矩阵指数函数的一种计算  

A Computation Method of Matrix Exponent Function

作　　者：张俊祖[1] 姜根明[1] 冯复科[1] 

机构地区：[1]长安大学理学院,西安710064

出　　处：《长安大学学报（自然科学版）》2006年第1期108-110,共3页Journal of Chang’an University(Natural Science Edition)

基　　金：国家自然科学基金项目(40201033)

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eA及eAt。Abstract： This paper expresses an expansion formula of exponential progression of matrix exponent function as a form of matrix polynomiat, 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.

关 键 词：矩阵指数函数 矩阵序列 矩阵幂级数 特征值 

分 类 号：O151.21[理学—数学]