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This paper develops the theory of the Extrapolated Successive Overrelaxation (ESOR) method as introduced by Sisler in [1], [2], [3] for the numerical solution of large sparse linear systems of the form Au=b, when A is a consistently ordered 2-cyclic matrix with non-vanishing diagonal elements and the Jacobi iteration matrix B possesses only real eigenvalues. The region of convergence for the ESOR method is described and the optimum values of the involved parameters are also determined. It is shown that if the minimum of the moduli of the eigenvalues of B, μ¯ does not vanish, then ESOR attains faster rate of convergence than SOR when 1−μ¯2<(1−μ¯2)12, where μ¯ denotes the spectral radius of B

The extrapolated successive overrelaxation (ESOR) method for consistently ordered matrices