Fast computation of angular power spectra and covariances of high-resolution cosmic microwave background maps using the Toeplitz approximation

Understand

We present a simple approximation that can speed up the computation of the mode-coupling matrices, which are usually the bottleneck for computing unbiased angular power spectra, as well as their associated covariance matrices, of the cosmic microwave background temperature and polarization anisotropies.

• The approximation results in the speed up of the MASTER algorithm by more than an order of magnitude with very little loss of precision.
• We demonstrate the performance on simulations of forthcoming cosmic microwave background surveys such as the Simons Observatory and CMB-S4 for a wide variety of survey window functions.