JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (6): 95-102.doi: 10.6040/j.issn.1671-9352.0.2020.463
DAI Li-fang, LIANG Mao-lin*, RAN Yan-ping
CLC Number:
| [1] COPPI R, BOLASCO S. Multiway data analysis[M]. Amsterdam: Elsevier Press, 1989. [2] GREUB W. Multilinear algebra[M]. New York: Springer-Verlag Press, 1978. [3] KOLDA T, BADER B. Tensor decompositions and applications[J]. SIAM Rev, 2009, 51(3):455-500. [4] QI Liqun, LUO Ziyan. Tensor analysis: spectral theory and special tensors[M]. Philadelphia: Society for Industrial and Applied Mathematics Press, 2017. [5] BRAZELL M, LI N, NAVASCA C, et al. Solving multilinear systems via tensor inversion[J]. SIAM J Matrix Anal Appl, 2013, 34(2):542-270. [6] DING Weiyang, WEI Yimin. Solving multi-linear systems with M-tensors[J]. J Sci Comput, 2016, 68:689-715. [7] YE Ke, HU Shenglong. Inverse eigenvalue problem for tensors[J]. Comm Math Sci, 2017, 15(6):1627-1649. [8] 周树荃,戴华.代数特征值反问题[M]. 郑州:河南科学技术出版社,1991. ZHOU Shuquan, DAI Hua. Algebraic eigenvalue inverse problems[M]. Zhengzhou: Henan Science and Technology Press, 1991. [9] EINSTEIN A. The foundation of the general theory of relativity[J]. Anna Der Phys, 1916, 49(7):769-822. [10] QI Liqun. Theory of tensors(hypermatrices)[R/OL].(2014-09-10)[2020-12-15]. ftp://159.226.92.8/pub/yyx/optimi/ICNONLA-PLENARY/Prof.%20Liqun%20Qi.pdf. [11] ITSKOV M. On the theory of fourth-order tensors and their applications in computational mechanics[J]. Comput Meth Appl Mech Eng, 2000, 189(2):419-438. [12] 沈世镒. Toeplitz张量的本征值分布公式及其应用[J]. 高校应用数学学报(A辑),1987,2:151-163. SHEN Shiyi. On the distribution formula of the eigenvalue of Toeplitz tensor and its application[J]. Appl Math J Chinese Univ, 1987, 2:151-163. [13] CUI Lubin, CHEN Chuan, LI Wen, et al. An eigenvalue problem for even order tensors with its applications[J]. Linear Multilinear Algebra, 2016, 64(4):602-621. [14] LIANG Maolin, ZHENG Bing, ZHAO Ruijuan. Tensor inversion and its application to the tensor equations with Einstein product[J]. Linear Multilinear Algebra, 2019, 67(4):843-870. [15] NI Guyan. Hermitian tensor and quantum mixed state[EB/OL].(2019-08-23)[2020-12-15]. https://arxiv.org/pdf/1902.02640.pdf. [16] SUN Lizhu, ZHENG Baodong, BU Changjiang, et al. Moore-Penrose inverse of tensors via Einstein product[J]. Linear Multilinear Algebra, 2016, 64(4):686-698. [17] LIANG Maolin, ZHENG Bing. Further results on Moore-Penrose inverses of tensors with application to tensor nearness problems[J]. Comput Math Appl, 2019, 77:1282-1293. [18] JI Jun, WEI Yimin. Weighted Moore-Penrose inverses and fundamental theorem of even-order tensors with Einstein product[J]. Front Math China, 2017, 12(6):1319-1337. [19] HIGHAM N. Computing a nearest symmetric positive semidefinite matrix[J]. Linear Algebra Appl, 1988, 103:103-118. [20] YUAN Yongxin, DAI Hua. The nearness problems for symmetric matrix with a submatrix constraint[J]. Comput Appl Math, 2008, 213:224-231. [21] HUANG G, NOSCHESE S, REICHEL L. Regularization matrices determined by matrix nearness problems[J]. Linear Algebra Appl, 2016, 502:41-57. [22] BADER B, KOLDA T, MAYO J, et al. MATLAB Tensor Toolbox Version 3.2[EB/OL].(2015-02-18)[2020-12-15]. http://www.tensortoolbox.org. |
| [1] | LIANG Mao-lin, DAI Li-fang, YANG Xiao-ya. The least-squares solutions and the optimal approximation of the inverse problem for row anti-symmetric matrices on linear manifolds [J]. J4, 2012, 47(4): 121-126. |
| [2] | YUE Jiang, CHANG Da-Wei. Preconditioned simultaneous displacement(PSD) method for rank deficient linear systems [J]. J4, 2009, 44(10): 30-35. |
| [3] | CHEN Bei . The inexact Newton method for inverse Toeplitz eigenvalue problems [J]. J4, 2008, 43(9): 89-93 . |
| [4] | SONG Jun-ling,TIAN Jin-ting,ZHAO Jian-li . The least-squares solutions of inverse problems for generalized(R,S)-symmetric matrices [J]. J4, 2008, 43(2): 48-51 . |
|
||
