Algorithm 1043: Faster Randomized SVD with Dynamic Shifts

• Published in: ACM transactions on mathematical software Vol. 50; no. 2; pp. 1 - 27
• Main Authors: Feng, Xu, Yu, Wenjian, Xie, Yuyang, Tang, Jie
• Format: Journal Article
• Language: English
• Published: New York, NY ACM 28.06.2024
• Subjects: Computing methodologies; Feature selection; Mathematics of computing; Numeric approximation algorithms; Parallel algorithms; Solvers; Theory of computation; sparse matrix; Truncated singular value decomposition; shifted power iteration; random embedding
• ISSN: 0098-3500; 1557-7295; 1557-7295
• DOI: 10.1145/3660629

Aiming to provide a faster and convenient truncated SVD algorithm for large sparse matrices from real applications (i.e., for computing a few of the 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 a randomized SVD algorithm or attains the 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.