Two iterative algorithms for the reflexive and Hermitian reflexive solutions of the generalized Sylvester matrix equation-Reference-Cited by-同舟云学术

Two iterative algorithms for the reflexive and Hermitian reflexive solutions of the generalized Sylvester matrix equation

Published:2013-07-08 Issue:3 Volume:21 Page:483-492
ISSN:1077-5463
Container-title:Journal of Vibration and Control
language:en
Short-container-title:Journal of Vibration and Control

Author:

Ramadan Mohamed A¹,El-Danaf Talaat S¹,Bayoumi Ahmed M E²

Affiliation:

1. Department of Mathematics, Menoufia University, Egypt

2. Department of Mathematics, Ain Shams University, Egypt

Abstract

This paper is concerned with iterative solutions to the generalized Sylvester matrix equation [Formula: see text]. Two iterative algorithms are presented to obtain the reflexive and Hermitian reflexive solutions. With these iterative algorithms, for any initial reflexive and Hermitian reflexive matrices the solutions can be obtained. Some needed lemmas are first stated, then two theorems are stated and proved where the iterative solutions are obtained. Finally, we report two numerical examples to verify the theoretical results.

Publisher

SAGE Publications

Subject

Mechanical Engineering,Mechanics of Materials,Aerospace Engineering,Automotive Engineering,General Materials Science

Link

http://journals.sagepub.com/doi/pdf/10.1177/1077546312474859

Reference25 articles.

1. Convergence of an iterative method for solving Sylvester matrix equations over reflexive matrices

2. Hierarchical least squares identification methods for multivariable systems

3. Gradient based iterative algorithms for solving a class of matrix equations

4. Hierarchical gradient-based identification of multivariable discrete-time systems

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