A convergence analysis of SOR iterative methods for linear systems with weakH-matrices

Cheng-yi Zhang, Zichen Xue, and Shuanghua Luo. "A convergence analysis of SOR iterative methods for linear systems with weakH-matrices." Open Mathematics 14.1 (2016): 747-760. <http://eudml.org/doc/287126>.

@article{Cheng2016,
abstract = {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.},
author = {Cheng-yi Zhang, Zichen Xue, Shuanghua Luo},
journal = {Open Mathematics},
keywords = {Convergence; Weak H-matrices; Nonstricly diagonally dominant matrices; Diagonally dominant matrices; Diagonally equipotent matrices; SOR iterative methods; convergence; weak -matrices; nonstricly diagonally dominant matrices; diagonally dominant matrices; diagonally equipotent matrices; iterative methods; numerical example; successive overrelaxation (SOR)},
language = {eng},
number = {1},
pages = {747-760},
title = {A convergence analysis of SOR iterative methods for linear systems with weakH-matrices},
url = {http://eudml.org/doc/287126},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Cheng-yi Zhang
AU - Zichen Xue
AU - Shuanghua Luo
TI - A convergence analysis of SOR iterative methods for linear systems with weakH-matrices
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 747
EP - 760
AB - 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.
LA - eng
KW - Convergence; Weak H-matrices; Nonstricly diagonally dominant matrices; Diagonally dominant matrices; Diagonally equipotent matrices; SOR iterative methods; convergence; weak -matrices; nonstricly diagonally dominant matrices; diagonally dominant matrices; diagonally equipotent matrices; iterative methods; numerical example; successive overrelaxation (SOR)
UR - http://eudml.org/doc/287126
ER -