Accurate principal component analysis via a few iterations of   alternating least squares
  A few iterations of alternating least squares with a random starting point provably suffice to produce nearly optimal spectral- and Frobenius-norm accuracies of low-rank approximations to a matrix; iterating to convergence is unnecessary. Thus, software implementing alternating least squares can be retrofitted via appropriate setting of parameters to calculate nearly optimally accurate low-rank approximations highly efficiently, with no need for convergence. 
Arthur Szlam, Andrew Tulloch, and Mark Tygert
math.NA cs.NA stat.CO