Algorithm xxx: Faster Randomized SVD with Dynamic Shifts
<|reference_start|>Algorithm xxx: Faster Randomized SVD with Dynamic Shifts: 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.<|reference_end|>
@article{feng2024algorithm,
    title={Algorithm xxx: Faster Randomized SVD with Dynamic Shifts},
    author={Xu Feng, Wenjian Yu, Yuyang Xie, and Jie Tang},
    journal={arXiv preprint arXiv:2404.09276},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.09276},
    primaryClass={cs.MS cs.NA math.NA}
}