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Energies, Group Invariant Kernels and Numerical Integration on Compact Manifolds.

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posted on 2009-05-27, 13:22 authored by S. B. Damelin, Jeremy Levesley, D. L. Ragozin, X. Sun
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.

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Citation

Journal of Complexity, 2009, 25 (2), pp. 152-162.

Published in

Journal of Complexity

Publisher

Elsevier

issn

0885-064X

Copyright date

2009

Available date

2009-05-27

Publisher version

http://www.sciencedirect.com/science/article/pii/S0885064X08000733

Language

en

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