An Iterative Algorithm for the Generalized Reflexive Solution Group of a System of Quaternion Matrix Equations

In the present paper, an iterative algorithm is proposed for solving the generalized (P, Q)- reflexive solution group of a system of quaternion matrix equations Sigma(M)(l=1) (A(ls)X(l)B(ls) + C-ls(X) over tilde D-l(ls)) = F-s, s = 1, 2, ..., N. A generalized (P, Q)-reflexive solution group, as well as the least Frobenius norm generalized (P, Q)-reflexive solution group, can be derived by choosing appropriate initial matrices, respectively. Moreover, the optimal approximate generalized (P, Q)-reflexive solution group to a given matrix group can be derived by computing the least Frobenius norm generalized (P, Q)-reflexive solution group of a reestablished system of matrix equations. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm.

Automated summary

In this paper, an iterative algorithm is proposed for solving the generalized (P, Q)-reflexive solution group of quaternion matrix equations. The algorithm can derive the generalized (P, Q)-reflexive solution group and the least Frobenius norm generalized (P, Q)-reflexive solution group by choosing appropriate initial matrices. Moreover, the optimal approximate generalized (P, Q)-reflexive solution group to a given matrix group can be obtained by computing the least Frobenius norm generalized (P, Q)-reflexive solution group of a reestablished system of matrix equations. Numerical examples are provided to illustrate the effectiveness of the algorithm.