Convergence analysis of the two preconditioned iterative methods for M-matrix linear systems

被引：3

作者：

Liu, Qingbing ^{[1
]}

Huang, Jian ^{[1
]}

Zeng, Shouzhen ^{[1
]}

机构：

[1] Zhejiang Wanli Univ, Comp Sci & Informat Technol Coll, Ningbo 315100, Zhejiang, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2015年 / 281卷

基金：

中国国家自然科学基金;

关键词：

M-matrix; Matrix splitting; Krylov subspace methods; Preconditioner; HERMITIAN SPLITTING METHODS; COMPARISON-THEOREMS; IMPROVEMENTS; SCHEMES;

D O I：

10.1016/j.cam.2014.11.034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present the two preconditioners I +(S) over cap and I +(S) over cap+ R for solving M-matrix linear systems and discuss the convergence of the two preconditioned iterative methods. Meanwhile, we obtain comparison theorems between the two preconditioned iterative methods and consider the solution of M-matrix linear systems by preconditioned Krylov subspace methods. Numerical experiments are given to validate the performance of the preconditioners. Crown Copyright (C) 2014 Published by Elsevier B.V. All rights reserved.

引用

页码：49 / 57

页数：9

共 50 条

[31] Rounding error analysis in solving M-matrix linear systems of block Hessenberg form
Gemignani, L
Lotti, G
NUMERICAL ALGORITHMS, 2004, 36 (02) : 157 - 168
[32] Rounding Error Analysis in Solving M-Matrix Linear Systems of Block Hessenberg Form
Luca Gemignani
Grazia Lotti
Numerical Algorithms, 2004, 36 : 157 - 168
[33] A SURVEY OF PRECONDITIONED ITERATIVE METHODS FOR LINEAR-SYSTEMS OF ALGEBRAIC EQUATIONS
AXELSSON, O
BIT, 1985, 25 (01): : 166 - 187
[34] Preconditioned SAOR iterative methods for H-matrices linear systems
Wang, Xue-Zhong
Ma, Lei
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2015, 19 (05) : 911 - 917
[35] Convergence analysis of directed signed networks via an M-matrix approach
Meng, Deyuan
INTERNATIONAL JOURNAL OF CONTROL, 2018, 91 (04) : 827 - 847
[36] Preconditioned SOR-type iterative methods for solving linear systems
Shen, Hai-Long
Zong, Yuan
Shao, Xin-Hui
Dongbei Daxue Xuebao/Journal of Northeastern University, 2009, 30 (08): : 1213 - 1216
[37] CONVERGENCE OF PRECONDITIONED GAUSS-SEIDEL ITERATIVE METHODS
Wang Xinmin(School of Information Technology&Management Engineering
Numerical Mathematics(Theory,Methods and Applications), 2000, (S1) : 142 - 145
[38] On the convergence of iterative methods for solving singular linear systems
Cao, ZH
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2002, 145 (01) : 1 - 9
[39] Seminorm Convergence of Iterative Methods for Semidefinite Linear Systems
Zhou, Sheng
Huang, Ting-Zhu
ADVANCES IN MATRIX THEORY AND ITS APPLICATIONS, VOL 1: PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON MATRIX THEORY AND ITS APPLICATIONS, 2008, : 476 - 479
[40] Monotone Convergence of Iterative Methods for Singular Linear Systems
Yongzhong Song
BIT Numerical Mathematics, 2002, 42 : 611 - 624

← 1 2 3 4 5 →