An Efficient Algorithm for the Reflexive Solution of the Quaternion Matrix Equation AXB+CXHD=F

We propose an iterative algorithm for solving the reflexive solution of the quaternion matrix equation AXB+CXHD=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 ite...

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Bibliographic Details
Published in:Journal of applied mathematics 2013, Vol.2013 (2013), p.1-14
Main Authors: Li, Ning, Jiang, Jing, Wang, Qing-Wen
Format: Article
Language:English
Online Access:Get full text
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Summary:We propose an iterative algorithm for solving the reflexive solution of the quaternion matrix equation AXB+CXHD=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 X0 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.
ISSN:1110-757X
1687-0042
DOI:10.1155/2013/217540