Three-step alternating and preconditioned scheme for rectangular matrices

In this article, a three-step alternating iterative scheme for rectangular system has been proposed. The convergence and comparison analysis of the proposed method has been discussed for the class of semi-monotone matrices and which confirms the faster convergence of our scheme. A preconditioned approach is also presented in this paper to relax the semi-monotonicity condition. The preconditioned approach is very promising and converges faster than some of existing schemes. We finally validated all the theoretical results by some numerical examples.