{"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/randomized-nystrom-approximation-of-non","title":"Randomized Nyström approximation of non-negative self-adjoint operators","arxiv_id":"2404.00960","date":"2024-04-01","proceeding":null,"authors":["David Persson","Nicolas Boullé","Daniel Kressner"],"abstract":"The randomized singular value decomposition (SVD) has become a popular approach to computing cheap, yet accurate, low-rank approximations to matrices due to its efficiency and strong theoretical guarantees. Recent work by Boull\\'e and Townsend (FoCM, 2023) presents an infinite-dimensional analog of the randomized SVD to approximate Hilbert-Schmidt operators. However, many applications involve computing low-rank approximations to symmetric positive semi-definite matrices. In this setting, it is well-established that the randomized Nystr\\\"om approximation is usually preferred over the randomized SVD. This paper explores an infinite-dimensional analog of the Nystr\\\"om approximation to compute low-rank approximations to non-negative self-adjoint trace-class operators. We present an analysis of the method and, along the way, improve the existing infinite-dimensional bounds for the randomized SVD. Our analysis yields bounds on the expected value and tail bounds for the Nystr\\\"om approximation error in the operator, trace, and Hilbert-Schmidt norms. Numerical experiments on integral operators arising from Gaussian process sampling and Bayesian inverse problems are used to validate the proposed infinite-dimensional Nystr\\\"om algorithm.","url_abs":"https://arxiv.org/abs/2404.00960v2","url_pdf":"https://arxiv.org/pdf/2404.00960v2.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":"randomized-nystrom-approximation-of-non","repo_url":"https://github.com/davpersson/infNystrom","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"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}