![]() ![]() Over-relaxation can be used to speed up convergence of a slow-converging process. If, then the new estimate lies on the extension of the vector joining the old estimate and the Gauss-Seidel estimate and hence the algorithm is termed: “over-relaxation” ( Figure 1). Under-relaxation can be used to help establish convergence if the method is diverging. If, then, the method gives a new estimate that lies somewhere between the old estimate and the Gauss-Seidel estimate, in this case, the algorithm is termed: “under-relaxation” ( Figure 1). Otherwise, to understand the effect of we will rearrange the above equation to: If, then the method is exactly the Gauss-Seidel method. Where can be obtained using Equation 1 in the Gauss-Seidel method. The successive over-relaxation (SOR) method is another form of the Gauss-Seidel method in which the new estimate at iteration for the component is calculated as the weighted average of the previous estimate and the estimate using Gauss-Seidel : The Successive Over-Relaxation (SOR) Method Open Educational Resources Iterative Methods: ![]()
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