Subproper and Regular Splitting for Restricted Rectangular Linear System
Applied Mathematics and Computation
Iterative schemes for approximating a solution to restricted rectangular but consistent linear system of equations Ax=b, x∈T, are considered. The methods are based upon so-called subproper splitting A=M−N, which is a generalization of the concept of subproper splitting introduced by Neumann and studied further by Berman and Neumann and others. We give a necessary and sufficient condition on the splitting such that the iterative sequence converges to a solution of Ax=b in the case of b∈AT for every x0, where A∈Cm×n and T is a subspace of Cn. Monotonicity and the concept of regular subproper splitting are used to determine a necessary and a sufficient condition for the convergence of the iterative scheme. Finally, we present two numerical examples to verify our conclusions.
Wei, Yimin, Xiezhang Li, Hebing Wu.
"Subproper and Regular Splitting for Restricted Rectangular Linear System."
Applied Mathematics and Computation, 136 (2-3): 535-547.
doi: 10.1016/S0096-3003(02)00078-4 source: https://www.sciencedirect.com/science/article/pii/S0096300302000784?via%3Dihub