Upper and lower estimates for numerical integration errors on spheres of arbitrary dimension

DOI10.1016/j.jco.2018.11.002zbMath1416.41037arXiv1801.05474OpenAlexW3102989819MaRDI QIDQ2001210

Peter J. Grabner, Tetiana A. Stepanyuk

Publication date: 2 July 2019

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

Full work available at URL: https://arxiv.org/abs/1801.05474

zbMATH Keywords

numerical integration\(t\)-designreproducing kernelquadrature rulesworst-case errorQMC design

Mathematics Subject Classification ID

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

Related Items

Lower bounds for integration and recovery in \(L_2\) ⋮ Complexity of Monte Carlo integration for Besov classes on the unit sphere ⋮ New lower bounds for the integration of periodic functions ⋮ Comparison of probabilistic and deterministic point sets on the sphere

Uses Software

• DLMF

Cites Work

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• Spherical harmonics
• Optimal lower bounds for cubature error on the sphere \(S^2\)
• Positive definite functions on spheres
• QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere
• Sums of distances between points on a sphere — an application of the theory of irregularities of distribution to discrete Geometry
• Quadrature rules and distribution of points on manifolds

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