Fast power spectrum estimation

Abstract

We present a new algorithm to rapidly and optimally compute power spectra. This new algorithm is based on a generalization of iterative multigrid, and has computational cost script O sign (N log N), compared to the standard brute force approach which costs script O sign(N3). The procedure retains this speed on the full sky and for ill-conditioned matrices. It is applicable to galaxy power spectra, cosmic microwave background (CMB), polarization and weak lensing data. We present a mathematical convergence analysis, and performance results.