The Successive Overrelaxation Method

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The Successive Overrelaxation Method


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 gif.

Figure: The SOR Method

Jack Dongarra
Mon Nov 20 08:52:54 EST 1995