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arxiv astro-ph/0508514 v3 pith:SOVW3BW2 submitted 2005-08-24 astro-ph gr-qcmath-phmath.MP

Fast spin +-2 spherical harmonics transforms and application in cosmology

Y. Wiaux (1) , L. Jacques (2) , P. Vandergheynst (1) ((1) Swiss Federal Institute of Technology , Lausanne , Switzerland , (2) Universite catholique de Louvain , Louvain-la-Neuve , Belgium) This is my paper
classification astro-ph gr-qcmath-phmath.MP
keywords fastharmonicssphericalspinalgorithmapplicationasymptoticcomplexity
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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(L^2 log^2_2(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(L^3) 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.

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