| 关于矩阵指数的PADE逼近新算法 |
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| 引用本文： | 顾传青.关于矩阵指数的PADE逼近新算法[J].自动化学报,1999,25(1):94-99. |
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| 作者姓名： | 顾传青 |
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| 作者单位： | 1.上海大学理学院,上海 |
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| 摘 要： | 基于广义逆矩阵Pade逼近的特点是在保持逼近阶的前提下,在构造过程中不需要
用到矩阵的乘法运算.利用该结果建立矩阵指数etA的一种新的非线性逼近算法.该方法与原
Pade近似法相比具有明显的优点,即它对奇异矩阵和高阶矩阵是适用的,并且所得到的算法
适合编程上机进行计算.给出的一个计算实例说明了算法的有效性.逼近公式的存在性和唯
一性得到了证明.
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| 关 键 词： | 矩阵指数 广义逆矩阵Pade逼近 |
| 收稿时间： | 1997-5-26 |
NEW ALGORITHM FOR MATRIX EXPONENTIALS BY PADE APPROXIMATION |
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| GU Chuanqing.NEW ALGORITHM FOR MATRIX EXPONENTIALS BY PADE APPROXIMATION[J].Acta Automatica Sinica,1999,25(1):94-99. |
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| Authors: | GU Chuanqing |
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| Affiliation: | 1.Science College of Shanghai University,Shanghai |
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| Abstract: | The matrix Pade approximants based on generalized inverse is characterized by keeping approximation order and without multiplication of matrices in the construction process. In this paper, a new nonlinear approximating method for matrix exponential functions is established by means of this result. This method is obviously superior to the original Pade method because it can be applied to singular matrices and higher order matrices, and the obtained algorithm is suitable to compute on computers. A computational example is given to illustrate the efficiency of the algorithm. Existence and uniqueness of approximation formulas are proven. |
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| Keywords: | Matrix exponentials generalized inverse matrix Pade approximants |
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