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Algorithm xxx: Faster Randomized SVD with Dynamic Shifts

arXiv.org, 2024-04

2024. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. ;http://arxiv.org/licenses/nonexclusive-distrib/1.0 ;EISSN: 2331-8422 ;DOI: 10.48550/arxiv.2404.09276

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  • Title:
    Algorithm xxx: Faster Randomized SVD with Dynamic Shifts
  • Author: Xu, Feng ; Yu, Wenjian ; Xie, Yuyang ; Tang, Jie
  • Subjects: Accuracy ; Algorithms ; Computer Science - Mathematical Software ; Computer Science - Numerical Analysis ; Hierarchies ; Mathematics - Numerical Analysis ; Sparse matrices ; Sparsity
  • Is Part Of: arXiv.org, 2024-04
  • Description: Aiming to provide a faster and convenient truncated SVD algorithm for large sparse matrices from real applications (i.e. for computing a few of largest singular values and the corresponding singular vectors), a dynamically shifted power iteration technique is applied to improve the accuracy of the randomized SVD method. This results in a dynamic shifts based randomized SVD (dashSVD) algorithm, which also collaborates with the skills for handling sparse matrices. An accuracy-control mechanism is included in the dashSVD algorithm to approximately monitor the per vector error bound of computed singular vectors with negligible overhead. Experiments on real-world data validate that the dashSVD algorithm largely improves the accuracy of randomized SVD algorithm or attains same accuracy with fewer passes over the matrix, and provides an efficient accuracy-control mechanism to the randomized SVD computation, while demonstrating the advantages on runtime and parallel efficiency. A bound of the approximation error of the randomized SVD with the shifted power iteration is also proved.
  • Publisher: Ithaca: Cornell University Library, arXiv.org
  • Language: English
  • Identifier: EISSN: 2331-8422
    DOI: 10.48550/arxiv.2404.09276
  • Source: Freely Accessible Journals
    arXiv.org
    ROAD: Directory of Open Access Scholarly Resources
    ProQuest Central
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