A class of preconditioners based on the (I+S(α))-type preconditioning matrices for solving linear systems

The purpose of this paper is to present a class of preconditioners based on the (I+S(α))-type preconditioning matrices provided by Evans et al. [D.J. Evans, M.M. Martins, M.E. Trigo, The AOR iterative method for new preconditioned linear systems, J. Comput. Appl. Math. 132 (2001) 461-466] and Zhang et al. [Y. Zhang, T.Z. Huang, X.P. Liu, Modified iterative methods for nonnegative matrices and M-matrices linear systems, Comput. Math. Appl. 50 (2005) 1587-1602]. Three mathematical models are presented to seek the optimal parameter for these preconditioners. Numerical results are presented, which show the improvements on the convergence rate of the Jacobi type and Gauss-Seidel type preconditioned iterative methods.