Accelerating Power Method with Fast Sketching for Stronger Low-Rank Approximation
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 Nyström approximation, which attain strong numerical performance on benchmark problems. The key novelty in our analysis is the use of re...
| Authors | Shabarish Chenakkod, Michał Dereziński |
|---|---|
| Primary category | math.NA |
| Published | 10 May 2026 |
| Last updated at source | 10 May 2026 |
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