Matrix multi-splitting multi-parameter relaxation methods

Abstract

In this paper, we propose a class of matrix multisplitting multiparameter relaxation methods, for solving large nonsingular systems of equations. This new class of method includes the well known matrix multisplitting relaxation methods such as the matrix multisplitting SOR, methods as well as the extrapolated matrix multisplitting AOR method as its special cases, as well as the matrix multisplitting SSOR and SAOR methods. It therefore forms a series of relaxation methods in the sense of matrix multisplitting which affords more flexible choices for practical application and also makes the parallel computation of serial relaxation methods become possible. The convergence theory of this new class of methods is established under the condition that the coefficient matrix of the system of equations is an H-matrix.