The least squares η-Hermitian problems of quaternion matrix equation AHXA + BHYB=C

Two special kinds of least squares solutions for the quaternion matrix equation AXB+CXD=E

Ela Two Special Kinds of Least Squares Solutions for the Quaternion Matrix Equation

By using the complex representation of quaternion matrices, the Moore–Penrose generalized inverse and the Kronecker product of matrices, the expressions of the least squares η-Hermitian solution with the least norm and the expressions of the least squares η-anti-Hermitian solution with the least norm are derived for the matrix equation AXB+CXD = E over quaternions.

The least-square bisymmetric solution to a quaternion matrix equation with applications

In this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation XA=B to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. Futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. As applications, we derive sufficient and necess...

Global least squares solution of matrix equation $sum_{j=1}^s A_jX_jB_j = E$

In this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s A_jX_jB_j = E$. This method is based on the global least squares (GL-LSQR) method for solving the linear system of equations with the multiple right hand sides. For applying the GL-LSQR algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. It is p...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations