Spherical Designs, Discrepancy and Numerical Integration

DOI10.2307/2153170zbMath0795.65011OpenAlexW4237546705MaRDI QIDQ4293972

Robert F. Tichy, Peter J. Grabner

Publication date: 10 July 1994

Full work available at URL: https://doi.org/10.2307/2153170

zbMATH Keywords

algorithmspherical designdiscrepancy boundsspherical cap discrepancyexact equal-weight quadrature formulae

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (16)

Spherical $t_\epsilon $-designs for approximations on the sphere ⋮ Discrepancy, separation and Riesz energy of finite point sets on the unit sphere ⋮ Polynomial discrepancy of sequences ⋮ Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy ⋮ On energy, discrepancy and group invariant measures on measurable subsets of Euclidean space ⋮ Energy functionals, numerical integration and asymptotic equidistribution on the sphere. ⋮ Efficient Spherical Designs with Good Geometric Properties ⋮ An enumerative formula for the spherical cap discrepancy ⋮ On the Wasserstein distance between classical sequences and the Lebesgue measure ⋮ Unnamed Item ⋮ Online uniformly inserting points on the sphere ⋮ Quadrature rules with neighborhood of spherical designs on the two-sphere ⋮ Quadrature points via heat kernel repulsion ⋮ Discrete and continuous Green energy on compact manifolds ⋮ On the Riesz energy of measures. ⋮ Distributing many points on spheres: minimal energy and designs

Cites Work

• Averaging sets: A generalization of mean values and spherical designs
• Spherical codes and designs
• Polynomial spaces
• Spherical harmonics
• Erdős-Turán type discrepancy bounds
• On averaging sets
• Hecke operators and distributing points on S². II
• Applications of Number Theory to Numerical Analysis
• Optimal Numerical Integration on a Sphere
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Spherical Designs, Discrepancy and Numerical Integration