Newton's iterative method to solve a nonlinear matrix equation

被引：4
|
作者：
Peng, Jingjing [1 ]
Liao, Anping [2 ]
Peng, Zhenyun [3 ]
Chen, Zhencheng [4 ]
机构：
[1] Shanghai Univ, Coll Sci, Shanghai, Peoples R China
[2] Hunan Univ, Coll Math & Econometr, Changsha, Hunan, Peoples R China
[3] Guilin Univ Elect Technol, Sch Math & Comp Sci, Guangxi Coll & Univ Key Lab Data Anal & Computat, Guilin 541004, Peoples R China
[4] Guilin Univ Elect Technol, Sch Life & Environm Sci, Guilin, Peoples R China
来源：
LINEAR & MULTILINEAR ALGEBRA | 2019年 / 67卷 / 09期
基金：
中国国家自然科学基金;
关键词：
Nonlinear matrix equation; iterative method; Newton's iterative method; fixed point iterative method; POSITIVE-DEFINITE SOLUTIONS; EXTREME SOLUTIONS; A-ASTERISK-X(-1)A; EXISTENCE; X-2;
D O I：
10.1080/03081087.2018.1472736
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, Newton's iterative method to solve the nonlinear matrix equation x + A* X-n A = Q is studied. For the given initial matrix Q, the main results that the matrix sequence generated by the iterative method is contained in a fixed open ball, and that the matrix sequence generated by the iterative method converges to the only solution of the nonlinear matrix equation in a fixed closed ball are proved. In addition, the error estimate of the approximate solution in the closed ball and a numerical example to illustrate the convergence results are given.
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页码：1867 / 1878
页数：12
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