On iterative methods for the quadratic matrix equation with M-matrix

被引：11
|
作者：
Yu, Bo [1 ]
Dong, Ning [1 ]
Tang, Qiong [1 ]
Wen, Feng-Hua [2 ]
机构：
[1] Hunan Univ Technol, Sch Sci, Zhuzhou 412008, Peoples R China
[2] Changsha Univ Sci & Technol, Sch Econometr & Management, Changsha 410114, Hunan, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 218卷 / 07期
基金：
湖南省自然科学基金;
关键词：
Quadratic matrix equation; M-matrix; Fixed-point iteration; Newton's method; Bernoulli's method; ALGEBRAIC RICCATI-EQUATIONS; EIGENVALUE PROBLEMS; NUMERICAL-SOLUTION; NEWTONS METHOD;
D O I：
10.1016/j.amc.2011.08.070
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider Newton's method and Bernoulli's method for a quadratic matrix equation arising from an overdamped vibrating system. By introducing M-matrix to this equation, we provide a sufficient condition for the existence of the primary solution. Moreover, we show that Newton's method and Bernoulli's method with an initial zero matrix converge to the primary solvent under the proposed sufficient condition. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：3303 / 3310
页数：8
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