Iterative convergence analysis of subpositive definite linear systems over quaternion field

In this paper, we discuss convergent splittings of sub-positive definite matrix A over quaternion field. Meanwhile, the QSOR iterative algorithm of the sub-positive definite linear systems AX = B over quaternion field are structured, and convergence of the algorithm is described by using right eigenvalue maximum norm of the quaternion matrix, and the optimal range of parameters are obtained. Secondly, applying the structure preserving iterative of QSOR to realize numerical solutions of the linear systems. The numerical results indicate the method presented in this paper is feasible and efficient.