Abstract and Applied Analysis

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

Huamin Zhang

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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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