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
