Gradient-based iterative algorithm for the extended coupled Sylvester matrix equations

机译：扩展耦合Sylvester矩阵方程的基于梯度的迭代算法

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A gradient-based iterative algorithm is established for solving the extended coupled Sylvester matrix equations AXB + AY B = F and CXD + CY D = F by using the hierarchical identification principle. We prove that the iterative solution converges fast to the exact one for any initial iterative value if the coupled matrix equations has a unique solution. A numerical example is offered to illustrate the efficiency of the proposed algorithm.

机译：建立了基于梯度的迭代算法，通过使用分层识别原理来求解扩展耦合的Sylvester矩阵方程AXB + AY B = F和CXD + CY D =F。我们证明，如果耦合矩阵方程具有唯一解，则对于任何初始迭代值，迭代解都可以快速收敛到精确的解。数值例子说明了所提算法的有效性。

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《Chinese Control and Decision Conference》|2017年|1562-1567|共6页
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Zhang Huamin;
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Iterative methods; Matrix decomposition; Stability analysis; Control systems; Parameter estimation; Electronic mail;

机译：迭代法;矩阵分解;稳定性分析;控制系统;参数估计;电子邮件;

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专利

1. Gradient-based iterative algorithms for generalized coupled Sylvester-conjugate matrix equations [J] . Huang Bao-Hua, Ma Chang-Feng Computers & mathematics with applications . 2018,第7期

机译：广义耦合Sylvester-共轭矩阵方程的基于梯度的迭代算法
2. The relaxed gradient-based iterative algorithms for a class of generalized coupled Sylvester-conjugate matrix equations [J] . Huang Baohua, Ma Changfeng Journal of the Franklin Institute . 2018,第6期

机译：一类广义耦合Sylvester-共轭矩阵方程的基于梯度的松弛迭代算法
3. An accelerated gradient-based iterative algorithm for solving extended Sylvester-conjugate matrix equations [J] . Bayoumi Ahmed M. E., Ramadan Mohamed A. Transactions of the Institute of Measurement and Control . 2018,第1期

机译：一种加速基于梯度的迭代算法，用于求解扩展Sylvester - 共轭矩阵方程
4. Gradient-based iterative algorithm for the extended coupled Sylvester matrix equations [C] . Zhang Huamin Chinese Control and Decision Conference . 2017

机译：扩展耦合Sylvester矩阵方程的梯度基迭代算法
5. A parallel algorithm for the Sylvester observer equation. [D] . Purkayastha, Avijit. 1993

机译：Sylvester观测器方程的并行算法。
6. An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations [O] . Zhongli Zhou, Guangxin Huang 2013

机译：一般耦合矩阵方程自反解的迭代算法
7. Gradient-based iterative algorithms for generalized coupled Sylvester-conjugate matrix equations [O] . Bao-Hua Huang, Chang-Feng Ma 2018

机译：广义耦合SYLVESTER - 共轭矩阵方程的基于梯度的迭代算法

Gradient-based iterative algorithm for the extended coupled Sylvester matrix equations

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