An iterative algorithm for least squares problem in quaternionic quantum theory Original Research Article

Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations image 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.