Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces

DOI10.1016/j.jmaa.2015.05.079zbMath1325.65037arXiv1407.8311OpenAlexW1595528267WikidataQ60138320 ScholiaQ60138320MaRDI QIDQ491833

Josef Dick, Edward B. Saff, Ian H. Sloan, Yu Guang Wang, Robert S. Womersley, Johann S. Brauchart

Publication date: 19 August 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.8311

zbMATH Keywords

Sobolev spacespherical designcovering radiusworst-case errorcubature on the spherequasi-Monte Carlo design sequences

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical integration (65D30)

Related Items (14)

Bypassing the quadrature exactness assumption of hyperinterpolation on the sphere ⋮ Asymptotic distributions of covering and separation measures on the hypersphere ⋮ One-bit sensing, discrepancy and Stolarsky's principle ⋮ Explicit Families of Functions on the Sphere with Exactly Known Sobolev Space Smoothness ⋮ Approximate Quadrature Measures on Data-Defined Spaces ⋮ Analysis of Framelet Transforms on a Simplex ⋮ Discrepancy and numerical integration on metric measure spaces ⋮ Optimal asymptotic bounds for designs on manifolds ⋮ Unnamed Item ⋮ Tight framelets and fast framelet filter bank transforms on manifolds ⋮ Points on manifolds with asymptotically optimal covering radius ⋮ Distributed Filtered Hyperinterpolation for Noisy Data on the Sphere ⋮ Numerical computation of triangular complex spherical designs with small mesh ratio ⋮ Distributing many points on spheres: minimal energy and designs

Uses Software

• DLMF

Cites Work

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