Old and new from SOR

From the long history of Successive Over Relaxation (SOR) between the end of second world war and today three points are considered: (1) Classical results of Young and Varga are described. (2) It is shown how results on semiiterative methods can be used to derive these classical results in a unifying way and to compare SOR with other iterative methods. (3) In the last 15 years the application of SOR to compute the stationary distribution of a homogeneous Markov chain has been discussed. These results are reported, considering especially the term “extended convergence” introduced by Kontovasilis, Plemmons and Stewart.