| 矩阵指数函数的一种计算 |
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| 引用本文： | 张俊祖,姜根明,冯复科. 矩阵指数函数的一种计算[J]. 长安大学学报(自然科学版), 2006, 26(1): 108-110 |
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| 作者姓名： | 张俊祖 姜根明 冯复科 |
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| 作者单位： | 长安大学,理学院,西安,710064 |
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| 摘 要： | 将矩阵指数函数的幂级数展开式表示为一个矩阵多项式形式，给出矩阵指数函数的一个有限展开式，通过矩阵特征值及矩阵指数函数的有限展开式的各阶导数，构造出一个线性方程组，用解线性方程组的方法给出该矩阵多项式的系数计算。从而给出了用求解线性方程组的方法计算矩阵指数函数e^A及e^At。
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| 关 键 词： | 矩阵指数函数 矩阵序列 矩阵幂级数 特征值 |
| 文章编号： | 1671-8879（2006）01-0108-03 |
| 收稿时间： | 2005-03-05 |
| 修稿时间： | 2005-03-05 |
A Computation Method of Matrix Exponent Function |
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| ZHANG Jun-zu,JIANG Gen-ming,FENG Fu-ke. A Computation Method of Matrix Exponent Function[J]. JOurnal of Chang’an University:Natural Science Edition, 2006, 26(1): 108-110 |
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| Authors: | ZHANG Jun-zu JIANG Gen-ming FENG Fu-ke |
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| Abstract: | This paper expresses an expansion formula of exponential progression of matrix exponent function as a form of matrix polynomial,and gives a finite expansion formula of matrix exponent function.The linear equations are constructed with eigenvalue of matrix and various rank differential coefficient of finite expansion formula of matrix exponent function.The coefficient calculation of the matrix polynomial is presented by using the method of solving linear equations.A method of solving linear equations is put forward to compute such matrix exponent function as e~A and e~(At).6 refs. |
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| Keywords: | exponent function of matrix sequence of matrix power series of matrix eigenvalue |
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