e^(Ax)的Thiele型矩阵有理逼近  

Thiele's matrix rational approximation of e^(Ax)

作　　者：张伟红[1] 檀结庆[1] 

机构地区：[1]合肥工业大学理学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2006年第10期1323-1326,共4页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(10171026;60473114);安徽省自然科学基金资助项目(03046102)

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。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.

关 键 词：Samelson逆 倒导数 矩阵连分式 Thiele连分式逼近 

分 类 号：O241.5[理学—计算数学]