Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Feng, Xu, Yu, Wenjian, Xie, Yuyang, Tang, Jie
Institution: Tsinghua University
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: 面向大数据智能处理的随机矩阵与张量算法研究
OpenAlex ID: W4394867950