A finite iterative algorithm for solving a single-variable quaternion system of matrix equations

This paper introduces a finite iterative algorithm for solving a single-variable quaternion system of matrix equations. It is theoretically proven that if the system is consistent, the solution can be achieved from any initial quaternion matrix within a finite number of iterations, assuming the absence of round-off errors. A special case of this equation is studied, which contains the k -conjugate of the unknown matrix. Numerical examples are provided to illustrate the effectiveness and computational efficiency of the proposed algorithms.