{"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/root-finding-via-local-measurement","title":"Root finding via local measurement","arxiv_id":"2302.13211","date":"2023-02-26","proceeding":null,"authors":["Jonathan Landy","YongSeok Jho"],"abstract":"We consider the problem of numerically identifying roots of a target function - under the constraint that we can only measure the derivatives of the function at a given point, not the function itself. We describe and characterize two methods for doing this: (1) a local-inversion \"inching process\", where we use local measurements to repeatedly identify approximately how far we need to move to drop the target function by the initial value over N, an input parameter, and (2) an approximate Newton's method, where we estimate the current function value at a given iteration via estimation of the integral of the function's derivative, using N samples. When applicable, both methods converge algebraically with N, with the power of convergence increasing with the number of derivatives applied in the analysis.","url_abs":"https://arxiv.org/abs/2302.13211v1","url_pdf":"https://arxiv.org/pdf/2302.13211v1.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":"root-finding-via-local-measurement","repo_url":"https://github.com/efavdb/inchwormrf","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}