(untitled) (Journal of Computational Mathematics, 2021)
Recently, M. Hanke and M. Neumann^[4] have derived a necessary and sufficient condition on a splitting of A=U-V, which leads to a fixed point system, such that the iterative sequence converges to the least squares solution of minimum 2-norm of the system Ax=b. In this paper, we give a necessary and sufficient condition on the splitting such that the iterative sequence converges to the weighted Moore-Penrose solution of the system Ax=b for every x_0C^n and every bC^m. We also provide a necessary and sufficient condition such that the iterative sequence is convergent for every x_0C^n.