Energies, group-invariant kernels and numerical integration on compact manifolds
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.
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
Damelin, Steven B., Jeremy Levesley, David L. Ragozin, and X. Sun. "Energies, group-invariant kernels and numerical integration on compact manifolds." Journal of Complexity 25, no. 2 (2009): 152-162.
Journal of Complexity