Optimum modified extrapolated jacobi method for some class of matrices

Abstract

In this paper we study a two parametric linear stationary iterative method, called Modified Extrapolated Jacobi (MEJ) method, for solving linear systems Ax = b, where A is nonsingular consistently ordered 2-cyclic matrix. We give sufficient and necessary conditions for strong convergence of the MEJ method and we determine the optimum extrapolation parameters and the optimum spectral radius of it, in the case where all the eigenvalues of the block Jacobi iteration matrix associated with A are purely imaginary. In the last section, we compare the MEJ with other known methods.