Accelerated alternating minimization algorithm for low-rank approximations in the Chebyshev norm
<|reference_start|>Accelerated alternating minimization algorithm for low-rank approximations in the Chebyshev norm: 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 $2$-way alternance of rank $r$. We show that the presence of a $2$-way alternance of rank $r$ 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.<|reference_end|>
@article{morozov2024accelerated,
    title={Accelerated alternating minimization algorithm for low-rank
  approximations in the Chebyshev norm},
    author={Stanislav Morozov, Dmitry Zheltkov, Alexander Osinsky},
    journal={arXiv preprint arXiv:2410.05247},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.05247},
    primaryClass={math.NA cs.NA}
}