{"paper":{"title":"Truncation Dimension for Function Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Friedrich Pillichshammer, G.W. Wasilkowski, Peter Kritzer","submitted_at":"2016-10-10T11:27:17Z","abstract_excerpt":"We consider approximation of functions of $s$ variables, where $s$ is very large or infinite, that belong to weighted anchored spaces. We study when such functions can be approximated by algorithms designed for functions with only very small number ${\\rm dim^{trnc}}(\\varepsilon)$ of variables. Here $\\varepsilon$ is the error demand and we refer to ${\\rm dim^{trnc}}(\\varepsilon)$ as the $\\varepsilon$-truncation dimension. We show that for sufficiently fast decaying product weights and modest error demand (up to about $\\varepsilon \\approx 10^{-5}$) the truncation dimension is surprisingly very s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02852","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"}