On parallel multisplitting methods for non-Hermitian positive definite linear systems

Abstract

To solve non-Hermitian linear system Ax = b on parallel and vector machines, some paralell multisplitting methods are considered. In this work, in particular: i) We establish the convergence results of the paralell multisplitting methods, together with its relaxed version, some of which can be regarded as generalizations of analogous results for the Hermitian positive definite case; ii) We extend the positive-definite and skew-Hermitian splitting (PSS) method methods in [SIAM J. Sci. Comput., 26:844-863, 2005] to the parallel PSS methods and propose the corresponding convergence results.