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Subproper splitting for rectangular matrices
Authors:M Neumann
Institution:Department of Applied Mathematics Technion—Israel Institute of Technology Haifa, Israel
Abstract:In this paper iterative schemes for approximating a solution to a rectangular but consistent linear system Ax = b are studied. Let A?Cm × nr. The splitting A = M ? N is called subproper if R(A) ? R(M) and R(A1) ?R(M1). Consider the iteration xi = M2Nxi?1 + M2b. We characterize the convergence of this scheme to a solution of the linear system. When A?Rm×nr, 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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