English

Weighted sampling of outer products

Data Structures and Algorithms 2014-10-17 v1

Abstract

This note gives a simple analysis of the randomized approximation scheme for matrix multiplication of Drineas et al (2006) with a particular sampling distribution over outer products. The result follows from a matrix version of Bernstein's inequality. To approximate the matrix product ABAB^\top to spectral norm error εAB\varepsilon\|A\|\|B\|, it suffices to sample on the order of (sr(A)sr(B))log(sr(A)sr(B))/ε2(\mathrm{sr}(A) \vee \mathrm{sr}(B)) \log(\mathrm{sr}(A) \wedge \mathrm{sr}(B)) / \varepsilon^2 outer products, where sr(M)\mathrm{sr}(M) is the stable rank of a matrix MM.

Keywords

Cite

@article{arxiv.1410.4429,
  title  = {Weighted sampling of outer products},
  author = {Daniel Hsu},
  journal= {arXiv preprint arXiv:1410.4429},
  year   = {2014}
}
R2 v1 2026-06-22T06:26:00.638Z