On Iterative Algorithm and Perturbation Analysis for the Nonlinear Matrix Equation

2021 ◽  
Author(s):  
Chacha Stephen Chacha
Keyword(s):  
Iterative Algorithm ◽  
Perturbation Analysis ◽  
Matrix Equation ◽  
Nonlinear Matrix Equation ◽  
Nonlinear Matrix

scholarly journals Comment on “Perturbation Analysis of the Nonlinear Matrix Equation ”

2013 ◽  
Vol 2013 ◽  
pp. 1-2 ◽  
Author(s):  
Maher Berzig ◽  
Erdal Karapınar
Keyword(s):  
Perturbation Analysis ◽  
Matrix Equation ◽  
Nonlinear Matrix Equation ◽  
The Matrix ◽  
Nonlinear Matrix

We show that the perturbation estimate for the matrix equation due to J. Li, is wrong. Our discussion is supported by a counterexample.

scholarly journals Perturbation Analysis of the Nonlinear Matrix Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jing Li
Keyword(s):  
Approximate Solution ◽  
Condition Number ◽  
Perturbation Analysis ◽  
Matrix Equation ◽  
Nonlinear Matrix Equation ◽  
Backward Error ◽  
Numerical Examples ◽  
Perturbation Bounds ◽  
Nonlinear Matrix ◽  
Theoretical Results

Consider the nonlinear matrix equation with . Two perturbation bounds and the backward error of an approximate solution to the equation are derived. Explicit expressions of the condition number for the equation are obtained. The theoretical results are illustrated by numerical examples.

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