On convergence of two-stage iterative scheme

Climent and Perea [Journal of Computational Applied Mathematics 58:43–48, 2003; MR2013603] proposed first the convergence theory two-stage iterative scheme for solving real rectangular linear systems. In this article, we revisit same theory. The main result provides some sufficient conditions which guarantee that induced splitting from a is proper weak regular splitting. We then establish few comparison results. Out these, many are even new in nonsingular matrix setting. Further, study monotone method. Besides also prove uniqueness under certain assumptions.