An Iterative Algorithm for the Generalized Reflexive Solution Group of a System of Quaternion Matrix Equations

In the present paper, an iterative algorithm is proposed for solving the generalized (P,Q)-reflexive solution group of a system of quaternion matrix equations ∑l=1M(AlsXlBls+ClsXl˜Dls)=Fs,s=1,2,…,N. A generalized (P,Q)-reflexive solution group, as well as the least Frobenius norm generalized (P,Q)-r...

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Bibliographic Details
Published in:Symmetry (Basel) Vol. 14; no. 4; p. 776
Main Authors: Jiang, Jing, Li, Ning
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.04.2022
Subjects:
Algorithms
Iterative algorithms
Iterative methods
Mathematical analysis
Matrix
Quaternions
ISSN:2073-8994, 2073-8994
Online Access:Get full text
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Summary:In the present paper, an iterative algorithm is proposed for solving the generalized (P,Q)-reflexive solution group of a system of quaternion matrix equations ∑l=1M(AlsXlBls+ClsXl˜Dls)=Fs,s=1,2,…,N. A generalized (P,Q)-reflexive solution group, as well as the least Frobenius norm generalized (P,Q)-reflexive solution group, can be derived by choosing appropriate initial matrices, respectively. Moreover, the optimal approximate generalized (P,Q)-reflexive solution group to a given matrix group can be derived by computing the least Frobenius norm generalized (P,Q)-reflexive solution group of a reestablished system of matrix equations. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm.
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content type line 14
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14040776