Proper Weak Regular Splitting and its Application to Convergence of Alternating Iterations

Debasisha Mishra


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.


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