Abstract
In this paper iterative schemes for approximating a solution to a rectangular but consistent linear system Ax = b are studied. Let A ϵ C m × n r . The splitting A = M − N is called subproper if R( A) ⊆ R( M) and R(A ∗) ⊆R(M ∗) . Consider the iteration x i = M †Nx i −1 + M †b . We characterize the convergence of this scheme to a solution of the linear system. When A ϵ R m × n r , monotonicity and the concept of subproper regular splitting are used to determine a necessary and a sufficient condition for the scheme to converge to a solution.
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