Title

Subproper and Regular Splitting for Restricted Rectangular Linear System

Document Type

Article

Publication Date

3-15-2003

Publication Title

Applied Mathematics and Computation

DOI

10.1016/S0096-3003(02)00078-4

ISSN

0096-3003

Abstract

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.

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