Iterative Solutions of a Set of Matrix Equations by Using the Hierarchical Identification Principle

This paper is concerned with iterative solution to a class of the real coupled matrix equations. By using thehierarchical identification principle, a gradient-based iterative algorithm is constructed to solve the real coupledmatrix equations A1XB1+A2XB2=F1 and C1XD1+C2XD2=F2. The range of the convergence factor is derived to guarantee that the iterative algorithm is convergent for any initial value. The analysis indicates thatif the coupled matrix equations have a unique solution, then the iterative solution converges fast to the exact onefor any initial value under proper conditions. A numerical example is provided to illustrate the effectiveness ofthe proposed algorithm