On energy, discrepancy and group invariant measures on measurable subsets of Euclidean space

DOI10.1007/s00041-010-9153-2zbMath1292.49041OpenAlexW2153177854MaRDI QIDQ620424

Fred J. Hickernell, Steven B. Damelin, David L. Ragozin, Xiaoyan Zeng

Publication date: 19 January 2011

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-010-9153-2

zbMATH Keywords

cubaturedistributionnumerical integrationcapacitysigned measurediscrepancyequilibrium measureRiesz kernelpositive definiteenergy minimizerpotential fieldgroup invariant kernelgroup invariant measurereproducing Hilbert space

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Approximate quadratures (41A55) Discrete potential theory (31C20) Numerical integration (65D30) Hausdorff and packing measures (28A78)

Related Items (14)

Balancing Geometry and Density: Path Distances on High-Dimensional Data ⋮ Positive definiteness and the Stolarsky invariance principle ⋮ A characterization theorem for the \(L^{2}\)-discrepancy of integer points in dilated polygons ⋮ An octahedral equal area partition of the sphere and near optimal configurations of points ⋮ 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 ⋮ The Stolarsky principle and energy optimization on the sphere ⋮ Bayesian Quadrature, Energy Minimization, and Space-Filling Design ⋮ A walk through energy, discrepancy, numerical integration and group invariant measures on measurable subsets of Euclidean space ⋮ Extension of the Schoenberg theorem to integrally conditionally positive definite functions ⋮ Generation of energy-minimizing point sets on spheres and their application in mesh-free interpolation and differentiation ⋮ Performance analysis of greedy algorithms for minimising a maximum mean discrepancy ⋮ Distributing many points on spheres: minimal energy and designs

Uses Software

• Matlab

Cites Work

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