Single-pass randomized QLP decomposition for low-rank approximation

Abstract

As a special UTV decomposition, the QLP decomposition is an effective alternative of the singular value decomposition (SVD) for the low-rank approximation. In this paper, we propose a single-pass randomized QLP decomposition algorithm for computing a low-rank matrix approximation. Compared with the randomized QLP decomposition, the complexity of the proposed algorithm does not increase significantly and the data matrix needs to be accessed only once. Therefore, our algorithm is suitable for a large matrix stored outside of memory or generated by streaming data. In the error analysis, we give the matrix approximation error analysis. We also provide singular value approximation error bounds, which can track the target largest singular values of the data matrix with high probability. Numerical experiments are also reported to verify our results.