The upper Jacobi and upper Gauss-Seidel type iterative methods for preconditioned linear systems

The preconditioner for solving the linear system Ax=b introduced in [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] is generalized. Results obtained in this paper show that the convergence rate of Jacobi and Gauss-Seidel type methods can be increased by using the preconditioned method when A is an M-matrix.