Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix

@article{Drineas2006FastMC,
title={Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix},
author={Petros Drineas and Ravi Kannan and Michael W. Mahoney},
journal={SIAM J. Comput.},
year={2006},
volume={36},
pages={158-183}
}

In many applications, the data consist of (or may be naturally formulated as) an m×n matrix A. It is often of interest to find a low-rank approximation to A, i.e., an approximation D to the matrix A of rank not greater than a specified rank k, where k is much smaller than m and n. Methods such as the singular value decomposition (SVD) may be used to find an approximation to A which is the best in a well-defined sense. These methods require memory and time which are superlinear in m and n; for… CONTINUE READING