A

method for finding the optimum successive over-relaxation parameter By J. K. Reid* A proof is given here of the well-known relation between the eigenvalues of the Jacobi and S.O.R. iteration matrices in the case having Property A and consistent ordering. This proof also yields a relationship between the corresponding eigenvectors, and we use this relation to form a method of obtaining an approximation to the optimum relaxation parameter. Analytical results We consider here the solution by successive over-relaxation of the set of linear equations and suppose that Ax =