研究论文

Thiele型张量连分式插值及其在张量指数计算中的应用

展开
  • 上海大学 理学院, 上海 200444
蒋祥龙(1989—), 男, 博士, 研究方向为数值代数. E-mail: jiangxl@shmtu.edu.cn

收稿日期: 2019-06-19

  网络出版日期: 2019-07-22

基金资助

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

Thiele-type tensor continued fraction interpolation and its application in the computation of the tensor exponential function

Expand
  • College of Sciences, Shanghai University, Shanghai 200444, China

Received date: 2019-06-19

  Online published: 2019-07-22

摘要

提出了Thiele型广义张量有理逼近的一种连分式插值方法, 并用该方法计算了张量指数函数的值, 由此来说明这种连分式插值方法的有效性.

本文引用格式

蒋祥龙, 顾传青 . Thiele型张量连分式插值及其在张量指数计算中的应用[J]. 上海大学学报(自然科学版), 2021 , 27(4) : 650 -658 . DOI: 10.12066/j.issn.1007-2861.2182

Abstract

A continued fraction interpolation method for Thiele-type generalised tensor rational approximation was proposed. This method was used to calculate the value of the tensor exponential function to illustrate the effectiveness of the proposed continued fraction interpolation method.

参考文献

[1] Neto E A D S. The exact derivative of the exponential of an unsymmetric tensor[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190:2377-2383.
[2] Gu C Q. Bivariate Thiele-type matrix valued rational interpolants[J]. Journal of Computational and Applied Mathematics, 1997, 80:71-82.
[3] Gu C Q. Thiele-type and Largrange-type generalized inverse rational interpolation for rectangular complex matrices[J]. Linear Algebra and Its Applications, 1999, 295:7-30.
[4] Gu C Q. Generalized inverse matrix Padé approximation on the basis of scalar products[J]. Linear Algebra and Its Applications, 2001, 322:141-167.
[5] Gu C Q. A practical two-dimensional Thiele-type matrix Padé approximation[J]. IEEE Trans-actions on Automat Control, 2003, 48:2259-2263.
[6] Hackbusch W. Tensor spaces and numerical tensor calculus[M]. Berlin: Springer-Verlag, 2012.
[7] Kilmer M E, Braman K, Hao N, et al. Third-order tensors as operators on matrices: a theoretical and computational framework with applications in imaging[J]. SIAM Journal on Matrix Analysis and Applications, 2013, 34:148-172.
[8] Kofidis E, Regalia P A. Tensor decompositions and applications[J]. SIAM Review, 2009, 51:455-500.
[9] Gu C Q, Liu Y. The tensor Padé-type approximant with application in computing tensor exponential function[J]. Journal of Function Spaces, 2018, 2018:2835175.
[10] 顾传青, 黄逸铮, 陈之兵. 广义逆张量Padé逼近的连分式递推算法[J]. 控制与决策, 2019, 34(8):1702-1708.
[10] Gu C Q, Huang Y Z, Chen Z B. A continued fractional recurrence algorithm for generalized inverse tensor Padé approximation[J]. Control and Decision, 2019, 34(8):1702-1708.
[11] 顾传青, 唐鹏飞, 陈之兵. 计算张量指数函数的广义逆张量$\varepsilon$-算法[J]. 自动化学报, 2020, 46(4):744-751.
[11] Gu C Q, Tang P F, Chen Z B. Generalized inverse tensor $\varepsilon$-algorithm for computing tensor exponential function[J]. Acta Automatica Sinica, 2020, 46(4):744-751.
[12] Qi L Q. Eigenvalues of a real supersymmetric tensor[J]. Journal of Symbolic Computation, 2005, 40:1302-1324.
文章导航

/