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Reference [11] investigated the almost sure weak convergence ofblock-coordinate fixed point algorithms and discussed their applications tononlinear analysis and optimization. This algorithmic framework features randomsweeping rules to select arbitrarily the blocks of variables that are activatedover the course of the iterations and it allows for stochastic errors in theevaluation of the operators. The present paper establishes results on themean-square and linear convergence of the iterates. Applications to monotoneoperator splitting and proximal optimization algorithms are presented.

Stochastic Quasi-Fej\'er Block-Coordinate Fixed Point Iterations With Random Sweeping II: Mean-Square and Linear Convergence