Projected Landweber iteration for matrix completion

Recovering an unknown low-rank or approximately low-rank matrix from a sampling set of its entries is known as the matrix completion problem. In this paper, a nonlinear constrained quadratic program problem concerning the matrix completion is obtained. A new algorithm named the projected Landweber iteration (PLW) is proposed, and the convergence is proved strictly. Numerical results show that the proposed algorithm can be fast and efficient under suitable prior conditions of the unknown low-rank matrix.