Accelerated alternating minimization algorithm for low-rank approximations in the Chebyshev norm
Abstract
Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise approximations have also received significant attention in the literature. In this paper, we propose an accelerated alternating minimization algorithm for solving the problem of low-rank approximation of matrices in the Chebyshev norm. Through the numerical evaluation we demonstrate the effectiveness of the proposed procedure for large-scale problems. We also theoretically investigate the alternating minimization method and introduce the notion of a -way alternance of rank . We show that the presence of a -way alternance of rank is the necessary condition of the optimal low-rank approximation in the Chebyshev norm and that all limit points of the alternating minimization method satisfy this condition.
Cite
@article{arxiv.2410.05247,
title = {Accelerated alternating minimization algorithm for low-rank approximations in the Chebyshev norm},
author = {Stanislav Morozov and Dmitry Zheltkov and Alexander Osinsky},
journal= {arXiv preprint arXiv:2410.05247},
year = {2026}
}