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Component separation is one of the key stages of any modern, cosmic microwavebackground (CMB) data analysis pipeline. It is an inherently non-linearprocedure and typically involves a series of sequential solutions of linearsystems with similar, albeit not identical system matrices, derived fordifferent data models of the same data set. Sequences of this kind arise forinstance in the maximization of the data likelihood with respect to foregroundparameters or sampling of their posterior distribution. However, they are alsocommon in many other contexts. In this work we consider solving the componentseparation problem directly in the measurement (time) domain, which can have anumber of important advantageous over the more standard pixel-based methods, inparticular if non-negligible time-domain noise correlations are present as itis commonly the case. The time-domain based approach implies, however,significant computational effort due to the need to manipulate the full volumeof time-domain data set. To address this challenge, we propose and studyefficient solvers adapted to solving time-domain-based, component separationsystems and their sequences and which are capable of capitalizing oninformation derived from the previous solutions. This is achieved either viaadapting the initial guess of the subsequent system or through a so-calledsubspace recycling, which allows to construct progressively more efficient,two-level preconditioners. We report an overall speed-up over solving thesystems independently of a factor of nearly 7, or 5, in the worked examplesinspired respectively by the likelihood maximization and likelihood samplingprocedures we consider in this work.

Accelerating linear system solvers for time domain component separation of cosmic microwave background data