Abstract
The SOR iteration method for solving linear systems of equations depends upon a relaxation parameter. A well-known theory for determining the relaxation parameter was given by Young for consistently ordered matrices. In this paper, we prove that the matrix of the linear system arisen from the 7-point Laplacian is consistently ordered in both point form and block form. Then by separating variables and solving difference equations, the optimum relaxation parameters of point and block SOR iterations for the system are given for the first time, respectively.
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