计算张量指数函数的广义逆张量ε-算法  

Generalized Inverse Tensor ε-algorithom for Computing Tensor Exponential Function

作　　者：顾传青[1] 唐鹏飞 陈之兵 GU Chuan-Qing;TANG Peng-Fei;CHEN Zhi-Bing(Department of Mathematics,Shanghai University,Shanghai 200444;School of Mathematics and Statistics,Shenzhen University,Shenzhen 518052)

机构地区：[1]上海大学数学系,上海200444 [2]深圳大学数学与统计学院,深圳518052

出　　处：《自动化学报》2020年第4期744-751,共8页Acta Automatica Sinica

基　　金：国家自然科学基金(11371243);上海市重点学科建设资助项目(S30104)资助。

摘　　要：张量指数函数已经广泛应用于工程领域.本文得到了一种有效的张量广义逆,并以此为基础构造了广义逆张量Pad′e逼近的一种ε-算法.该算法可以编程实施递推的计算,其特点是,在计算过程中,不必计算张量的乘积,也不必计算张量的逆.给出的计算张量指数函数的数值实验显示,将本文的方法与目前通常使用的截断法进行比较,在不降低逼近阶的条件下,ε-算法能很好地降低计算复杂度,尤其是在张量的维数比较大的时候.Tensor exponent functions have been widely used in engineering. In this paper, an effective tensor generalized inverse is obtained, and based on it, an ε-algorithm of generalized inverse tensor Pad′e approximation is presented. The algorithm can be programmed to implement recursive calculations, which are characterized by the fact that it is not necessary to calculate the product of the tensors in the calculation nor to calculate the inverse of tensors. The numerical experiment of calculating tensor exponential function shows that compared with the commonly used truncation method,the ε-algorithm can reduce computational complexity well without reducing the approximation order, especially when the dimension of tensor is relatively large.

关 键 词：张量指数函数 广义逆张量Padé逼近 张量ε-算法 张量指数函数的截断法 

分 类 号：O174[理学—数学]