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Previous: The Gauss-Seidel Method
Up: Stationary Iterative Methods
Next: The Symmetric Successive Overrelaxation Method
Previous Page: The Gauss-Seidel Method
Next Page: Choosing the Value of Omega
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 .
