An iterative algorithm for least squares problem in quaternionic quantum theory

Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations AXB=EAXB=E that is appropriate when there is error in the matrix E. In this paper, by means of real representation of a quaternion matrix, we introduce a concept of norm of quaternion matrices, which is different from that in [T. Jiang, L. Chen, Algebraic algorithms for least squares problem in quaternionic quantum theory, Comput. Phys. Comm. 176 (2007) 481–485; T. Jiang, M. Wei, Equality constrained least squares problem over quaternion field, Appl. Math. Lett. 16 (2003) 883–888], and derive an iterative method for finding the minimum-norm solution of the QLS problem in quaternionic quantum theory.