Guaranteed convergence rate estimates for a class of iterative procedures: their comparison (Q2487542)

Asynchronous methods for approximating the solution of a system of nonlinear equations in fixed point form (in a general Banach space setting) are considered. Besides the standard sequential approximation method, where all components of the approximate solution are synchronously updated in each iteration step, more general iterative procedures are discussed, where only some of the components of the approximate solution are updated in each step. In particular the case is studied where the subsets of updated components change periodically. For this class of methods convergence rate estimates are derived and the question of optimal strategies for selecting the subsets of updated components is addressed.