{"paper":{"title":"Computing minimal interpolants in $C^{1,1}(\\mathbb{R}^d)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.NA","math.CA"],"primary_cat":"math.NA","authors_text":"Ariel Herbert-Voss, Frederick McCollum, Matthew J. Hirn","submitted_at":"2014-11-20T20:41:10Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5668","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}