The Successive Overrelaxation Method, or SOR, is devised by applying extrapolation to the Gauss-Seidel method. This extrapolation takes the form of a weighted average between the previous iterate and the computed Gauss-Seidel iterate successively for each component:
(where denotes a Gauss-Seidel iterate, and is the extrapolation factor). The idea is to choose a value for that will accelerate the rate of convergence of the iterates to the solution.
In matrix terms, the SOR algorithm can be written as follows:
The pseudocode for the SOR algorithm is given in Figure .
Figure: The SOR Method