Gräf, Manuel ; Kunis, Stefan ; Potts, Daniel : On the computation of nonnegative quadrature weights on the sphere

Author(s):

Gräf, Manuel
Kunis, Stefan
Potts, Daniel

Title:

On the computation of nonnegative quadrature weights on the sphere

Electronic source:

application/postscript
application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 13, 2008

Mathematics Subject Classification:

65T99			[ None of the above, but in this section ]
33C55			[ Spherical harmonics ]
42C10			[ Fourier series in special orthogonal functions ]
65T50			[ Discrete and fast Fourier transforms ]

Abstract:

We compute quadrature weights for scattered nodes on the two-dimensional unit-sphere, which are exact for spherical polynomials of high degree N. Different algorithms are proposed and numerical examples show that we can compute nonnegative quadrature weights if approximately 4N^2/3 well distributed nodes are used. We compare these results with theoretical statements which guarantee nonnegative quadrature weights. The proposed algorithms are based on fast spherical Fourier algorithms for arbitrary nodes which are publicly available. Numerical experiments are presented to demonstrate that we are able to compute quadrature weights for circa 1.5 million nodes which are exact for spherical polynomials up to N=1024.

Keywords:

two-sphere, quadrature, nonequispaced fast spherical Fourier transform, NFFT, FFT

Language:

English

Publication time:

7 / 2008