| 矩阵方程AX+XB+F对称解的递推算法 |
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| 引用本文： | 于蕾,张凯院.矩阵方程AX+XB+F对称解的递推算法[J].昆明理工大学学报(理工版),2005,30(5):120-124. |
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| 作者姓名： | 于蕾 张凯院 |
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| 作者单位： | 西北工业大学应用数学系,陕西西安710072 |
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| 基金项目： | 国家自然科学基金资助项目(项目编号:2003CG0101) |
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| 摘 要： | 提出一种求矩阵方程AX＋XB=F对称解的递推算法,该算法不仅能够用于对称解存在性的判断问题,而且能够用于对称解的计算问题.选取特殊的初始矩阵时,该算法能够求出矩阵方程的极小范数对称解,以及对给定的对称矩阵进行最佳逼近的对称解.
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| 关 键 词： | 矩阵方程 对称解 最佳逼近解 |
| 文章编号： | 1007-855X(2005)05-0120-05 |
| 修稿时间： | 2004年12月23 |
Recursive Algorithm of a Linear Matrix Equation AX+XB=F over Symmetric Solutions |
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| YU Lei,ZHANG Kai-yuan.Recursive Algorithm of a Linear Matrix Equation AX+XB=F over Symmetric Solutions[J].Journal of Kunming University of Science and Technology(Natural Science Edition),2005,30(5):120-124. |
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| Authors: | YU Lei ZHANG Kai-yuan |
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| Abstract: | An recursive algorithm to solve the linear matrix equation AX+XB=F over symmetric solutions is put forward in this paper.The algorithm is used not only to determine the solvability of the equation over symmetric solutions,but also to calculate symmetric solutions.The symmetric solutions can be obtained with the algorithm and its least-norm symmetric solution can be given by choosing a special initial matrix.Finally,its optimal approximation solution to a given matrix can be derived. |
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| Keywords: | matrix equation symmetric solution optimal approximation solution |
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