Every sufficiently big matrix with small spectral norm has a nearby low-rank matrix if the distance is measured in the maximum norm (Udell & Townsend, SIAM J Math Data Sci, 2019). We use the Hanson--Wright inequality to improve the estimate of the distance for matrices with incoherent column and row spaces. In numerical experiments with several classes of matrices we study how well the theoretical upper bound describes the approximation errors achieved with the method of alternating projections.

翻译：每个谱范数足够小的充分大矩阵，在最大范数度量下都存在邻近的低秩矩阵（Udell & Townsend, SIAM J Math Data Sci, 2019）。我们利用Hanson–Wright不等式改进了对列空间与行空间非相干的矩阵的该距离估计。通过数值实验研究多类矩阵，我们检验了理论上限对交替投影方法所达到近似误差的描述程度。