$\mathop{\min}\limits_{X\in\mathbb{R}^{m\times n}} {\rm rank}(X) \,\, {\rm such\, that}\, \ P_\Omega(X)=P_\Omega(Y).$

Our algorithm is literally a generalization of OR1MP algorithm [Z. Wang, M. J. Lai, Z. Lu, W. Fan, H. Davulcu and J. Ye, SIAM Journal on Scientific Computing, 2015] in the sense that multiple $s$ candidates are identified per iteration by low-rank matrix approximation. Owing to the selection of multiple $s$ candidates, our approach is finished with much smaller number of iterations when compared to the OR1MP. In addition, we extend the OR1MP algorithm to deal with tensor completion problem.