TY - JOUR
T1 - Frontal Slice Approaches for Tensor Linear Systems
AU - Luo , Hengrui
AU - Ma , Anna
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 353
EP - 394
PY - 2025
DA - 2025/05
SN - 18
DO - http://doi.org/10.4208/nmtma.OA-2024-0096
UR - https://global-sci.org/intro/article_detail/nmtma/24069.html
KW - Tensor linear system, t-product, iterative method, tensor sketching.
AB - <p style="text-align: justify;">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.</p>