Quasi-Monte Carlo rules for numerical integration over the unit sphere \({\mathbb{S}^2}\)

DOI10.1007/s00211-011-0444-6zbMath1258.65003arXiv1101.5450OpenAlexW1993553799MaRDI QIDQ443857

Johann S. Brauchart, Josef Dick

Publication date: 13 August 2012

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.5450

zbMATH Keywords

reproducing kernel Hilbert spacesworst-case errorasymptotically uniformly distributionspherical cap \(L_{2}\)-discrepancyspherical rectangle discrepancy

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Multidimensional problems (41A63) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Irregularities of distribution, discrepancy (11K38) Well-distributed sequences and other variations (11K36) General theory of distribution modulo (1) (11K06) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (11)

QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere ⋮ Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy ⋮ Complexity of Monte Carlo integration for Besov classes on the unit sphere ⋮ The spherical ensemble and quasi-Monte-Carlo designs ⋮ Bypassing the quadrature exactness assumption of hyperinterpolation on the sphere ⋮ Explicit Families of Functions on the Sphere with Exactly Known Sobolev Space Smoothness ⋮ Unnamed Item ⋮ Optimal \(N\)-point configurations on the sphere: ``magic numbers and Smale's 7th problem ⋮ Transformations and Hardy--Krause Variation ⋮ Numerical computation of triangular complex spherical designs with small mesh ratio ⋮ Distributing many points on spheres: minimal energy and designs

Uses Software

• TOMS659
• sobol.cc

Cites Work

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