A walk through energy, discrepancy, numerical integration and group invariant measures on measurable subsets of Euclidean space

DOI10.1007/s11075-008-9187-6zbMath1152.41017OpenAlexW2027168163WikidataQ125916750 ScholiaQ125916750MaRDI QIDQ937179

Steven B. Damelin

Publication date: 20 August 2008

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-008-9187-6

zbMATH Keywords

spherical harmonicnumerical integrationprojective spacequadratureRiesz kernelinvariant polynomialspotential fieldCompact homogeneous manifoldequilibrum measureinvariant kernelsprojection kernelsreflexive manifold

Mathematics Subject Classification ID

Approximate quadratures (41A55)

Related Items (7)

Optimal Quadrature-Sparsification for Integral Operator Approximation ⋮ Discrepancy, separation and Riesz energy of finite point sets on the unit sphere ⋮ Computational aspects of Cui-Freeden statistics for equidistribution on the sphere ⋮ Classifying minimum energy states for interacting particles: regular simplices ⋮ Eignets for function approximation on manifolds ⋮ Computational cost of the Fekete problem. I: The forces method on the 2-sphere ⋮ A solution to the energy minimization problem constrained by a density function

Cites Work

• On energy, discrepancy and group invariant measures on measurable subsets of Euclidean space
• Energies, group-invariant kernels and numerical integration on compact manifolds
• Energy functionals, numerical integration and asymptotic equidistribution on the sphere.
• Scattered cardinal Hermite interpolation by positive definite functions
• Approximation by weighted polynomials
• Strictly positive definite functions on the unit circle
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