An efficient method for least-squares problem of the quaternion matrix equation X - A(X)over-capB = C

In this paper, we consider the quaternion matrix equation X - A (X) over capB = C, and study its minimal norm least squares solution,j-self-conjugate least-squares solution and anti-j-self-conjugate least-squares solution. By the real representation matrices of quaternion matrices, their particular structure and the properties of Frobenius norm, we convert above least-squares problems into corresponding problems of real matrix equations. The final results of the expressions only involve real matrices, and thus, the corresponding algorithms only involve real operations. Compared with the existing results, they are more convenient and efficient, which are also illustrated by the last two numerical examples.

Automated summary

This paper investigates the minimal norm least squares solution, j-self-conjugate least-squares solution, and anti-j-self-conjugate least-squares solution of the quaternion matrix equation. By converting the quaternion matrix into a real matrix equation, the algorithms involved only real matrices and operations. These algorithms are more convenient and efficient compared to existing results.