The local modified extrapolated Gauss–Seidel (LMEGS) method

In this paper we present the convergence analysis of the Local Modified Extrapolated Gauss–Seidel (LMEGS) method. The related theory of convergence is developed. Convergence ranges and optimum values for the involved parameters of the LMEGS method are obtained. It is proved that even if μ, the smallest in absolute value eigenvalue of the iteration matrix of the Jacobi method, becomes larger than unity LMEGS will converge. In fact, the larger μ the faster the convergence of LMEGS.