  Reference [11] investigated the almost sure weak convergence of
block-coordinate fixed point algorithms and discussed their applications to
nonlinear analysis and optimization. This algorithmic framework features random
sweeping rules to select arbitrarily the blocks of variables that are activated
over the course of the iterations and it allows for stochastic errors in the
evaluation of the operators. The present paper establishes results on the
mean-square and linear convergence of the iterates. Applications to monotone
operator splitting and proximal optimization algorithms are presented.
