Gradient-based iteration for a class of matrix equations

被引：0
|
作者：
Zhang, Huamin [1 ]
机构：
[1] Bengbu Coll, Dept Math & Phys, Bengbu 233000, Peoples R China
来源：
26TH CHINESE CONTROL AND DECISION CONFERENCE (2014 CCDC) | 2014年
关键词：
Gradient iteration; Hierarchical identification principle; Matrix equation; Convergence factor; HIERARCHICAL IDENTIFICATION PRINCIPLE; LEAST-SQUARES SOLUTIONS; PARAMETER-ESTIMATION; SYSTEMS; ALGORITHMS;
D O I：
暂无
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, an iterative algorithm is established for solving a class of matrix equations with complex unknowns. By using the hierarchical identification principle, the gradient-based iterative algorithms are constructed to solve the equation AX B C X" D = I and the coupled equations A(1)XB(1) + A(2)X(H)B(2) = F-1 and C-1 X D-1 + C-2 X-H D-2 = F-2. The the convergence factor is presented to guarantee that the iterative algorithms are effective for any initial values. The analysis indicates that if the matrix equation has a unique solution, then the iterative solutions converge to the exact one for any initial value under proper conditions. A numerical example is provided to illustrate the effectiveness of the proposed algorithm.
引用
收藏
页码：1201 / 1205
页数：5
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