It is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative methods are convergent for linear systems with weak H-matrices. Furthermore, some numerical examples are given to demonstrate the convergence results obtained in this paper.
@article{bwmeta1.element.doi-10_1515_math-2016-0065,
author = {Cheng-yi Zhang and Zichen Xue and Shuanghua Luo},
title = {A convergence analysis of SOR iterative methods for linear systems with weakH-matrices},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {747-760},
zbl = {1352.65114},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0065}
}
Cheng-yi Zhang; Zichen Xue; Shuanghua Luo. A convergence analysis of SOR iterative methods for linear systems with weakH-matrices. Open Mathematics, Tome 14 (2016) pp. 747-760. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0065/