Structured perturbation analysis for an infinite size quasi-Toeplitz matrix equation with applications

2021 ◽  
Author(s):  
Hyun-Min Kim ◽  
Jie Meng
Keyword(s):  
Perturbation Analysis ◽  
Matrix Equation ◽  
Toeplitz Matrix

PERTURBATION ANALYSIS FOR THE COMPLEX MATRIX EQUATION X – AH √X-1 A = I

2005 ◽  
Vol 38 (1) ◽  
pp. 43-47
Author(s):  
Vera Angelova ◽  
Mihail Konstantinov ◽  
Petko Petkov ◽  
Ivan Popchev
Keyword(s):  
Perturbation Analysis ◽  
Matrix Equation ◽  
Complex Matrix

Least squares Toeplitz matrix solutions of the matrix equation

2016 ◽  
Vol 65 (9) ◽  
pp. 1867-1877 ◽  
Author(s):  
Yongxin Yuan ◽  
Wenhua Zhao ◽  
Hao Liu
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Toeplitz Matrix ◽  
The 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 Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zhigang Jia ◽  
Meixiang Zhao ◽  
Minghui Wang ◽  
Sitao Ling
Keyword(s):  
Iterative Algorithm ◽  
Perturbation Analysis ◽  
Matrix Equation ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Polynomial Matrix ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Solvability Theory ◽  
Adjoint Polynomial

The solvability theory of an important self-adjoint polynomial matrix equation is presented, including the boundary of its Hermitian positive definite (HPD) solution and some sufficient conditions under which the (unique or maximal) HPD solution exists. The algebraic perturbation analysis is also given with respect to the perturbation of coefficient matrices. An efficient general iterative algorithm for the maximal or unique HPD solution is designed and tested by numerical experiments.

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