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

Cheng-yi Zhang; Zichen Xue; Shuanghua Luo

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 747-760
- ISSN: 2391-5455

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topCheng-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 -