{"paper":{"title":"The Discrete Empirical Interpolation Method: Canonical Structure and Formulation in Weighted Inner Product Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Arvind K. Saibaba, Zlatko Drma\\v{c}","submitted_at":"2017-04-21T15:38:25Z","abstract_excerpt":"New contributions are offered to the theory and practice of the Discrete Empirical Interpolation Method (DEIM). These include a detailed characterization of the canonical structure; a substantial tightening of the error bound for the DEIM oblique projection, based on index selection via a strong rank revealing QR factorization; and an extension of the DEIM approximation to weighted inner products defined by a real symmetric positive-definite matrix $W$. The weighted DEIM ($W$-DEIM) can be deployed in the more general framework where the POD Galerkin projection is formulated in a discretization"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06606","kind":"arxiv","version":4},"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"}