Another step toward an optimal two-parameter SOR method (Q1011837)

The author deals with the successive overrelaxation (SOR) method, which is a well-known iterative method for solving linear systems. The paper refers to a two-parameter version of this method, which was already proved to be not superior to the standard version for cyclic and positive-definite matrices. This paper generalizes such result. Moreover a range value of the second parameter is provided, for which the two-parameter method has faster convergence than the standard SOR method. It is interesting that such range is proved on the basis of geometrical arguments, when the eigenvalues of the SOR method are restricted to a certain configuration in the complex plane.