{"paper":{"title":"Adaptive algorithms in sampling recovery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dinh D\\~ung","submitted_at":"2011-02-17T10:09:09Z","abstract_excerpt":"We study optimal algorithms in adaptive sampling recovery of smooth functions defined on the unit $d$-cube ${\\II}^d:= [0,1]^d$. The recovery error is measured in the quasi-norm $\\|\\cdot\\|_q$ of $L_q := L_q(\\II^d)$. For $B$ a subset in $L_q,$ we define a sampling algorithm of recovery with the free choice of sample points and recovering functions from $B$ as follows. For each $f$ from the quasi-normed Besov space $B^\\alpha_{p,\\theta}$, we choose $n$ sample points. This choice defines $n$ sampled values. Based on these sample points and sampled values, we choose a function from $B$ for recoverin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3540","kind":"arxiv","version":2},"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"}