Accelerating the cosmic microwave background map-making procedure through preconditioning

Estimation of the sky signal from sequences of time ordered data is one of the key steps in cosmic microwave background (CMB) data analysis, commonly referred to as the map-making problem. Some of the most popular and general methods proposed for this problem involve solving generalised least-squares (GLS) equations with non-diagonal noise weights given by a block-diagonal matrix with Toeplitz blocks. In this work, we study new map-making solvers potentially suitable for applications to the largest anticipated data sets. They are based on iterative conjugate gradient (CG) approaches enhanced with novel, parallel, two-level preconditioners. We apply the proposed solvers to examples of simulated non-polarised and polarised CMB observations and a set of idealised scanning strategies with sky coverage ranging from a nearly full sky down to small sky patches. We discuss their implementation for massively parallel computational platforms and their performance for a broad range of parameters that characterise the simulated data sets in detail. We find that our best new solver can outperform carefully optimised standard solvers used today by a factor of as much as five in terms of the convergence rate and a factor of up to four in terms of the time to solution, without significantly increasing the memory consumption and the volume of inter-processor communication. The performance of the new algorithms is also found to be more stable and robust and less dependent on specific characteristics of the analysed data set. We therefore conclude that the proposed approaches are well suited to address successfully challenges posed by new and forthcoming CMB data sets.