{"paper":{"title":"Mean squared error minimization for inverse moment problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"CTU/FEE), Didier Henrion (LAAS, Jean-Bernard Bernard Lasserre (LAAS), Martin Mevissen","submitted_at":"2012-08-31T06:41:07Z","abstract_excerpt":"We consider the problem of approximating the unknown density $u\\in L^2(\\Omega,\\lambda)$ of a measure $\\mu$ on $\\Omega\\subset\\R^n$, absolutely continuous with respect to some given reference measure $\\lambda$, from the only knowledge of finitely many moments of $\\mu$. Given $d\\in\\N$ and moments of order $d$, we provide a polynomial $p_d$ which minimizes the mean square error $\\int (u-p)^2d\\lambda$ over all polynomials $p$ of degree at most $d$. If there is no additional requirement, $p_d$ is obtained as solution of a linear system. In addition, if $p_d$ is expressed in the basis of polynomials "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6398","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"}