| eAx的Thiele型矩阵有理逼近 |
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| 引用本文： | 张伟红,檀结庆. eAx的Thiele型矩阵有理逼近[J]. 合肥工业大学学报(自然科学版), 2006, 29(10): 1323-1326 |
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| 作者姓名： | 张伟红 檀结庆 |
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| 作者单位： | 合肥工业大学,理学院,安徽,合肥,230009;合肥工业大学,理学院,安徽,合肥,230009 |
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| 基金项目： | 国家自然科学基金 , 安徽省自然科学基金 |
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| 摘 要： | 矩阵指数函数eAx的计算在线性系统理论及半群理论中有着特殊的作用,在现代控制理论中,无论是齐次方程还是非齐次方程的求解,主要取决于矩阵指数函数eAx的计算和近似。文章利用代数知识给出了矩阵指数函数eAx的连分式逼近函数的一个重要性质和定理,并在此基础上对矩阵指数函数eAx的连分式算法进行改进,最后用数值例子来验证其可行性。
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| 关 键 词： | Samelson逆 倒导数 矩阵连分式 Thiele连分式逼近 |
| 文章编号： | 1003-5060(2006)10-1323-04 |
| 修稿时间： | 2005-10-28 |
Thiele's matrix rational approximation of eAx |
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| ZHANG Wei-hong,TAN Jie-qing. Thiele's matrix rational approximation of eAx[J]. Journal of Hefei University of Technology(Natural Science), 2006, 29(10): 1323-1326 |
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| Authors: | ZHANG Wei-hong TAN Jie-qing |
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| Abstract: | Calculating the functions of the matrix exponential e~~(Ax) has special significance in the theory of linear systems and the theory of semi-groups.Especially,in the modern control theory,no matter the equation is homogeneous or non-homogeneous,the result depends on the calculation of the matrix exponential e~~(Ax).In this paper,an important property and a theorem have been given about the matrix Thiele's continued fraction which is used to approximate the function of e~~(Ax).Based on the property,the Thiele algorithm is improved.A numeral example is also provided. |
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| Keywords: | Samelson inverse reciprocal derivative matrix continued fraction Thiele's continued fraction approximation |
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