolation: a constructive polynomial approximation on the sphere
• Numerical integration over spheres of arbitrary dimension
• Best approximation of functions on the ball on the weighted Sobolev space equipped with a Gaussian measure
• Widths of weighted Sobolev classes on the ball
• Stochastic properties of quadrature formulas
• Deterministic and stochastic error bounds in numerical analysis
• Fractional derivatives and best approximations
• Optimal Monte Carlo methods for \(L^2\)-approximation
• Weighted approximation of functions on the unit sphere
• Computational complexity of the integration problem for anisotropic classes
• Optimal cubature formulas in weighted Besov spaces with \(A _{\infty }\) weights on multivariate domains
• Optimal pointwise sampling for \(L^2\) approximation
• On the norm of the hyperinterpolation operator on the unit ball
• Change of variable in spaces of mixed smoothness and numerical integration of multivariate functions on the unit cube
• A universal algorithm for multivariate integration
• On filtered polynomial approximation on the sphere
• Localized polynomial frames on the ball
• Quadrature in Besov spaces on the Euclidean sphere
• A lower bound for the worst-case cubature error on spheres of arbitrary dimension
• A sharp upper bound for sampling numbers in \(L_2\)
• The Role of Frolov's Cubature Formula for Functions with Bounded Mixed Derivative
• Some Results on the Complexity of Numerical Integration
• Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball
• CUBATURE FORMULAS FOR CLASSES OF FUNCTIONS WITH BOUNDED MIXED DIFFERENCE
• Summability of Fourier orthogonal series for Jacobi weight on a ball in ℝ^{𝕕}
• Cubature formulae for Besov classes
• ON A WAY OF OBTAINING LOWER ESTIMATES FOR THE ERRORS OF QUADRATURE FORMULAS
• Approximation Theory and Harmonic Analysis on Spheres and Balls
• OPTIMAL LOWER ESTIMATES FOR THE WORST CASE CUBATURE ERROR AND THE APPROXIMATION BY HYPERINTERPOLATION OPERATORS IN THE SOBOLEV SPACE SETTING ON THE SPHERE
• Quadrature rules and distribution of points on manifolds
• Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square
• Complexity of deterministic and randomized methods for multivariate integration problems for the class HpΛ(Id)
• A Monte Carlo Method for Integration of Multivariate Smooth Functions
• On the optimality of linear methods for operator approximation in convex classes of functions

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