  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.
