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

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2024-12-02 DOI:10.1007/s00006-024-01367-2

Weihua Chen, Caiqin Song

引用次数: 0

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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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.