Random relaxation of fixed-point iteration

This paper considers a stochastic fixed-point iteration where each coordinate is updated with a certain probability and otherwise left unchanged. The iteration is interesting from the viewpoint of parallel distributed computation because the realized sequences belong to the class of asynchronous fixed-point iterations. It is demonstrated with a linear system that the convergence conditions for randomly relaxed iterations are less stringent than their asynchronous counterparts, and that they can illuminate the tightness of the convergence conditions for asynchronous iterations, which are typically worst-case conditions.