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Conjugate gradient-type method for the tensor linear system via the T-product and its application in the calculation of Moore-Penrose inverse

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  • Huang, Baohua

Abstract

We develop a conjugate gradient-type method for solving a class of tensor linear system with a T-product structure. The finite termination of the proposed method is proven without considering the rounding error. As an application, we obtain the numerical approximation of the tensor Moore-Penrose inverse based on the tensor T-product by solving the tensor linear system that are considered. Some numerical experiments are given to show the performance of the proposed method including the application in the numerical calculation of the tensor Moore-Penrose inverse and the color image deblurring.

Suggested Citation

  • Huang, Baohua, 2024. "Conjugate gradient-type method for the tensor linear system via the T-product and its application in the calculation of Moore-Penrose inverse," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    • Handle: RePEc:eee:apmaco:v:472:y:2024:i:c:s0096300324000997
    DOI: 10.1016/j.amc.2024.128627
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    References listed on IDEAS

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    1. Meng-Meng Zheng & Zheng-Hai Huang & Yong Wang, 2021. "T-positive semidefiniteness of third-order symmetric tensors and T-semidefinite programming," Computational Optimization and Applications, Springer, vol. 78(1), pages 239-272, January.
    2. Xuezhong Wang & Maolin Che & Yimin Wei, 2020. "Tensor neural network models for tensor singular value decompositions," Computational Optimization and Applications, Springer, vol. 75(3), pages 753-777, April.
    3. Mustapha Hached & Khalide Jbilou & Christos Koukouvinos & Marilena Mitrouli, 2021. "A Multidimensional Principal Component Analysis via the C-Product Golub–Kahan–SVD for Classification and Face Recognition," Mathematics, MDPI, vol. 9(11), pages 1-17, May.
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