Some basic results on M-matrices in connection with the Accelerated Overrelaxation (AOR) method

This paper extends some recent results by Varga concerning the theory of M-matrices, in connection with the well known iterative methods of Jacobi, of Extrapolated Jacobi and of Successive Over-relaxation, in two directions: i) The iteration matrix of the iterative scheme considered is more general than that of the aforementioned methods and may include a diagonal part and ii) the theory is presented in such a way that the number of equivalent statements given in the text covers the Accelerated Overrelaxation (AOR) method introduced by the present author not long ago.