ON THE EXTREME SOLUTIONS OF A CLASS OF NONLINEAR MATRIX EQUATION

被引：0
作者：
Meng, Jie [1 ]
Lee, Hosoo [2 ]
Kim, Hyun-Min [1 ,3 ]
机构：
[1] Pusan Natl Univ, Finance Fishery Manufacture Ind Math Ctr Big Data, Busan 46241, South Korea
[2] Jeju Natl Univ, Elementary Educ Res Inst, Jeju 63294, South Korea
[3] Pusan Natl Univ, Dept Math, Busan 46241, South Korea
来源：
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2020年 / 21卷 / 01期
基金：
新加坡国家研究基金会;
关键词：
Nonlinear matrix equation; positive definite solution; cyclic reduction; convergence analysis; POSITIVE-DEFINITE SOLUTIONS;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The nonlinear matrix equation X + A*(X) over bar (-1) A = Q, where both the coefficient matrices and the unknown are complex matrices and Q is Hermitian positive definite, is considered. Some new and useful properties of the maximal and minimal positive definite solutions of the matrix equation are obtained. We show that an iteration method with a quadratic convergence rate can be effectively applied to compute the extreme solutions. This iteration method is based on cyclic reduction. Numerical examples and comparisons are provided to show the efficiency of the proposed iteration method.
引用
收藏
页码：77 / 87
页数：11
相关论文
共 50 条
  • [21] On positive definite solutions of nonlinear matrix equation Xs-A*X-tA = Q
    Yin, Xiao-yan
    Liu, San-yang
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (01) : 27 - 34
  • [22] AN ITERATIVE METHOD TO SOLVE A NONLINEAR MATRIX EQUATION
    Peng, Jingjing
    Liao, Anping
    Peng, Zhenyun
    [J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2016, 31 : 620 - 632
  • [23] NEWTON'S METHOD FOR A NONLINEAR MATRIX EQUATION
    Hasanov, Vejdi
    Hakkaev, Sevdzhan
    [J]. COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, 2015, 68 (08): : 973 - 982
  • [24] On the nonlinear matrix equation based on engineering calculation
    Gao, Dongjie
    [J]. TRENDS IN BUILDING MATERIALS RESEARCH, PTS 1 AND 2, 2012, 450-451 : 158 - 161
  • [25] ON A NONLINEAR MATRIX EQUATION ARISING IN NANO RESEARCH
    Guo, Chun-Hua
    Kuo, Yueh-Cheng
    Lin, Wen-Wei
    [J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2012, 33 (01) : 235 - 262
  • [26] Some investigation on Hermitian positive-definite solutions of a nonlinear matrix equation
    Pei, Weijuan
    Wu, Guoxing
    Zhou, Duanmei
    Liu, Yitian
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2014, 91 (05) : 872 - 880
  • [27] An accelerated technique for solving the positive definite solutions of a class of nonlinear matrix equations
    Chiang, Chun-Yueh
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2017, 354 (15): : 7088 - 7118
  • [28] Solvability for a Nonlinear Matrix Equation
    J. Li
    Y. H. Zhang
    [J]. Bulletin of the Iranian Mathematical Society, 2018, 44 : 1171 - 1184
  • [29] On equations that are equivalent to the nonlinear matrix equation X plus A*X-α A = Q
    Wang, Xing Tao
    Li, Yuan Min
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (08) : 2441 - 2449
  • [30] Some iterative methods for the largest positive definite solution to a class of nonlinear matrix equation
    Bao-Hua Huang
    Chang-Feng Ma
    [J]. Numerical Algorithms, 2018, 79 : 153 - 178
12345