Complexity of numerical integration over spherical caps in a Sobolev space setting

DOI10.1016/j.jco.2010.09.002zbMath1227.65028OpenAlexW1972445139MaRDI QIDQ544128

Kerstin Hesse

Publication date: 14 June 2011

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

Full work available at URL: https://doi.org/10.1016/j.jco.2010.09.002

zbMATH Keywords

complexitySobolev spaceerror estimatesnumerical integrationspherical capworst-case error

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Complexity and performance of numerical algorithms (65Y20)

Related Items

Randomized approximation numbers on Besov classes with mixed smoothness ⋮ Numerical integration with polynomial exactness over a spherical cap

Cites Work

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• Numerical integration with polynomial exactness over a spherical cap
• Numerical integration over spheres of arbitrary dimension
• Multivariate polynomial approximation
• Hyperinterpolation on the sphere at the minimal projection order
• Kolmogorov width of classes of smooth functions on the sphere \(\mathbb S^{d-1}\)
• Local quadrature formulas on the sphere
• Positive cubature formulas and Marcinkiewicz-Zygmund inequalities on spherical caps
• Quadrature in Besov spaces on the Euclidean sphere
• A lower bound for the worst-case cubature error on spheres of arbitrary dimension
• Cubature over the sphere \(S^{2}\) in Sobolev spaces of arbitrary order
• Optimal lower bounds for cubature error on the sphere \(S^2\)
• Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
• Approximation by Ridge Functions and Neural Networks
• Worst-case errors in a Sobolev space setting for cubature over the sphere S²

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