Abstract
In this paper, the modified SSOR (MSSOR) method is further investigated for solving augmented linear systems, including both the nonsingular and singular cases. The selection of quasi-optimal iteration parameters are discussed to minimize the radius of the MSSOR iteration matrix for the nonsingular case. The obtained optimality result is unified, which includes those for some existing methods as special cases. Besides, semi-convergence analysis of the MSSOR method for singular case is given using a singular preconditioning technique, which results in much better convergence behavior than some existing nonsingular preconditioning techniques. Numerical experiments are presented to confirm the theoretical results.
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