| 矩阵方程A1Z+ZB1=C1的广义自反最佳逼近解的迭代算法 |
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| 引用本文： | 杨家稳,孙合明.矩阵方程A1Z+ZB1=C1的广义自反最佳逼近解的迭代算法[J].数学杂志,2014,34(5):968-976. |
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| 作者姓名： | 杨家稳 孙合明 |
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| 作者单位： | 滁州职业技术学院基础部;河海大学理学院; |
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| 基金项目： | 安徽省教育厅自然科学基金资助(KJ2011B119) |
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| 摘 要： | 本文研究了Sylvester复矩阵方程A_1Z+ZB_1=c_1的广义自反最佳逼近解.利用复合最速下降法,提出了一种的迭代算法.不论矩阵方程A_1Z+ZB_1=C_1是否相容,对于任给初始广义自反矩阵Z_0,该算法都可以计算出其广义自反的最佳逼近解.最后,通过两个数值例子,验证了该算法的可行性.
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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 广义自反矩阵 |
| 收稿时间： | 2012/6/25 0:00:00 |
| 修稿时间： | 2012/9/14 0:00:00 |
AN ITERATIVE ALGORITHM FOR THE GENERALIZED REFLEXIVE OPTIMAL APPROXIMATION SOLUTIONS OF MATRIX EQUATIONS A1Z+ZB1=C1 |
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| YANG Jia-wen and SUN He-ming.AN ITERATIVE ALGORITHM FOR THE GENERALIZED REFLEXIVE OPTIMAL APPROXIMATION SOLUTIONS OF MATRIX EQUATIONS A1Z+ZB1=C1[J].Journal of Mathematics,2014,34(5):968-976. |
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| Authors: | YANG Jia-wen and SUN He-ming |
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| Institution: | Department of Basic Courses, Chuzhou Vocational and Technical College, Chuzhou 239000, China;College of Science, Hohai University, Nanjing 210098, China and College of Science, Hohai University, Nanjing 210098, China |
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| Abstract: | In this paper, we present an iterative algorithm to calculate the optimal approximation solutions of the Sylvester complex matrix equations A1Z+ZB1=C1 over generalized reflexive (anti-reflexive) matrices by using the hybrid steepest descent method. Whether matrix equations A1Z+ZB1=C1 are consistent or not, for arbitrary initial reflexive (anti-reflexive) matrix Z0, the given algorithm can be used to compute the reflexive (anti-reflexive) optimal approximation solutions. 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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