On positive definite solutions of the nonlinear matrix equation X+A★X−nA=I

2004 ◽  
Vol 151 (2) ◽  
pp. 533-541 ◽  
Author(s):  
Salah M. El-Sayed ◽  
Asmaa M. Al-Dbiban
Keyword(s):  
Matrix Equation ◽  
Positive Definite ◽  
Nonlinear Matrix Equation ◽  
Nonlinear Matrix

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.

On the Nonlinear Matrix Equation Based on Engineering Calculation

2012 ◽  
Vol 450-451 ◽  
pp. 158-161
Author(s):  
Dong Jie Gao
Keyword(s):  
Matrix Equation ◽  
Iteration Method ◽  
Engineering Calculation ◽  
Positive Definite ◽  
Nonlinear Matrix Equation ◽  
Positive Definite Solution ◽  
Nonlinear Matrix ◽  
Definite Solution

We consider the positive definite solution of the nonlinear matrix equation . We prove that the equation always has a unique positive definite solution. The iteration method for the equation is given.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Panpan Liu ◽  
Shugong Zhang ◽  
Qingchun Li
Keyword(s):  
Matrix Equation ◽  
Positive Definite ◽  
Nonlinear Matrix Equation ◽  
Nonlinear Matrix
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