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The paper describes, discusses, and numerically illustrates the method for obtaining a priori estimates of the optimum relaxation factor in the SOR iteration method. The computational strategy of this method uses the so-called Sigma-SOR algorithm based on the theoretical result proven in the paper. The method presented is especially efficient for problems with slowly convergent iteration process and in this case is strongly competitive with adaptive procedures used for determining dynamically the optimum relaxation factor during the course of the SOR solution.

The sigma-SOR algorithm and the optimal strategy for the utilization of the SOR iterative method