On the Nonlinear Matrix Equation Based on Engineering Calculation

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.

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Perturbation Analysis of a Nonlinear Matrix Equation Arising in Tree-Like Stochastic Processes

Advanced Computing in Industrial Mathematics - Studies in Computational Intelligence ◽

10.1007/978-3-319-97277-0_4 ◽

2018 ◽

pp. 37-50

Author(s):

Vera Angelova

Keyword(s):

Stochastic Processes ◽

Perturbation Analysis ◽

Matrix Equation ◽

Nonlinear Matrix Equation ◽

Nonlinear Matrix

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On the existence of extremal positive definite solutions of the nonlinear matrix equation Xr+∑i=1mAi∗XδiAi=I

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2009.12.021 ◽

2010 ◽

Vol 51 (9-10) ◽

pp. 1107-1117 ◽

Cited By ~ 12

Author(s):

A.M. Sarhan ◽

Naglaa M. El-Shazly ◽

Enas M. Shehata

Keyword(s):

Matrix Equation ◽

Positive Definite ◽

Nonlinear Matrix Equation ◽

Nonlinear Matrix

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Residual bounds of the nonlinear matrix equation X + A*F(X)A = Q

International Journal of Data Science ◽

10.1504/ijds.2016.081370 ◽

2016 ◽

Vol 1 (4) ◽

pp. 340

Author(s):

Ivan Popchev ◽

Vera Angelova

Keyword(s):

Matrix Equation ◽

Nonlinear Matrix Equation ◽

Nonlinear Matrix

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

Applied Mathematics and Computation ◽

10.1016/s0096-3003(03)00360-6 ◽

2004 ◽

Vol 151 (2) ◽

pp. 533-541 ◽

Cited By ~ 22

Author(s):

Salah M. El-Sayed ◽

Asmaa M. Al-Dbiban

Keyword(s):

Matrix Equation ◽

Positive Definite ◽

Nonlinear Matrix Equation ◽

Nonlinear Matrix

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On the Positive Definite Solutions of a Nonlinear Matrix Equation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.380-384.1434 ◽

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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