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

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 Finite Iterative Algorithm for Solving a Complex of Conjugate and Transpose Matrix Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Mohamed A. Ramadan ◽  
Talaat S. El-Danaf ◽  
Ahmed M. E. Bayoumi
Keyword(s):  
Iterative Algorithm ◽  
Matrix Equation ◽  
Complex Matrix ◽  
Existence Of A Solution ◽  
Numerical Example ◽  
Iterative Solutions ◽  
Theoretical Results

We consider an iterative algorithm for solving a complex matrix equation with conjugate and transpose of two unknowns of the form: A1VB1+C1WD1+A2V¯B2+C2W¯D2+A3VHB3+C3WHD3+A4VTB4 + C4WTD4=E. With the iterative algorithm, the existence of a solution of this matrix equation can be determined automatically. When this matrix equation is consistent, for any initial matrices V1, W1 the solutions can be obtained by iterative algorithm within finite iterative steps in the absence of round-off errors. Some lemmas and theorems are stated and proved where the iterative solutions are obtained. A numerical example is given to illustrate the effectiveness of the proposed method and to support the theoretical results of this paper.

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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