Year: 2018
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Wu, Nianci, Xiang, Hua
Institution: Wuhan University
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2900865982