Numerical performance of an asynchronous Jacobi iteration

Abstract

We examine the effect of removing synchronisation points from a parallel implementation of a simple iterative algorithm—Jacobi’s method for linear systems. We find that in some cases the asynchronous version requires fewer iterations to converge than its synchronous counterpart. We show that this behaviour can be explained in terms of the presence or absence of oscillations in the sequence of error vectors in the synchronous version, and that removing the synchronisation point can damp the oscillations.