preprint · arXiv (Cornell University) · 2018

Randomized QLP algorithm and error analysis

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Abstract

In this paper, we describe the randomized QLP (RQLP) algorithm and its enhanced version (ERQLP) for computing the low rank approximation to $A$ of size $m\times n$ efficiently such that $A\approx QLP$, where $L$ is the rank-$k$ lower-triangular matrix, $Q$ and $P$ are column orthogonal matrices. The theoretical cost of the implementation of RQLP and ERQLP only needs $\mathcal{O}(mnk)$. Moreover, we derive the upper bounds of the expected approximation error $\mathbb{E}\left [ (σ_{j}(A) - σ_{j} (L))/ σ_{j}(A) \right] $ for $j=1,\cdots, k$, and prove that the $L$-values of the proposed methods can track the singular values of $A$ accurately. These claims are supported by extensive numerical experiments.

Cite this paper

APA 7

Wu, N., & Xiang, H. (2018). Randomized QLP algorithm and error analysis. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1811.09334

MLA 9

Wu, Nian‐Ci, and Hua Xiang. “Randomized QLP algorithm and error analysis.” arXiv (Cornell University), 2018, https://doi.org/10.48550/arxiv.1811.09334.

Chicago

Wu, Nian‐Ci, and Hua Xiang. 2018. “Randomized QLP algorithm and error analysis.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.1811.09334.

Harvard

Wu, N. and Xiang, H. (2018) ‘Randomized QLP algorithm and error analysis’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.1811.09334.

BibTeX

@misc{wu2018randomized,
  title = {{Randomized QLP algorithm and error analysis}},
  author = {Wu, Nian‐Ci and Xiang, Hua},
  journal = {arXiv (Cornell University)},
  year = {2018},
  doi = {10.48550/arxiv.1811.09334}
}

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