| 沈海龙,彭程,邵新慧,张铁.基于梯度的Sylvester共轭矩阵方程的迭代解[J].数学研究及应用,2017,37(3):351~366 |
| 基于梯度的Sylvester共轭矩阵方程的迭代解 |
| Gradient Based Iterative Solutions for Sylvester-Conjugate Matrix Equations |
| 投稿时间：2016-05-04 修订日期：2016-11-23 |
| DOI：10.3770/j.issn:2095-2651.2017.03.013 |
| 中文关键词: Sylvester共轭矩阵方程 迭代法 收敛 松弛参数 |
| 英文关键词:Sylvester-conjugate matrix equations iterative solutions convergence relaxation parameter |
| 基金项目:国家自然科学基金 (Grant No.11071033). |
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| 中文摘要: |
| 本文提出了一种基于梯度的Sylvester共轭矩阵方程的迭代算法.通过引入一个松弛参数和采用递阶辨识原理,构造一个迭代算法求解Sylvester矩阵方程.通过应用复矩阵的实数表达以及实数表示的一些性质,收敛性分析表明在一定假设条件下,对于任意初始值,迭代方法均收敛到精确解,数值算例也表明了所给方法的有效性. |
| 英文摘要: |
| This paper presents a gradient based iterative algorithm for Sylvester-conjugate matrix equations with a unique solution. By introducing a relaxation parameter and applying the hierarchical identification principle, an iterative algorithm is constructed to solve Sylvester matrix equations. By applying a real representation of a complex matrix as a tool and using some properties of the real representation, convergence analysis indicates that the iterative solutions converge to the exact solutions for any initial values under certain assumptions. Numerical examples are given to illustrate the efficiency of the proposed approach. |
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