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

TL;DR

This paper introduces a Toeplitz approximation that significantly accelerates the computation of angular power spectra and covariances in high-resolution CMB maps, with minimal precision loss, benefiting upcoming surveys.

Contribution

The authors propose a simple Toeplitz-based approximation to speed up mode-coupling matrix calculations in CMB analysis, reducing computation time by over tenfold.

Findings

Speed up of the MASTER algorithm by more than an order of magnitude

Minimal loss of precision in power spectrum and covariance estimates

Effective performance demonstrated on simulations for upcoming CMB surveys

Abstract

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.