A multi-parameters preconditioned AOR iterative method for linear systems

In order to improve the convergence rates of iterative method solving the linear system Ax=b, a preconditioned AOR iterative method with a multi-parameters preconditioner I+S∼α is proposed. Some convergence and comparison results for αi∈[0,1] are given when A is an L-matrix. When A is an H-matrix, the convergence of the corresponding methods is discussed for αi∈[0,αi′), where αi>1. Furthermore, effectiveness of the new preconditioner method is shown by numerical experiments. Numerical experiments show that our methods are superior to the basic AOR iterative methods.