{"paper":{"title":"Convergence analysis of the Generalized Empirical Interpolation Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"G. Turinici, O. Mula, Y. Maday","submitted_at":"2016-05-25T04:36:32Z","abstract_excerpt":"Let $F$ be a compact set of a Banach space $\\mathcal{X}$. This paper analyses the \"Generalized Empirical Interpolation Method\" (GEIM) which, given a function $f\\in F$, builds an interpolant $\\mathcal{J}_n[f]$ in an $n$-dimensional subspace $X_n \\subset \\mathcal{X}$ with the knowledge of $n$ outputs $(\\sigma_i(f))_{i=1}^n$, where $\\sigma_i\\in \\mathcal{X}'$ and $\\mathcal{X}'$ is the dual space of $\\mathcal{X}$. The space $X_n$ is built with a greedy algorithm that is adapted to $F$ in the sense that it is generated by elements of $F$ itself. The algorithm also selects the linear functionals $(\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07730","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"}