文献类型：期刊文献

英文题名：Lower bounds for the low-rank matrix approximation

作者：Li, Jicheng[1];Liu, Zisheng[1,2];Li, Guo[3]

第一作者：Li, Jicheng

通讯作者：Liu, ZS[1];Liu, ZS[2]

机构：[1]Xi An Jiao Tong Univ, Sch Math & Stat, 28 Xianning West Rd, Xian 710049, Shaanxi, Peoples R China;[2]Henan Univ Econ & Law, Sch Stat, 180 Jinshui East Rd, Zhengzhou, Henan, Peoples R China;[3]Shenzhen Univ, Coll Math & Stat, 3688 Nanhai Ave, Shenzhen 518060, Peoples R China

第一机构：Xi An Jiao Tong Univ, Sch Math & Stat, 28 Xianning West Rd, Xian 710049, Shaanxi, Peoples R China

通讯机构：[1]corresponding author), Xi An Jiao Tong Univ, Sch Math & Stat, 28 Xianning West Rd, Xian 710049, Shaanxi, Peoples R China;[2]corresponding author), Henan Univ Econ & Law, Sch Stat, 180 Jinshui East Rd, Zhengzhou, Henan, Peoples R China.|[1048415]河南财经政法大学统计与大数据学院;[10484]河南财经政法大学;

年份：2017

卷号：2017

外文期刊名：JOURNAL OF INEQUALITIES AND APPLICATIONS

收录：;Scopus(收录号：2-s2.0-85035775156);WOS:【SCI-EXPANDED(收录号:WOS:000416135700001)】；

基金：This work is partially supported by the National Natural Science Foundation of China under grant No. 11671318, and the Fundamental Research Funds for the Central Universities (Xi'an Jiaotong University, Grant No. xkjc2014008).

语种：英文

外文关键词：low-rank matrix; approximation; error estimation; pseudo-inverse; matrix norms

摘要：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 A is a low-rank matrix approximation of D, where D and A are matrices. Based on a useful decomposition of , for the unitarily invariant norm , when and , two sharp lower bounds of are derived respectively. The presented simulations and applications demonstrate our results when the approximation matrix A is low-rank and the perturbation matrix is sparse.