The reflexive least squares solutions of the general coupled matrix equations with a submatrix constraint

In this paper, we construct an iterative method to solve the general coupled matrix equations∑j=1lAijXjBij=Ci,i=1,2,…,t,where Xj∈Rnj×nj(j=1,2,…,l) is a reflexive matrix with a specified central principal submatrix. The algorithm produces suitable [X1,X2,…,Xl][X1,X2,…,Xl] such that ∑i=1t∑j=1lAijXjBij-Ci=min within finite iteration steps in the absence of roundoff errors. We show that the algorithm is stable any case. The algorithm requires little storage capacity. Given numerical examples show that the algorithm is efficient.