Accurate Low Rank Approximation at a Low Computational Cost

Given an algorithm A for computing a crude Low Rank Approximation (LRA) of a matrix having fast decaying spectra of singular values, we greatly decreased the spectral norm of its output error matrix at sublinear additional computational cost. Furthermore, for a variety of synthetic and real world inputs we tested numerically variants where our entire algorithms run at sublinear cost, and in most cases we still obtained accurate or even near-optimal LRAs. Towards enhancing our progress to a larger class of matrices, we nontrivially extended to LRA the popular technique of iterative refinement.