Further results on alternating two-stage iterative method

Matrix splitting is an efficient and readily used technique for study of solution of linear systems, iteratively. Migallón et al. [Adv. Eng. Softw. 41:13-21, 2010] proposed alternating two-stage methods in which the inner iterations are accomplished by an alternating method. However, the convergence theory of an alternating two-stage iteration scheme for various class of matrix splittings is a literature gap. In this article, we establish convergence theory of alternating two-stage iterative methods for nonsingular, consistent singular and inconsistent rectangular (or singular) linear systems for different class of matrix splittings. Finally, numerical computations are performed which illustrate that this method has some advantages over simple two-stage iterative method.