Chaotic relaxation

In this paper we consider relaxation methods for solving linear systems of equations. These methods are suited for execution on a parallel system of processors. They have the feature of allowing a minimal amount of communication of computational status between the computers, so that the relaxation process, while taking on a chaotic appearance, reduces programming and processor time of a bookkeeping nature. We give a precise characterization of chaotic relaxation, some examples of divergence, and conditions guaranteeing convergence. © 1969.