Randomized average block coordinate descent method with heavy-ball momentum for tensor least squares problem under the t-product
Abstract
A tensor randomized average block coordinate descent method with heavy-ball momentum is proposed for the tensor least squares problem with respect to the t-product. Theoretical analysis for tensor block coordinate descent method is established and average techniques are applied to avoid the computation of tensor Moore--Penrose inverse. To further accelerate convergence, a heavy-ball momentum scheme is incorporated into the block coordinate descent method, where the step size and momentum parameters are adaptively determined by a two-dimensional minimal residual projection. Theoretical analyses give the convergence of the new method and provide an improved bound on the linear convergence rate. Numerical experiments further verify the efficiency of the proposed method in terms of the number of iterations and the better video recovery performance.
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BibTeX
@misc{ji2026randomized,
title = {{Randomized average block coordinate descent method with heavy-ball momentum for tensor least squares problem under the t-product}},
author = {Li-Lin Ji and Ni-Hong Ke and Jun-Feng Yin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14516},
eprint = {2609.14516},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14516},
}
RIS
TY - UNPB
TI - Randomized average block coordinate descent method with heavy-ball momentum for tensor least squares problem under the t-product
AU - Li-Lin Ji
AU - Ni-Hong Ke
AU - Jun-Feng Yin
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14516
UR - https://arxiv.org/abs/2609.14516
AB - A tensor randomized average block coordinate descent method with heavy-ball momentum is proposed for the tensor least squares problem with respect to the t-product. Theoretical analysis for tensor block coordinate descent method is established and average techniques are applied to avoid the computation of tensor Moore--Penrose inverse. To further accelerate convergence, a heavy-ball momentum scheme is incorporated into the block coordinate descent method, where the step size and momentum parameters are adaptively determined by a two-dimensional minimal residual projection. Theoretical analyses give the convergence of the new method and provide an improved bound on the linear convergence rate. Numerical experiments further verify the efficiency of the proposed method in terms of the number of iterations and the better video recovery performance.
ER -