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

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.