A Subspace-Approximating Algorithm For Matrix Completion

In this paper, the matrix completion is studied in more detail. We propose two kinds of subspace-approximating algorithms for matrix completion which based on the least squares approximating to the known elements in the subspace of singular vectors of the partial singular value decomposition. One of the methods can form new feasible matrices by the best approximation to the feasible part in the subspace of the left and right singular vectors. And then, under the condition of the error of the feasible part is gradually reduced, the sequences of feasible matrices converge to the optimal solution. The other method is a modified algorithm of the subspace-approximating. It does not need to be modified as a feasible matrix in each iteration. So it can save the time of extraction and reduce the CPU time in general. In theory, we prove the convergence of the algorithms under some conditions. Compared with the orthogonal rank-one matrix pursuit and the augmented Lagrange multiplier methods by numerical experiments, we show the effectiveness of the two new algorithms in time and accuracy.