The Coulomb energy of spherical designs on \(S^{2}\)

DOI10.1007/s10444-007-9026-7zbMath1176.31011OpenAlexW2045685925MaRDI QIDQ930348

Kerstin Hesse, Paul Leopardi

Publication date: 30 June 2008

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-007-9026-7

zbMATH Keywords

orthogonal polynomialsspherical designsCoulomb energywell separated

Mathematics Subject Classification ID

Discrete potential theory (31C20)

Related Items (10)

Asymptotically optimal designs on compact algebraic manifolds ⋮ Discrepancy, separation and Riesz energy of finite point sets on the unit sphere ⋮ A component-by-component approach to efficient numerical integration over products of spheres ⋮ Upper bounds for energies of spherical codes of given cardinality and separation ⋮ Estimates for Logarithmic and Riesz Energies of Spherical t-Designs ⋮ Efficient Spherical Designs with Good Geometric Properties ⋮ Comparison of probabilistic and deterministic point sets on the sphere ⋮ Upper energy bounds for spherical designs of relatively small cardinalities ⋮ Well-separated spherical designs ⋮ The \(s\)-energy of spherical designs on \(S^{2}\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On means of distances on the surface of a sphere (lower bounds)
• On means of distances on the surface of a sphere. II: Upper bounds
• Spherical codes and designs
• On the distribution of Fekete points
• Hyperinterpolation on the sphere at the minimal projection order
• A constructive finite field method for scattering points on the surface of \(d\)-dimensional spheres
• Minimal discrete energy on the sphere
• McLaren's improved snub cube and other new spherical designs in three dimensions
• Cubature over the sphere \(S^{2}\) in Sobolev spaces of arbitrary order
• Alternative proof of a sharpened forms of bernstein's inequality for legendre polynomials: corrigendum
• Asymptotics for minimal discrete energy on the sphere
• Worst-case errors in a Sobolev space setting for cubature over the sphere S²
• Alternative Proof of a Sharpened Form of Bernstein's Inequality for Legendre Polynomials
• Spherical faraday cage for the case of equal point charges and chebyshev-type quadrature on the sphere
• Existence of Solutions to Systems of Underdetermined Equations and Spherical Designs
• About the second term of the asymptotics for optimal Riesz energy on the sphere in the potential-theoretical case
• On the Densest Packing of Spherical Caps
• Phase-Shift Calculation of High-Energy Electron Scattering

This page was built for publication: The Coulomb energy of spherical designs on \(S^{2}\)