  We give a new proof of local convergence of a multigrid method called
iterative aggregation/disaggregation (IAD) for computing steady-states of
Markov chains. Our proof leads naturally to a precise and interpretable
estimate of the asymptotic rate of convergence. We study IAD as a model of more
complex methods from statistical physics for computing nonequilibrium
steady-states, such as the nonequilibrium umbrella sampling method of
Warmflash, et al. We explain why it may be possible to use methods like IAD to
efficiently calculate steady-states of models in statistical physics and how to
choose parameters to optimize efficiency.
