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

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  • Huamin Zhang

Abstract

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 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 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.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:649524
DOI: 10.1155/2014/649524
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