Complexity of numerical integration over spherical caps in a Sobolev space setting
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Publication:544128
DOI10.1016/j.jco.2010.09.002zbMath1227.65028OpenAlexW1972445139MaRDI QIDQ544128
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
Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Complexity and performance of numerical algorithms (65Y20)
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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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