Abstract
This paper extends the convergence theory of the Accelerated Overrelaxation (AOR) method to cases analogous to those considered first by Ostrowski and then by Varga in connection with the Successive Overrelaxation (SOR) method. Among others, the Ostrowski Theorem, some of the theorems by Varga on the extensions of the SOR theory, and some recent results by Niethammer and by the authors are obtained as special cases of the work presented in this paper. In addition, several points are raised which suggest further research.