Energies, group-invariant kernels and numerical integration on compact manifolds

Abstract

The purpose of this paper is to derive quadrature estimates on compact, homogeneous manifolds embedded in Euclidean spaces, via energy functionals associated with a class of group-invariant kernels which are generalizations of zonal kernels on the spheres or radial kernels in euclidean spaces. Our results apply, in particular, to weighted Riesz kernels defined on spheres and certain projective spaces. Our energy functionals describe both uniform and perturbed uniform distribution of quadrature point sets.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1016/j.jco.2008.09.001

Keywords

Compact homogeneous manifold, Discrepancy, Energy, Group, Invariant kernels, Invariant polynomial, Numerical integration, Projection kernels, Projective space, Quadrature, Reflexive manifold, Riesz kernel, Sphere, Spherical harmonic, Torus, Weight

Publication Date

1-1-2009

Journal Title

Journal of Complexity

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