A finite iterative algorithm for generalized quaternion matrix equation with Hamiltonian solution

Purpose This paper presents a finite iterative algorithm for a generalized quaternion matrix equation with a Hamiltonian solution. It is proven that if the quaternion matrix equation is consistent, the solution can be obtained for any initial quaternion matrix within a finite number of iterative steps, in the absence of round-off errors. Design/methodology/approach (1) It is proven that if the quaternion matrix equation is consistent. (2) The solution can be obtained for any initial quaternion matrix within a finite number of iterative steps, in the absence of round-off errors. (3) Two numerical examples are presented to demonstrate the efficiency of this method. These algorithms can run over Mat-Lab or Maple software in the presence of quaternion backage. Findings This paper presents a finite iterative algorithm for a generalized quaternion matrix equation with a Hamiltonian solution. It is proven that if the quaternion matrix equation is consistent, the solution can be obtained for any initial quaternion matrix within a finite number of iterative steps, in the absence of round-off errors. Two numerical examples are presented to demonstrate the efficiency of this method. These algorithms can run over Mat-Lab or Maple software in the presence of quaternion backage. Originality/value This study provides a novel iterative algorithm for a generalized quaternion matrix equation with a Hamiltonian solution, which has not been explored in previous literature.