Generalized bilateral inverses of tensors via Einstein product with applications to singular tensor equations

被引：3
|
作者：
Kheirandish, Ehsan [1 ]
Salemi, Abbas [1 ]
机构：
[1] Shahid Bahonar Univ Kerman, Dept Appl Math, Kerman, Iran
来源：
COMPUTATIONAL & APPLIED MATHEMATICS | 2023年 / 42卷 / 08期
关键词：
Tensor; Generalized bilateral inverse of tensor; Dual; CMP inverse; DMP inverse; Einstein product;
D O I：
10.1007/s40314-023-02483-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a unified approach for various extended inverses of tensors, the generalized bilateral inverse of tensors via Einstein products, is introduced and we show that a number of known generalized tensor inverses can be regarded as special cases of this idea. Some characterizations of the CMP, DMP, and MPD inverse of tensors by using Einstein products are provided. The notion of generalized bilateral inverses' dual and self-duality are investigated. In addition, the bilateral inverse solutions for singular linear tensor equations are studied.
引用
收藏
页数：19
相关论文
共 50 条
  • [21] SENSITIVITY OF SOME TENSOR EQUATIONS WITH EINSTEIN PRODUCT
    Wu, Yiling
    JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2019, 43 (02): : 125 - 154
  • [22] Tensor inversion and its application to the tensor equations with Einstein product
    Liang, Mao-lin
    Zheng, Bing
    Zhao, Rui-juan
    LINEAR & MULTILINEAR ALGEBRA, 2019, 67 (04): : 843 - 870
  • [23] Krylov subspace methods to solve a class of tensor equations via the Einstein product
    Huang, Baohua
    Xie, Yajun
    Ma, Changfeng
    NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2019, 26 (04)
  • [24] The Generalized Tensor Decomposition with Heterogeneous Tensor Product for Third-Order Tensors
    Liu, Yun-Yang
    Zhao, Xi-Le
    Ding, Meng
    Wang, Jianjun
    Jiang, Tai-Xiang
    Huang, Ting-Zhu
    JOURNAL OF SCIENTIFIC COMPUTING, 2024, 100 (03)
  • [25] Standard tensor and its applications in problem of singular values of tensors
    Yang, Qingzhi
    Li, Yiyong
    FRONTIERS OF MATHEMATICS IN CHINA, 2019, 14 (05) : 967 - 987
  • [26] Standard tensor and its applications in problem of singular values of tensors
    Qingzhi Yang
    Yiyong Li
    Frontiers of Mathematics in China, 2019, 14 : 967 - 987
  • [27] Tensor sparse representation via Einstein product
    Addi, Ferdaous Ait
    Bentbib, Abdeslem Hafid
    Jbilou, Khalide
    COMPUTATIONAL & APPLIED MATHEMATICS, 2024, 43 (04):
  • [28] A dominance notion for singular matrices with applications to nonnegative generalized inverses
    Mishra, Debasisha
    Sivakumar, K. C.
    LINEAR & MULTILINEAR ALGEBRA, 2012, 60 (08): : 911 - 920
  • [29] An optimal preconditioner for tensor equations involving Einstein product
    Xie, Ze-Jia
    Jin, Xiao-Qing
    Sin, Vai-Kuong
    LINEAR & MULTILINEAR ALGEBRA, 2020, 68 (05): : 886 - 902
  • [30] Numerical solutions of Cauchy singular integral equations using generalized inverses
    Kim, S
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1999, 38 (5-6) : 183 - 195
12345