Accelerating Power Method with Fast Sketching for Stronger Low-Rank Approximation
Abstract
The power method is one of the most fundamental tools for extracting top principal components from data through low-rank matrix approximation. Yet, when the target rank is large, the cost of matrix multiplication associated with this procedure becomes a major bottleneck. We develop an algorithmic and theoretical framework for accelerating the power method using fast sketching, which is a popular paradigm in randomized linear algebra. Our framework leads to simple and provably efficient methods for singular value decomposition, low-rank factorization, and Nystr\"om approximation, which attain strong numerical performance on benchmark problems. The key novelty in our analysis is the use of regularized spectral approximation, a property of fast sketching methods which proves more flexible in generalizing power method guarantees than traditional arguments.
Cite
@article{arxiv.2605.09755,
title = {Accelerating Power Method with Fast Sketching for Stronger Low-Rank Approximation},
author = {Shabarish Chenakkod and Michał Dereziński},
journal= {arXiv preprint arXiv:2605.09755},
year = {2026}
}