Real iterative algorithms for a common solution to the complex conjugate matrix equation system

摘要

In this paper, we propose a new algorithm for the computation of the common solution to the complex conjugate matrix equation system AiXBi+CiX¯Di=Ei,i=1,2,…,N. The algorithms only need finite iteration steps, requiring only real computation. Furthermore, the algorithm can be extended to solve a more general complex matrix equation system. Two numerical examples are given to illustrate the effectiveness of the proposed algorithm.