ITERATIVE ALGORITHM FOR THE GENERALIZED (P;Q)-REFLEXIVE SOLUTION OF A QUATERNION MATRIX EQUATION WITH j-CONJUGATE OF THE UNKNOWNS

In the present paper, we propose an iterative algorithm for solving the generalized (P;Q)-reflexive solution of the quater-nion matrix equation Σu l=1 AlXBl+ Σv s=1 Cs eX Ds = F. By this iterative algorithm, the solvability of the problem can be determined auto- matically. When the matrix equation is consistent over a general- ized (P;Q)-re exive matrix X, a generalized (P;Q)-re exive solu- tion can be obtained within nite iteration steps in the absence of roundoff errors, and the least Frobenius norm generalized (P;Q)- re exive solution can be obtained by choosing an appropriate initial iterative matrix. Furthermore, the optimal approximate general- ized (P;Q)-re exive solution to a given matrix X0 can be derived by nding the least Frobenius norm generalized (P;Q)-re exive so- lution of a new corresponding quaternion matrix equation. Finally, two numerical examples are given to illustrate the efficiency of the proposed methods.