  In this paper, we study the convergence of Alternating Projection (AP)
algorithm for the matrix completion and compressed sensing problems. We also
present computational evidence for the excellent performance of the algorithm.
Also, in the last section, we prove using algebraic-geometric techniques that,
fixing the known positions, if a rank r matrix can be completed in finitely
many ways using one given set of known entries, then, for almost all set of
known entries, the matrix can be only completed into a rank r matrix in
finitely many ways.
