GENERALIZED EXTRAPOLATION PRINCIPLE AND CONVERGENCE OF SOME GENERALIZED ITERATIVE METHODS

To solve the linear system Ax = b, this paper presents a generalized extrapolated method by replacing the extrapolation parameter omega with the diagonal matrix OMEGA, and systematically gives the basic results for its convergence. Based upon these results, the paper considers the convergence of the GJ and GAOR iterative methods and, using the set of the equimodularized diagonally similar matrices defined here, gives some new further convergence results for H-matrices and their subclasses, strictly or irreducibly diagonally dominant matrices, which unify, improve, and extend previously given various results. Finally, conditions equivalent to the statement that A is a nonsingular H-matrix or a strictly (or an irreducibly) diagonally dominant matrix are given in connection with the GJ and GAOR methods.