{"paper":{"title":"Efficient Algorithms for Approximate Smooth Selection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Bernat Guillen Pegueroles, Charles Fefferman","submitted_at":"2019-05-08T20:17:57Z","abstract_excerpt":"In this paper we provide efficient algorithms for approximate $\\mathcal{C}^m(\\mathbb{R}^n, \\mathbb{R}^D)-$selection. In particular, given a set $E$, constants $M_0 > 0$ and $0 <\\tau \\leq \\tau_{\\max}$, and convex sets $K(x) \\subset \\mathbb{R}^D$ for $x \\in E$, we show that an algorithm running in $C(\\tau) N \\log N$ steps is able to solve the smooth selection problem of selecting a point $y \\in (1+\\tau)\\blacklozenge K(x)$ for $x \\in E$ for an appropriate dilation of $K(x)$, $(1+\\tau)\\blacklozenge K(x)$, and guaranteeing that a function interpolating the points $(x, y)$ will be $\\mathcal{C}^m(\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04156","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"}