Stopping criteria, forward and backward errors for perturbed asynchronous linear fixed point methods in finite precision

This paper deals with perturbed linear fixed point methods in the presence of round-off errors. Successive approximations as well as the more general asynchronous iterations are treated. Forward and backward error estimates are presented, and these are used to propose theoretical stopping criteria for these methods. In the case of asynchronous iterations, macro-iterations are used as a tool in order to obtain estimates.