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

作者：Zhang Huamin^*

来源：Abstract and Applied Analysis, 2014, 2014: 649524.

DOI：10.1155/2014/649524

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 equationsA(1)Chi B-1 +A(2)Chi B-2 =F-1 and C-1 Chi D-1 + C-2 Chi 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.

• 出版日期2014
• 单位蚌埠学院