Open AccessThree special kinds of least squares solutions for the quaternion generalized Sylvester matrix equation
Author(s) -
Anli Wei,
AUTHOR_ID,
Ying Li,
Wenxv Ding,
Jianli Zhao,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022280
Subject(s) - quaternion , mathematics , matrix (chemical analysis) , sylvester equation , representation (politics) , real representation , algebra over a field , norm (philosophy) , matrix representation , algorithm , pure mathematics , eigenvalues and eigenvectors , geometry , irreducible representation , physics , materials science , quantum mechanics , politics , political science , law , composite material , group (periodic table)
In this paper, we propose an efficient method for some special solutions of the quaternion matrix equation $ AXB+CYD = E $. By integrating real representation of a quaternion matrix with $ \mathcal{H} $-representation, we investigate the minimal norm least squares solution of the previous quaternion matrix equation over different constrained matrices and obtain their expressions. In this way, we first apply $ \mathcal{H} $-representation to solve quaternion matrix equation with special structure, which not only broadens the application scope of $ \mathcal{H} $-representation, but further expands the research idea of solving quaternion matrix equation. The algorithms only include real operations. Consequently, it is very simple and convenient, and it can be applied to all kinds of quaternion matrix equation with similar problems. The numerical example is provided to illustrate the feasibility of our algorithms.