Convergence of the Madd preconditioner (top panel) when including sky mask (Planck Collaboration XI 2016) in the model (bottom panel). We fit a single CMB component to hypothetical foreground-cleaned maps on all nine Planck bands, specifying a fiducial Cℓ prior for the CMB power spectrum. We plot the convergence when using a diagonal preconditioner (grey) and the Madd preconditioner developed in Sect. 4 (black). Section 5 gives details on the benchmark setup.
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