A randomized algorithm for the QR decomposition-based approximate SVD

Xiaohui Ni; An-Bao Xu

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arXiv · 2305.11450

A randomized algorithm for the QR decomposition-based approximate SVD

Xiaohui Ni·An-Bao Xu

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Abstract

Matrix decomposition is a very important mathematical tool in numerical linear algebra for data processing. In this paper, we introduce a new randomized matrix decomposition algorithm, which is called randomized approximate SVD based on Qatar Riyal decomposition (RCSVD-QR). Our method utilize random sampling and the OR decomposition to address a serious bottlenck associated with classical SVD. RCSVD-QR gives satisfactory convergence speed as well as accuracy as compared to those state-of-the-art algorithms. In addition, we provides an estimate for the expected approximation error in Frobenius norm. Numerical experiments verify these claims.

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Xiaohui Ni, An-Bao Xu. 2023-05-19. A randomized algorithm for the QR decomposition-based approximate SVD. https://arxiv.org/abs/2305.11450

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