{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-block-bidiagonalization-method-for-fixed","title":"A Block Bidiagonalization Method for Fixed-Accuracy Low-Rank Matrix Approximation","arxiv_id":"2101.01247","date":"2021-01-04","proceeding":null,"authors":["Eric Hallman"],"abstract":"We present randUBV, a randomized algorithm for matrix sketching based on the block Lanzcos bidiagonalization process. Given a matrix $\\bf{A}$, it produces a low-rank approximation of the form ${\\bf UBV}^T$, where $\\bf{U}$ and $\\bf{V}$ have orthonormal columns in exact arithmetic and $\\bf{B}$ is block bidiagonal. In finite precision, the columns of both ${\\bf U}$ and ${\\bf V}$ will be close to orthonormal. Our algorithm is closely related to the randQB algorithms of Yu, Gu, and Li (2018) in that the entries of $\\bf{B}$ are incrementally generated and the Frobenius norm approximation error may be efficiently estimated. Our algorithm is therefore suitable for the fixed-accuracy problem, and so is designed to terminate as soon as a user input error tolerance is reached. Numerical experiments suggest that the block Lanczos method is generally competitive with or superior to algorithms that use power iteration, even when $\\bf{A}$ has significant clusters of singular values.","url_abs":"https://arxiv.org/abs/2101.01247v2","url_pdf":"https://arxiv.org/pdf/2101.01247v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-block-bidiagonalization-method-for-fixed","repo_url":"https://github.com/erhallma/randUBV","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}