Extended convergence regions for the AOR method

摘要

In this paper, we give sufficient conditions for the convergence of the (AOR) method, when the matrix A for Ax = b is a strictly diagonally dominant matrix. These results improve the conclusions obtained in the Theorem 4 [10].With the notion of generalized diagonal dominant matrix, we enlarge the convergence regions given in Theorem 9 [10], when A is a nonsingular H-matrix.In the last section we generalize theorem 6 of Robert [11] and we present some results which extend the convergence regions for the (AOR) method.