Spherical designs, discrepancy and numerical integration

Grabner, Peter J.; Tichy, Robert F.

doi:10.1090/S0025-5718-1993-1155573-5

Spherical designs, discrepancy and numerical integration

Authors: Peter J. Grabner and Robert F. Tichy
Journal: Math. Comp. 60 (1993), 327-336
MSC: Primary 11K45; Secondary 65C05
DOI: https://doi.org/10.1090/S0025-5718-1993-1155573-5
MathSciNet review: 1155573
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Abstract: A spherical design is a point configuration on the sphere, which yields exact equal-weight quadrature formulae for polynomials up to a given degree. Until now only very specific constructions for spherical designs are known. We establish connections to spherical cap discrepancy and show some general discrepancy bounds. Furthermore, we reformulate the problem of constructing designs as an optimization problem and develop an algorithm for finding 'practical designs'.

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