Successive Over-Relaxation (SOR) is an iterative method used to solve systems of linear equations, particularly those that arise from discretization of partial differential equations or in the context of numerical linear algebra. It is an extension of the Gauss-Seidel method and is used to accelerate the convergence of the iteration.
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For a splitting , successive over-relaxation updatesIt reduces to the Gauss-Seidel method at . If is symmetric positive definite, the Householder-John theorem applies to , , since is positive definite for .