Real structure-preserving algorithm for quaternion equality constrained least squares problem

Quaternion equality constrained least squares problem is an extremely effective tool in studying quantum mechanics and quantum field theory. However, the computation of the quaternion equality constrained least squares problem is extremely complex. In this paper, we first prove that quaternion equality constrained least squares problem is equivalent to weighted quaternion least squares problem when the parameter tau -> +infinity. Then, for weighted quaternion least squares problem, applying the special structure of real representation of quaternion, we propose real structure-preserving algorithm to obtain the solution of quaternion equality contained least squares problem. At last, we give numerical examples to illustrate the effectiveness of our method.