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2013 An Efficient Algorithm for the Reflexive Solution of the Quaternion Matrix Equation A X B + C X H D = F
Ning Li, Qing-Wen Wang, Jing Jiang
J. Appl. Math. 2013(SI03): 1-14 (2013). DOI: 10.1155/2013/217540

Abstract

We propose an iterative algorithm for solving the reflexive solution of the quaternion matrix equation A X B + 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.

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Ning Li. Qing-Wen Wang. Jing Jiang. "An Efficient Algorithm for the Reflexive Solution of the Quaternion Matrix Equation A X B + C X H D = F ." J. Appl. Math. 2013 (SI03) 1 - 14, 2013. https://doi.org/10.1155/2013/217540

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1268.65060
MathSciNet: MR3032252
Digital Object Identifier: 10.1155/2013/217540

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI03 • 2013
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