Newton's iterative method to solve a nonlinear matrix equation

被引：5

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.

引用

页码：1867 / 1878

页数：12

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