An effective real structure-preserving algorithm for the quaternion indefinite least squares problem

This paper concentrates on the quaternion indefinite least squares (QILS) problem. Firstly, we define the quaternion J-unitary matrix and the quaternion hyperbolic Givens rotation, and study their properties. Then, based on these, we investigate the quaternion hyperbolic QR factorization, and purpose its real structure-preserving (SP) algorithm by the real representation (Q-RR) matrix of the quaternion matrix. Immediately after, we explore the solution of the QILS problem, and give a real SP algorithm of solving the QILS problem. Eventually, to illustrate the effectiveness of proposed algorithms, we offer numerical examples.