## Abstract and Applied Analysis

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

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 ${A}_{1}X{B}_{1}+{A}_{2}X{B}_{2}={F}_{1}$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 649524, 10 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412276962

Digital Object Identifier
doi:10.1155/2014/649524

Mathematical Reviews number (MathSciNet)
MR3208556

Zentralblatt MATH identifier
07022826

#### Citation

Zhang, Huamin. Iterative Solutions of a Set of Matrix Equations by Using the Hierarchical Identification Principle. Abstr. Appl. Anal. 2014 (2014), Article ID 649524, 10 pages. doi:10.1155/2014/649524. https://projecteuclid.org/euclid.aaa/1412276962

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