Single-pass randomized QLP decomposition for low-rank approximation

TL;DR

This paper introduces single-pass randomized algorithms for QLP decomposition that efficiently compute low-rank approximations of large matrices with minimal data access, suitable for streaming or out-of-core data.

Contribution

It proposes novel single-pass randomized QLP algorithms that maintain accuracy while significantly reducing data access compared to deterministic methods.

Findings

Algorithms achieve comparable accuracy to deterministic QLP.

Complexity remains similar to deterministic methods.

Numerical experiments confirm theoretical error bounds.

Abstract

The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the low-rank matrix approximation. Compared with the deterministic QLP decomposition, the complexity of the proposed algorithms does not increase significantly and the system matrix needs to be accessed only once. Therefore, our algorithms are very suitable for a large matrix stored outside of memory or generated by stream data. In the error analysis, we give the bounds of matrix approximation error and singular value approximation error. Numerical experiments also reported to verify our results.