{"paper":{"title":"Multivariate approximation of functions on irregular domains by weighted least-squares methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Giovanni Migliorati","submitted_at":"2019-07-29T09:44:24Z","abstract_excerpt":"We propose and analyse numerical algorithms based on weighted least squares for the approximation of a real-valued function on a general bounded domain $\\Omega \\subset \\mathbb{R}^d$. Given any $n$-dimensional approximation space $V_n \\subset L^2(\\Omega)$, the analysis in [6] shows the existence of stable and optimally converging weighted least-squares estimators, using a number of function evaluations $m$ of the order $n \\log n$. When an $L^2(\\Omega)$-orthonormal basis of $V_n$ is available in analytic form, such estimators can be constructed using the algorithms described in [6,Section 5]. If"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.12304","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.12304/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}