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We present a simple approximation that can speed up the computation of themode-coupling matrices, which are usually the bottleneck for computing unbiasedangular power spectra, as well as their associated covariance matrices, of thecosmic microwave background temperature and polarization anisotropies. Theapproximation results in the speed up of the MASTER algorithm by more than anorder of magnitude with very little loss of precision. We demonstrate theperformance on simulations of forthcoming cosmic microwave background surveyssuch as the Simons Observatory and CMB-S4 for a wide variety of survey windowfunctions.

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