scholarly journals The iterative methods for solving nonlinear matrix equation X+A⋆X−1A+B⋆X−1B=Q

2013 ◽  
Vol 2013 (1) ◽  
pp. 229 ◽  
Author(s):  
Sarah Vaezzadeh ◽  
Seyyed Vaezpour ◽  
Reza Saadati ◽  
Choonkil Park
Keyword(s):  
Iterative Methods ◽  
Matrix Equation ◽  
Nonlinear Matrix Equation ◽  
Nonlinear Matrix

scholarly journals Elegant Iterative Methods for Solving a Nonlinear Matrix Equation X-A* eX A=I

2021 ◽  
Vol 47 (3) ◽  
pp. 1033-1040
Author(s):  
Chacha S Chacha
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Newton’S Method ◽  
Matrix Equation ◽  
Newton's Method ◽  
Fixed Point Method ◽  
Point Method ◽  
Computational Time ◽  
Nonlinear Matrix Equation ◽  
Nonlinear Matrix

The nonlinear matrix equation   was solved by Gao (2016) via standard fixed point method. In this paper, three more elegant iterative methods are proposed to find the approximate solution of the nonlinear matrix equation  namely: Newton’s method; modified fixed point method and a combination of Newton’s method and fixed point method. The convergence of Newton’s method and modified fixed point method are derived. Comparative numerical experimental results indicate that the new developed algorithms have both less computational time and good convergence properties when compared to their respective standard algorithms. Keywords: Hermitian positive definite solution; nonlinear matrix equation; modified fixed point method; iterative method

scholarly journals On the Positive Definite Solutions of a Nonlinear Matrix Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1434-1438
Author(s):  
Ming Hui Wang ◽  
Chun Yan Liang ◽  
Shan Rui Hu
Keyword(s):  
Fixed Point ◽  
Matrix Equation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Positive Definite ◽  
Matrix Inversion ◽  
Nonlinear Matrix Equation ◽  
Nonlinear Matrix

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case are discussed. An algorithm that avoids matrix inversion with the case is proposed.

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