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

Abstract EN

This paper is concerned with iterative solution to a class of the real coupled matrix equations.

By using the hierarchical identification principle, a gradient-based iterative algorithm is constructed to solve the real coupled matrix equations A 1 X B 1 + A 2 X B 2 = F 1 and C 1 X D 1 + C 2 X D 2 = F 2 .

The range of the convergence factor is derived to guarantee that the iterative algorithm is convergent for any initial value.

The analysis indicates that if the coupled matrix equations have a unique solution, then the iterative solution converges fast to the exact one for any initial value under proper conditions.

A numerical example is provided to illustrate the effectiveness of the proposed algorithm.