  The low rank approximation of matrices is a crucial component in many data
mining applications today. A competitive algorithm for this class of problems
is the randomized block Lanczos algorithm - an amalgamation of the traditional
block Lanczos algorithm with a randomized starting matrix. While empirically
this algorithm performs quite well, there has been scant new theoretical
results on its convergence behavior and approximation accuracy, and past
results have been restricted to certain parameter settings. In this paper, we
present a unified singular value convergence analysis for this algorithm, for
all valid choices of the block size parameter. We present novel results on the
rate of singular value convergence and show that under certain spectrum
regimes, the convergence is superlinear. Additionally, we provide results from
numerical experiments that validate our analysis.
