### abstract ###
We consider a problem of significant practical importance,  namely, the reconstruction of a low-rank data matrix from a small subset of its entries
This problem appears in many areas such as  collaborative filtering, computer vision and wireless sensor networks
In this paper, we focus on the matrix completion problem  in the case when the observed samples are corrupted by noise
We compare the performance of  three state-of-the-art matrix completion algorithms  (OptSpace, ADMiRA and FPCA) on a single simulation platform  and present numerical results
We show that in practice  these efficient algorithms can be used to reconstruct real data matrices, as well as randomly generated matrices, accurately
### introduction ###
We consider the problem of reconstructing an  SYMBOL   low rank matrix  SYMBOL  from a small set of observed entries possibly corrupted by noise
This problem is of considerable practical interest and has many applications
One example is collaborative filtering, where users submit rankings  for small subsets of, say, movies, and the goal is  to infer the preference of unrated movies for a recommendation system  CITATION
It is believed that the movie-rating matrix is approximately low-rank,  since only a few factors contribute to a user's preferences
Other examples of matrix completion include the problem of inferring  3-dimensional structure from motion  CITATION  and triangulation from incomplete  data of distances between wireless sensors  CITATION
