Accelerated algorithms for low-rank matrix recovery

In recent years, Low-rank matrix recovery from corrupted noise matrix has attracted interests as a very effective method in high-dimensional data. And its fast algorithm has become a research focus. This paper we first review the basic theory and typical accelerated algorithms. All these methods are proposed to mitigating the computational burden, such as the iteration count before convergence, especially the frequent large-scale Singular Value Decomposition (SVD). For better convergence, we employ the Augmented Lagrange Multipliers to solve the optimization problem. Recent the endeavors have focused on smaller-scale SVD, especially the method based on submatrix. Finally, we present numerical experiments on large-scale date.