  In this paper, we propose a computationally efficient iterative algorithm for
proper orthogonal decomposition (POD) using random sampling based techniques.
In this algorithm, additional rows and columns are sampled and a merging
technique is used to update the dominant POD modes in each iteration. We derive
bounds for the spectral norm of the error introduced by a series of merging
operations. We use an existing theorem to get an approximate measure of the
quality of subspaces obtained on convergence of the iteration. Results on
various datasets indicate that the POD modes and/or the subspaces are
approximated with excellent accuracy with a significant runtime improvement
over computing the truncated SVD. We also propose a method to compute the POD
modes of large matrices that do not fit in the RAM using this iterative
sampling and merging algorithms.
