2005/08/31 by Yves Wiaux, Y. Wiaux, Laurent Jacques +3 · 47 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Cosmic microwave background #Cosmology #Cosmology and Gravitation Theories #Geometry #Geophysics and Gravity Measurements #Harmonics #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Radio Astronomy Observations and Technology #Scalar (mathematics) #Spherical harmonics #Spin-weighted spherical harmonics #astro-ph #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1016/j.jcp.2007.07.005
published in Journal of Computational Physics 226(2), 2359-2371 (Elsevier BV) · 20 pages, 2 figures. Version accepted for publication in J. Comput. Phys.
openalex publication_date 2007/07/31 · arxiv created 2007/08/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A fast and exact algorithm is developed for the spin +-2 spherical harmonics transforms on equi-angular pixelizations on the sphere. It is based on the Driscoll and Healy fast scalar spherical harmonics transform. The theoretical exactness of the transform relies on a sampling theorem. The associated asymptotic complexity is of order O(L2 log22(L)), where 2L stands for the square-root of the number of sampling points on the sphere, also setting a band limit L for the spin +-2 functions considered. The algorithm is presented as an alternative to existing fast algorithms with an asymptotic complexity of order O(L3) on other pixelizations. We also illustrate these generic developments through their application in cosmology, for the analysis of the cosmic microwave background (CMB) polarization data.