Journal of Applied Mathematics
Volume 2013 (2013), Article ID 217540, 14 pages
http://dx.doi.org/10.1155/2013/217540
Research Article

An Efficient Algorithm for the Reflexive Solution of the Quaternion Matrix Equation

Ning Li,1,2 Qing-Wen Wang,1 and Jing Jiang3

1Department of Mathematics, Shanghai University, Shanghai 200444, China
2School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250002, China
3Department of Mathematics, Qilu Normal University, Jinan 250013, China

Received 3 October 2012; Accepted 4 December 2012

Academic Editor: P. N. Shivakumar

Copyright © 2013 Ning Li et al. 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.

Abstract

We propose an iterative algorithm for solving the reflexive solution of the quaternion matrix equation . When the matrix equation is consistent over reflexive matrix , a reflexive solution can be obtained within finite iteration steps in the absence of roundoff errors. By the proposed iterative algorithm, the least Frobenius norm reflexive solution of the matrix equation can be derived when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate reflexive solution to a given reflexive matrix can be derived by finding the least Frobenius norm reflexive solution of a new corresponding quaternion matrix equation. Finally, two numerical examples are given to illustrate the efficiency of the proposed methods.