A modified SSOR iterative method for a class of block two-by-two linear systems

Abstract

An interesting phenomenon when it comes to solving a class of complex linear systems is that the modified symmetric successive overrelaxation (MSSOR) method with two parameters seems to enjoy the fine convergence performance over symmetric successive overrelaxation (SSOR) which is recently proposed by Liang 19 and Bai 30. Owing to the flexible selection of the parameters, the MSSOR method possesses the valuable role to solve some large scale linear systems including the complex situation. Meanwhile, we also establish an accelerated MSSOR (AMSSOR) which can offer a meaningful improvement on MSSOR method. This has been illustrated experimentally and shown theoretically in this study. Our results may provide an analytical justification for popularity of SSOR and its accelerated version as efficient solvers for some linear systems.