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《Numerical Mathematics A Journal of Chinese Universities》 2018-02
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ERROR BOUNDS FOR SPARSE AND LOW-RANK MATRIX APPROXIMATION BASED ON RESTRICTED ISOMETRIC PROPERTIES

Liu Zisheng;Li Jicheng;Bai Jianchao;School of Mathematics and Statistics, Xi'an Jiaotong University;School of Statistics,Henan University of Economics and Law;School of Mathematics and Statistics,Xi'an Jiaotong University;  
In this paper, we consider the sparse and low-rank matrices approximation problem, which is regarded as a separable convex optimization problem subjected to linearly equality constraint. For such problem, we focus on estimating the error bounds of sparse matrix recovery. Based on the restricted isometric properties(RIP), a sufficient condition is given for exact reconstruction of sparse matrix in the ideal case. For noisy measurements, the robustness of sparse matrix restoration is analyzed and the upper bound of approximation error is also provided. Numerical simulations on solving a practical application example show that our RIP-Bound is correct.
【Fund】: 国家自然科学基金(11671318);; 中央高校基本科研业务费学科交叉重点项目(xkjc2014008)
【CateGory Index】: O151.21
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