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Abstract It is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H -matrices (whose comparison matrices are nonsingular M -matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H -matrices (whose comparison matrices are singular M -matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative methods are convergent for linear systems with weak H -matrices. Furthermore, some numerical examples are given to demonstrate the convergence results obtained in this paper.
Zhang et al. (Fri,) studied this question.