## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2013, Special Issue (2012), Article ID 217540, 14 pages.

### An Efficient Algorithm for the Reflexive Solution of the Quaternion Matrix Equation $AXB+C{X}^{H}D=F$

Ning Li, Qing-Wen Wang, and Jing Jiang

#### Abstract

We propose an iterative algorithm for solving the reflexive solution of the quaternion matrix equation $AXB+C{X}^{H}D=F$. When the matrix equation is consistent over reflexive matrix $X$, 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 ${X}_{0}$ 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.

#### Article information

**Source**

J. Appl. Math., Volume 2013, Special Issue (2012), Article ID 217540, 14 pages.

**Dates**

First available in Project Euclid: 14 March 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1394807330

**Digital Object Identifier**

doi:10.1155/2013/217540

**Mathematical Reviews number (MathSciNet)**

MR3032252

**Zentralblatt MATH identifier**

1268.65060

#### Citation

Li, Ning; Wang, Qing-Wen; Jiang, Jing. An Efficient Algorithm for the Reflexive Solution of the Quaternion Matrix Equation $AXB+C{X}^{H}D=F$. J. Appl. Math. 2013, Special Issue (2012), Article ID 217540, 14 pages. doi:10.1155/2013/217540. https://projecteuclid.org/euclid.jam/1394807330