Springer Nature
Advances in Applied Clifford Algebras
,  volume 35 ,  issue 1 ,  publication number 6

STP Method for Solving the Least Squares Special Solutions of Quaternion Matrix Equations

Weihua Chen 1
, 
Caiqin Song 1
1
 
School of Mathematical Sciences, University of Jinan, Jinan, China | 
Publication type: Journal Article
Publication date: 2024-12-02
Springer Nature
scimago Q2
wos Q2
SJR: 0.636
CiteScore: 2.5
Impact factor: 1.2
ISSN: 01887009, 16614909
Abstract
In this paper, we apply the semi-tensor product of matrices and the real vector representation of a quaternion matrix to find the least squares lower (upper) triangular Toeplitz solution of $$AX-XB=C$$ , $$AXB-CX^{T}D=E$$ and (anti)centrosymmetric solution of $$AXB-CYD=E$$ . And the expressions of the least squares lower (upper) triangular Toeplitz and (anti)centrosymmetric solution for the studied equations are derived. Additionally, the necessary and sufficient conditions for the existence of solutions and general expression of the studied equations are given. Eventually, some numerical examples are provided for showing the validity and superiority of our method.
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Chen W. et al. STP Method for Solving the Least Squares Special Solutions of Quaternion Matrix Equations // Advances in Applied Clifford Algebras. 2024. Vol. 35. No. 1. 6
GOST all authors (up to 50) Copy
Chen W., Song C. STP Method for Solving the Least Squares Special Solutions of Quaternion Matrix Equations // Advances in Applied Clifford Algebras. 2024. Vol. 35. No. 1. 6
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RIS Copy
TY - JOUR
DO - 10.1007/s00006-024-01367-2
UR - https://link.springer.com/10.1007/s00006-024-01367-2
TI - STP Method for Solving the Least Squares Special Solutions of Quaternion Matrix Equations
T2 - Advances in Applied Clifford Algebras
AU - Chen, Weihua
AU - Song, Caiqin
PY - 2024
DA - 2024/12/02
PB - Springer Nature
IS - 1
VL - 35
SN - 0188-7009
SN - 1661-4909
ER -
BibTex
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@article{2024_Chen,
author = {Weihua Chen and Caiqin Song},
title = {STP Method for Solving the Least Squares Special Solutions of Quaternion Matrix Equations},
journal = {Advances in Applied Clifford Algebras},
year = {2024},
volume = {35},
publisher = {Springer Nature},
month = {dec},
url = {https://link.springer.com/10.1007/s00006-024-01367-2},
number = {1},
pages = {6},
doi = {10.1007/s00006-024-01367-2}
}