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

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 [{\em SIAM J. Sci. Comput.}, 26:844--863, 2005] to the parallel PSS methods and propose the corresponding convergence results

On parallel multisplitting block iterative methods for linear systems arising in the numerical solution of Euler equations

The paper studies the convergence of some parallel multisplitting block iterative methods for the solution of linear systems arising in the numerical solution of Euler equations. Some sufficient conditions for convergence are proposed. As special cases the convergence of the parallel block generalized AOR (BGAOR), the parallel block AOR (BAOR), the parallel block generalized SOR (BGSOR), the parallel block SOR (BSOR), the extrapolated parallel BAOR and the extrapolated parallel BSOR methods are presented. Furthermore, the convergence of the parallel block iterative methods for linear systems with special block tridiagonal matrices arising in the numerical solution of Euler equations are discussed. Finally, some examples are given to demonstrate the convergence results obtained in this paper