| 求矩阵方程AXB+CYD=E自反最佳逼近解的迭代算法 |
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| 引用本文： | 孙合明,祁正萍,杨家稳. 求矩阵方程AXB+CYD=E自反最佳逼近解的迭代算法[J]. 江西师范大学学报(自然科学版), 2012, 36(2): 171-176 |
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| 作者姓名： | 孙合明 祁正萍 杨家稳 |
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| 作者单位： | 1. 河海大学理学院,江苏南京,211100
2. 滁州职业技术学院基础部,安徽滁州,239000 |
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| 基金项目： | 安徽省高校省级自然科学基金(KJ2011B119)资助项目 |
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| 摘 要： | 利用复合最速下降法的迭代算法对基于自反矩阵(或反自反矩阵)下广义Sylvester矩阵方程AXB+CYD=E最佳逼近解进行了研究,证明了无论矩阵方程AXB+CYD=E是否相容,该算法都可以用于计算其最佳逼近解.最后,通过2个数值实验证明了该算法的可行性.
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| 关 键 词： | Sylvester矩阵方程 Kronecker积 复合最速下降法 最佳逼近 自反矩阵 |
The Iterative Algorithm for the Reflexive Optimal Approximation Solutions of Matrix Equations AXB+CYD=E |
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| SUN He-ming , QI Zheng-ping , YANG Jia-wen. The Iterative Algorithm for the Reflexive Optimal Approximation Solutions of Matrix Equations AXB+CYD=E[J]. Journal of Jiangxi Normal University (Natural Sciences Edition), 2012, 36(2): 171-176 |
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| Authors: | SUN He-ming QI Zheng-ping YANG Jia-wen |
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| Affiliation: | 1.College of Science,Hehai University,Nanjing Jiangsu 211100,China;2.Department of Fundations,Chuzhou Vocational and Technical College,Chuzhou Anhui 239000,China) |
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| Abstract: | An iterative algorithm to calculate the optimal approximation solutions of the generalized Sylvester matrix equations AXB+CYD=E over reflexive(anti-reflexive) matrix is studied by making use of the hybrid steepest descent method(HSDM).The given algorithm can be used to compute the optimal approximation solutions whether matrix equations AXB+CYD=E are consistent or not.The effectiveness of the proposed algorithm is verified by two numerical examples. |
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| Keywords: | Sylvester matrix equations Kronecker product hybrid steepest descent method optimal approximation reflexive matrix |
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