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Successive Over-relaxation Method (SOR). This method of solving a linear system of equations Ax = b derived by extrapolating 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.
if ω = 1, the SOR method simplifies to the Gauss-Seidel method. A theorem due to Kahan (1958) shows that SOR fails to converge if ω is outside of the interval (0, 2). In general, it is not possible to compute in advance the value of ω that will maximize the rate of convergence of SOR.
The successive over-relaxation method can be derived from the Gauss-Seidel method by introducing an extrapolation parameter omega. This method can converge faster than Gauss-Seidel by an order of magnitude
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