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Title: Energies, Group Invariant Kernels and Numerical Integration on Compact Manifolds.
Authors: Damelin, S. B.
Levesley, Jeremy
Ragozin, D. L.
Sun, X.
First Published: Apr-2009
Publisher: Elsevier
Citation: Journal of Complexity, 2009, 25 (2), pp. 152-162.
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.
DOI Link: 10.1016/j.jco.2008.09.001
ISSN: 0885-064X
Type: Article
Rights: This is the author's final draft of the paper published as Journal of Complexity, 2009, 25 (2), pp. 152-162. The final version is available from Doi: 10.1016/j.jco.2008.09.001
Appears in Collections:Published Articles, Dept. of Mathematics

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