#### 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.

#### Recommended Citation

Wei, Yimin, Xiezhang Li, Hebing Wu.
2003.
"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

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/552