Li Jicheng, Liu Zisheng, Li Guo
School of Mathematics and Statistics, Xi'an Jiaotong University, No. 28, Xianning West Road, Xi'an, 710049 China.
School of Statistics, Henan University of Economics and Law, No. 180, Jinshui East Road, Zhengzhou, 450046 China.
J Inequal Appl. 2017;2017(1):288. doi: 10.1186/s13660-017-1564-z. Epub 2017 Nov 21.
Low-rank matrix recovery is an active topic drawing the attention of many researchers. It addresses the problem of approximating the observed data matrix by an unknown low-rank matrix. Suppose that is a low-rank matrix approximation of , where and are [Formula: see text] matrices. Based on a useful decomposition of [Formula: see text], for the unitarily invariant norm [Formula: see text], when [Formula: see text] and [Formula: see text], two sharp lower bounds of [Formula: see text] are derived respectively. The presented simulations and applications demonstrate our results when the approximation matrix is low-rank and the perturbation matrix is sparse.
