{"paper":{"title":"Fitting a Sobolev function to data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Arie Israel, Charles L. Fefferman, Garving K. Luli","submitted_at":"2014-11-06T22:42:46Z","abstract_excerpt":"We exhibit an algorithm to solve the following extension problem: Given a finite set $E \\subset \\mathbb{R}^n$ and a function $f: E \\rightarrow \\mathbb{R}$, compute an extension $F$ in the Sobolev space $L^{m,p}(\\mathbb{R}^n)$, $p>n$, with norm having the smallest possible order of magnitude, and secondly, compute the order of magnitude of the norm of $F$. Here, $L^{m,p}(\\mathbb{R}^n)$ denotes the Sobolev space consisting of functions on $\\mathbb{R}^n$ whose $m$th order partial derivatives belong to $L^p(\\mathbb{R}^n)$. The running time of our algorithm is at most $C N \\log N$, where $N$ denote"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1786","kind":"arxiv","version":1},"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"}