$11.$ Write an Rfunction to perform matrixc ompletion as in Algorithm$12\mathrm{.}1,$ and as outlined in Section $12\mathrm{.}5\mathrm{.}2.$ In each iteration, the function should keep track of the relative error, as well as the iteration count. Iterations should continue until the relative error is small enough or until some maximum number of iterations is reached $($set a default value for this maximum number$).$ Furthermore, there should be an option to print out the progress in each iteration.