Year: 2025
Author: Hengrui Luo, Anna Ma
Numerical Mathematics: Theory, Methods and Applications, Vol. 18 (2025), Iss. 2 : pp. 353–394
Abstract
Inspired by the row and column action methods for solving large-scale linear systems, in this work, we explore the use of frontal slices for solving tensor linear systems. In particular, this paper presents a novel approach for using frontal slices of a tensor $\mathcal{A}$ to solve tensor linear systems $\mathcal{A} ∗\mathcal{X} = \mathcal{B}$ where ∗ denotes the $t$-product. In addition, we consider variations of this method, including cyclic, block, and randomized approaches, each designed to optimize performance in different operational contexts. Our primary contribution lies in the development and convergence analysis of these methods. Experimental results on synthetically generated and real-world data, including applications such as image and video deblurring, demonstrate the efficacy of our proposed approaches and validate our theoretical findings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2024-0096
Numerical Mathematics: Theory, Methods and Applications, Vol. 18 (2025), Iss. 2 : pp. 353–394
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 42
Keywords: Tensor linear system t-product iterative method tensor sketching.