# An improved analysis and unified perspective on deterministic and randomized low rank matrix approximations

arXiv: https://arxiv.org/abs/1910.00223 · HTML: https://mlsanity.com/paper/1910.00223/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2019.

## Built on by (most cited first, 1 of 1)

- [Accelerating Large-Scale Regularized High-Order Tensor Recovery](https://mlsanity.com/paper/2506.09594/) (2025)

## Abstract (arXiv)

We introduce a Generalized LU-Factorization (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.