![]() Now think of this as the Gauss-Seidel correction ( x ( k+1) − x ( k)) GS. We can subtract x ( k) from both sides to get First, notice that we can write the Gauss-Seidel equation as Here is how we derive the SOR Method from the Gauss-Seidel Method. This direction is the vector x ( k+1) − x ( k), since x ( k+1) = x ( k) + ( x ( k+1) − x ( k)). If we assume that the direction from x ( k) to x ( k+1) is taking us closer, but not all the way, to the true solution x, then it would make sense to move in the same direction x ( k+1) − x ( k), but farther along that direction. ![]() Here is the idea:įor any iterative method, in finding x ( k+1) from x ( k), we move a certain amount in a particular direction from x ( k) to x ( k+1). ![]() A third iterative method, called the Successive Overrelaxation (SOR) Method, is a generalization of and improvement on the Gauss-Seidel Method.
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