{"paper":{"title":"Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NA","authors_text":"Albert Cohen, Fabio Nobile, Giovanni Migliorati","submitted_at":"2016-10-24T07:40:48Z","abstract_excerpt":"We analyze the accuracy of the discrete least-squares approximation of a function $u$ in multivariate polynomial spaces $\\mathbb{P}_\\Lambda:={\\rm span} \\{y\\mapsto y^\\nu \\,: \\, \\nu\\in \\Lambda\\}$ with $\\Lambda\\subset \\mathbb{N}_0^d$ over the domain $\\Gamma:=[-1,1]^d$, based on the sampling of this function at points $y^1,\\dots,y^m \\in \\Gamma$. The samples are independently drawn according to a given probability density $\\rho$ belonging to the class of multivariate beta densities, which includes the uniform and Chebyshev densities as particular cases. We restrict our attention to polynomial space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07315","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"}