  Context. The numerical modeling of the generation and transfer of polarized
radiation is a key task in solar and stellar physics research and has led to a
relevant class of discrete problems that can be reframed as linear systems. In
order to solve such problems, it is common to rely on efficient stationary
iterative methods. However, the convergence properties of these methods are
problem-dependent, and a rigorous investigation of their convergence
conditions, when applied to transfer problems of polarized radiation, is still
lacking. Aims. After summarizing the most widely employed iterative methods
used in the numerical transfer of polarized radiation, this article aims to
clarify how the convergence of these methods depends on different design
elements, such as the choice of the formal solver, the discretization of the
problem, or the use of damping factors. The main goal is to highlight
advantages and disadvantages of the different iterative methods in terms of
stability and rate of convergence. Methods. We first introduce an algebraic
formulation of the radiative transfer problem. This formulation allows us to
explicitly assemble the iteration matrices arising from different stationary
iterative methods, compute their spectral radii and derive their convergence
rates, and test the impact of different discretization settings, problem
parameters, and damping factors. Conclusions. The general methodology used in
this article, based on a fully algebraic formulation of linear transfer
problems of polarized radiation, provides useful estimates of the convergence
rates of various iterative schemes. Additionally, it can lead to novel solution
approaches as well as analyses for a wider range of settings, including the
unpolarized case.
