International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 1, Pages 49-60
On some extensions of the accelerated overrelaxation (AOR) theory
Department of Mathematics, University of loannina, loannina, Greece
Received 5 June 1980; Revised 30 March 1981
Copyright © 1982 A. Hadjidimos and A. Yeyios. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.