Optimum second order stationary extrapolated iterative schemes

In this paper the construction of a stationary second order scheme of de Phillis' type, with optimal convergence rates, for the solution of a linear system is presented. Numerical tests have shown that the new scheme compares favorably with the very fast nonstationary second order one proposed by Manteuffel. It is also proved that a class of already known second order Extrapolated Alternating Direction Implicit schemes can be obtained directly by using the methods of this paper.