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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 831656, 15 pages
Research Article

Iterative Algorithm for Solving a Class of Quaternion Matrix Equation over the Generalized -Reflexive Matrices

1School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong Province 250002, China
2Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 18 April 2013; Accepted 12 August 2013

Academic Editor: Douglas Anderson

Copyright © 2013 Ning Li and Qing-Wen Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The matrix equation which includes some frequently investigated matrix equations as its special cases, plays important roles in the system theory. In this paper, we propose an iterative algorithm for solving the quaternion matrix equation over generalized -reflexive matrices. The proposed iterative algorithm automatically determines the solvability of the quaternion matrix equation over generalized -reflexive matrices. When the matrix equation is consistent over generalized -reflexive matrices, the sequence generated by the introduced algorithm converges to a generalized -reflexive solution of the quaternion matrix equation. And the sequence converges to the least Frobenius norm generalized -reflexive solution of the quaternion matrix equation when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate generalized -reflexive solution for a given generalized -reflexive matrix can be derived. The numerical results indicate that the iterative algorithm is quite efficient.