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ADCM
2004

Extremal Systems of Points and Numerical Integration on the Sphere

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Extremal Systems of Points and Numerical Integration on the Sphere
This paper considers extremal systems of points on the unit sphere Sr Rr+1, related problems of numerical integration and geometrical properties of extremal systems. Extremal systems are systems of dn = dim Pn points, where Pn is the space of spherical polynomials of degree at most n, which maximize the determinant of an interpolation matrix. Extremal systems for S2 of degrees up to 191 (36, 864 points) provide well distributed points, and are found to yield interpolatory cubature rules with positive weights. We consider the worst case cubature error in a certain Hilbert space and its relation to a generalized discrepancy. We also consider geometrical properties such as the minimal geodesic distance between points and the mesh norm. The known theoretical properties fall well short of those suggested by the numerical experiments.
Ian H. Sloan, Robert S. Womersley
Added 16 Dec 2010
Updated 16 Dec 2010
Type Journal
Year 2004
Where ADCM
Authors Ian H. Sloan, Robert S. Womersley
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