{"paper":{"title":"Sequential sampling for optimal weighted least squares approximations in hierarchical spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.ST","stat.TH"],"primary_cat":"math.NA","authors_text":"Albert Cohen, Benjamin Arras, Markus Bachmayr","submitted_at":"2018-05-28T07:54:42Z","abstract_excerpt":"We consider the problem of approximating an unknown function $u\\in L^2(D,\\rho)$ from its evaluations at given sampling points $x^1,\\dots,x^n\\in D$, where $D\\subset \\mathbb{R}^d$ is a general domain and $\\rho$ is a probability measure. The approximation is picked in a linear space $V_m$ where $m=\\dim(V_m)$ and computed by a weighted least squares method. Recent results show the advantages of picking the sampling points at random according to a well-chosen probability measure $\\mu$ that depends both on $V_m$ and $\\rho$. With such a random design, the weighted least squares approximation is prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10801","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"}