{"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/an-o-1-algorithm-for-the-numerical-evaluation","title":"An O(1) Algorithm for the Numerical Evaluation of the Prolate Spheroidal Wave Functions of Order 0","arxiv_id":"1905.04415","date":"2019-05-11","proceeding":null,"authors":["Xinge Zhang","James Bremer"],"abstract":"The standard algorithm for the numerical evaluation of the prolate spheroidal wave function $\\mathsf{Ps}\\hskip.05em{}_{n}(x;\\gamma^2)$ of order $0$, bandlimit $\\gamma > 0$ and characteristic exponent $n$ has running time which grows with both $n$ and $\\gamma$. Here, we describe an alternate approach which runs in time independent of these quantities. We present the results of numerical experiments demonstrating the properties of our scheme, and we have made our implementation of it publicly available.","url_abs":"http://arxiv.org/abs/1905.04415v1","url_pdf":"http://arxiv.org/pdf/1905.04415v1.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":"an-o-1-algorithm-for-the-numerical-evaluation","repo_url":"https://github.com/JamesCBremerJr/Prolates","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}