The low-rank matrix approximation problem is ubiquitous in computational mathematics. Traditionally, this problem is solved in spectral or Frobenius norms, where the accuracy of the approximation is related to the rate of decrease of the singular values of the matrix. However, recent results indicate that this requirement is not necessary for other norms. In this paper, we propose a method for solving the low-rank approximation problem in the Chebyshev norm, which is capable of efficiently constructing accurate approximations for matrices, whose singular values do not decrease or decrease slowly.

翻译：低级矩阵近似问题在计算数学中普遍存在。 传统上,这个问题在光谱或弗罗贝尼乌斯规范中解决,因为光谱或弗罗贝尼乌斯规范的准确性与矩阵单值的下降速度有关。 但是,最近的结果显示,这一要求对于其他规范来说并不必要。 在本文件中,我们提出了解决Chebyshev规范中低级近近似问题的方法,它能够有效地构建矩阵的准确近近似值,而矩阵的单值不会缓慢地减少或减少。