{"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/computing-minimal-interpolants-in-c-11-mathbb","title":"Computing minimal interpolants in $C^{1,1}(\\mathbb{R}^d)$","arxiv_id":"1411.5668","date":"2014-11-20","proceeding":null,"authors":["Ariel Herbert-Voss","Matthew J. Hirn","Frederick McCollum"],"abstract":"We consider the following interpolation problem. Suppose one is given a finite set $E \\subset \\mathbb{R}^d$, a function $f: E \\rightarrow \\mathbb{R}$, and possibly the gradients of $f$ at the points of $E$. We want to interpolate the given information with a function $F \\in C^{1,1}(\\mathbb{R}^d)$ with the minimum possible value of $\\mathrm{Lip} (\\nabla F)$. We present practical, efficient algorithms for constructing an $F$ such that $\\mathrm{Lip} (\\nabla F)$ is minimal, or for less computational effort, within a small dimensionless constant of being minimal.","url_abs":"http://arxiv.org/abs/1411.5668v4","url_pdf":"http://arxiv.org/pdf/1411.5668v4.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":"computing-minimal-interpolants-in-c-11-mathbb","repo_url":"https://github.com/matthew-hirn/C-1-1-Interpolation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}