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.
引用
收藏
页码：1867 / 1878
页数：12
相关论文
共 50 条
  • [41] An Iterative Discontinuous Galerkin Method for Solving the Nonlinear Poisson Boltzmann Equation
    Yin, Peimeng
    Huang, Yunqing
    Liu, Hailiang
    COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2014, 16 (02) : 491 - 515
  • [42] TWO INVERSION-FREE ITERATIVE ALGORITHMS FOR COMPUTING THE MAXIMAL POSITIVE DEFINITE SOLUTION OF THE NONLINEAR MATRIX EQUATION
    Huang, Na
    Ma, Changfeng
    APPLIED AND COMPUTATIONAL MATHEMATICS, 2015, 14 (02) : 158 - 167
  • [43] Two modifications of efficient newton-type iterative method and two variants of Super-Halley's method for solving nonlinear equations
    Hu, Yunhong
    Fang, Liang
    JOURNAL OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING, 2019, 19 (01) : 13 - 22
  • [44] Some iterative methods for the largest positive definite solution to a class of nonlinear matrix equation
    Bao-Hua Huang
    Chang-Feng Ma
    Numerical Algorithms, 2018, 79 : 153 - 178
  • [45] On the nonlinear matrix equation
    Jin, Zhixiang
    Zhai, Chengbo
    LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (19) : 4467 - 4482
  • [46] Note on the improvement of Newton's method for system of nonlinear equations
    Wu, Xinyuan
    APPLIED MATHEMATICS AND COMPUTATION, 2007, 189 (02) : 1476 - 1479
  • [47] An iterative method to solve the algebraic eigenvalue problem
    Emili Besalú
    Ramon Carbó‐Dorca
    Journal of Mathematical Chemistry, 1997, 21 : 395 - 412
  • [48] NONLINEAR WAVES IN NEWTON'S CRADLE AND THE DISCRETE p-SCHRODINGER EQUATION
    James, Guillaume
    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2011, 21 (11) : 2335 - 2377
  • [49] An Efficient Sixth-Order Convergent Newton-type Iterative Method for Nonlinear Equations
    Hu, Zhongyong
    Fang, Liang
    Li, Lianzhong
    Chen, Rui
    ADVANCES IN MANUFACTURING TECHNOLOGY, PTS 1-4, 2012, 220-223 : 2585 - 2588
  • [50] Enhancing the practicality of Newton–Cotes iterative method
    Ramya Sadananda
    Santhosh George
    Ajil Kunnarath
    Jidesh Padikkal
    Ioannis K. Argyros
    Journal of Applied Mathematics and Computing, 2023, 69 : 3359 - 3389
12345