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The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular matrices. Secondly, we propose an alternating iterative method for solving rectangular linear systems by using the Moore-Penrose inverse and discuss its convergence theory, by extending the work of Benzi and Szyld Numererische Mathematik 76 (1997) 309-321; MR1452511]. Furthermore, a comparison result is obtained which insures faster convergence rate of the proposed alternating iterative scheme.

Properweak regular splitting and its application to convergence of alternating iterations