Accelerating Power Method with Fast Sketching for Stronger Low-Rank Approximation

Shabarish Chenakkod; Michał Dereziński

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arXiv · 2605.09755

Accelerating Power Method with Fast Sketching for Stronger Low-Rank Approximation

Shabarish Chenakkod·Michał Dereziński

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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.

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Shabarish Chenakkod, Michał Dereziński. 2026-05-10. Accelerating Power Method with Fast Sketching for Stronger Low-Rank Approximation. https://arxiv.org/abs/2605.09755

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