Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices

被引：166
|
作者：
Bai, Zhong-Zhi [1 ]
Golub, Gene H.
Li, Chi-Kwong
机构：
[1] Fudan Univ, Dept Math, Shanghai 200433, Peoples R China
[2] Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Comp Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China
[3] Stanford Univ, Dept Comp Sci, Sci Comp & Computat Math Program, Stanford, CA 94305 USA
[4] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2006年 / 28卷 / 02期
关键词：
non-Hermitian matrix; Hermitian matrix; skew-Hermitian matrix; splitting iteration method; optimal iteration parameter;
D O I：
10.1137/050623644
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The optimal parameter of the Hermitian/skew-Hermitian splitting (HSS) iteration method for a real two-by-two linear system is obtained. The result is used to determine the optimal parameters for linear systems associated with certain two-by-two block matrices and to estimate the optimal parameters of the HSS iteration method for linear systems with n-by-n real coefficient matrices. Numerical examples are given to illustrate the results.
引用
收藏
页码：583 / 603
页数：21
相关论文
共 50 条
  • [21] Extended Convergence Analysis of the Newton-Hermitian and Skew-Hermitian Splitting Method
    Argyros, Ioannis K.
    George, Santhosh
    Godavarma, Chandhini
    Magrenan, Alberto A.
    SYMMETRY-BASEL, 2019, 11 (08):
  • [22] A splitting method for shifted skew-Hermitian linear system
    Angang Cui
    Haiyang Li
    Chengyi Zhang
    Journal of Inequalities and Applications, 2016
  • [23] A splitting method for shifted skew-Hermitian linear system
    Cui, Angang
    Li, Haiyang
    Zhang, Chengyi
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016,
  • [24] Several matrix trace inequalities on Hermitian and skew-Hermitian matrices
    Gao, Xiangyu
    Wang, Guoqiang
    Zhang, Xian
    Tan, Julong
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
  • [25] Hermitian and skew-Hermitian splitting methods for solving a tensor equation
    Li, Tao
    Wang, Qing-Wen
    Zhang, Xin-Fang
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2021, 98 (06) : 1274 - 1290
  • [26] Several matrix trace inequalities on Hermitian and skew-Hermitian matrices
    Xiangyu Gao
    Guoqiang Wang
    Xian Zhang
    Julong Tan
    Journal of Inequalities and Applications, 2014
  • [27] A new generalization of the Hermitian and skew-Hermitian splitting method for solving the continuous Sylvester equation
    Salkuyeh, Davod Khojasteh
    Bastani, Mehdi
    TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, 2018, 40 (01) : 303 - 317
  • [28] Some Refined Eigenvalue Perturbation Bounds for Two-by-Two Block Hermitian Matrices
    Wu, Xianping
    Li, Wen
    Peng, Xiaofei
    EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2015, 5 (02) : 126 - 137
  • [29] Improved convergence theorems for new Hermitian and skew-Hermitian splitting methods
    Li, Cui-Xia
    Wu, Shi-Liang
    LINEAR & MULTILINEAR ALGEBRA, 2017, 65 (03): : 510 - 513
  • [30] Asymmetric Hermitian and skew-Hermitian splitting algorithm for linear complementarity problem
    Duan, Banxiang
    Zhu, Xiaoping
    Wu, Jiaoyu
    PROCEEDINGS OF 2010 3RD IEEE INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND INFORMATION TECHNOLOGY, VOL 9 (ICCSIT 2010), 2010, : 188 - 191
12345