# Fast spin $\pm 2$ spherical harmonics transforms and application in cosmology

Type
Publication
Journal of Computational Physics

Abstract: A fast and exact algorithm is developed for the spin $$\pm2$$ 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 $$O\big(L^2, (\log_2 L)^{2}\big)$$, 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 $$\pm2$$ 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.