Reduced-rank gradient-based algorithms for generalized coupled Sylvester matrix equations and its applications

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• 作者：Huamin Zhang ^{zhangeasymail@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Reduced-rank gradient-based algorithm ; Coupled matrix equations ; Spectral radius ; Convergence analysis
• 刊名：Computers & Mathematics with Applications
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：70
• 期：8
• 页码：2049-2062
• 全文大小：841 K

文摘

In this paper, by constructing an objective function and using the gradient search, full-rank and reduced-rank gradient-based algorithms are suggested for solving generalized coupled Sylvester matrix equations. It is proved that the reduced-rank iterative algorithm is convergent for proper initial iterative values. By analyzing the spectral radius of the related matrices, the convergence properties are studied and the optimal convergence factor of the reduced-rank algorithm is determined. The relationship between the reduced-rank algorithm and the full-rank algorithm is discussed. Consequently, the computation load can be reduced greatly for solving a class of matrix equation. A numerical example is provided to illustrate the effectiveness of the proposed algorithms and testify the conclusions suggested in this paper.