QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere
type: Item
instance of: scholarly article
title: QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere
zbMATH Open document ID: 1315.65003
DOI: 10.1090/S0025-5718-2014-02839-1
author: Johann S. Brauchart
author: Robert S. Womersley
author: E. B. Saff
author: Ian H. Sloan
published in: Mathematics of Computation
publication date: 2014-09-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1208.3267
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 6342379
zbMATH Keywords: discrepancy
zbMATH Keywords: spherical design
zbMATH Keywords: numerical integration
zbMATH Keywords: worst-case error
zbMATH Keywords: quadrature
zbMATH Keywords: quasi Monte Carlo designs
zbMATH Keywords: numerical experiment
describes a project that uses: QSHEP3D
describes a project that uses: Digital Library of Mathematical Functions
MaRDI profile type: Publication
arXiv ID: 1208.3267
cites work: Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy
cites work: Uniform distribution, discrepancy, and reproducing kernel Hilbert spaces
cites work: Minimizing the discrete logarithmic energy on the sphere: The role of random polynomials
cites work: Tight spherical designs. I
cites work: Tight Spherical Disigns, II
cites work: Sums of distances between points on a sphere — an application of the theory of irregularities of distribution to discrete Geometry
cites work: Q4726347
cites work: Distributions of positive mass, which maximize a certain generalized energy integral
cites work: Optimal asymptotic bounds for spherical designs
cites work: Distribution of points on spheres and approximation by zonotopes
cites work: Quadrature rules and distribution of points on manifolds
cites work: Quasi-Monte Carlo rules for numerical integration over the unit sphere \({\mathbb{S}^2}\)
cites work: A simple proof of Stolarsky's invariance principle
cites work: Numerical integration over spheres of arbitrary dimension
cites work: Computational existence proofs for spherical \(t\)-designs
cites work: Equidistribution on the Sphere
cites work: Spherical codes and designs
cites work: Sequences, discrepancies and applications
cites work: A lower bound for the worst-case cubature error on spheres of arbitrary dimension
cites work: Quadrature in Besov spaces on the Euclidean sphere
cites work: Optimal lower bounds for cubature error on the sphere \(S^2\)
cites work: Worst-case errors in a Sobolev space setting for cubature over the sphere S2
cites work: Cubature over the sphere \(S^{2}\) in Sobolev spaces of arbitrary order
cites work: Q2762587
cites work: Spherical faraday cage for the case of equal point charges and chebyshev-type quadrature on the sphere
cites work: Asymptotics for minimal discrete energy on the sphere
cites work: Diameter bounds for equal area partitions of the unit sphere
cites work: Spherical harmonics
cites work: Minimal discrete energy on the sphere
cites work: Multivariate interpolation of large sets of scattered data
cites work: Positive definite functions on spheres
cites work: Averaging sets: A generalization of mean values and spherical designs
cites work: Extremal systems of points and numerical integration on the sphere
cites work: A variational characterisation of spherical designs
cites work: Sums of Distances Between Points on a Sphere. II
cites work: Small time Gaussian estimates of heat diffusion kernels. II: The theory of large deviations
cites work: On means of distances on the surface of a sphere. II: Upper bounds
description: scientific article