Improving AOR method for consistent linear systems

Milaszewicz [J.P. Milaszewicz, Improving Jacobi and Gauss-Seidel iterations, Linear Algebra Appl. 93 (1987) 161-170] and Gunawardena et al. [A.D. Gunawardena, S.K. Jain, L. Snyder, Modified iteration methods for consistent linear systems, Linear Algebra Appl. 154-156 (1991) 123-143] presented preconditioned methods for linear system in order to improve the convergence rates of Jacobi and Gauss-Seidel iterative schemes, respectively. In this paper, we apply AOR and SOR iterative schemes to the preconditioned linear systems and provide two theorems to improve the convergence rates of these iterative methods. Meanwhile, the methods in this paper can be used to more class of linear systems.