On an accelerated overrelaxation iterative method for linear systems with strictly diagonally dominant matrix

Abstract

We consider a linear system A x = b Ax = b of n simultaneous equations, where A is a strictly diagonally dominant matrix. We get bounds for the spectral radius of the matrix L r , ω {L_{r,\omega }} , which is accociated with the Accelerated Overrelaxation iterative method (AOR). Sufficient conditions for the convergence of that method will be given, which improve the results of Theorem 3, Section 4 of [2], applied to this type of matrices.