An improved analysis and unified perspective on deterministic and randomized low rank matrix approximations
Numerical Analysis
2019-10-02 v1 Data Structures and Algorithms
Numerical Analysis
Abstract
We introduce a Generalized LU-Factorization (\textbf{GLU}) for low-rank matrix approximation. We relate this to past approaches and extensively analyze its approximation properties. The established deterministic guarantees are combined with sketching ensembles satisfying Johnson-Lindenstrauss properties to present complete bounds. Particularly good performance is shown for the sub-sampled randomized Hadamard transform (SRHT) ensemble. Moreover, the factorization is shown to unify and generalize many past algorithms. It also helps to explain the effect of sketching on the growth factor during Gaussian Elimination.
Keywords
Cite
@article{arxiv.1910.00223,
title = {An improved analysis and unified perspective on deterministic and randomized low rank matrix approximations},
author = {James Demmel and Laura Grigori and Alexander Rusciano},
journal= {arXiv preprint arXiv:1910.00223},
year = {2019}
}