{"paper":{"title":"Near-optimal Frequency-weighted Interpolatory Model Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NA"],"primary_cat":"cs.SY","authors_text":"Christopher Beattie, Serkan Gugercin, Tobias Breiten","submitted_at":"2013-08-31T17:37:37Z","abstract_excerpt":"This paper develops an interpolatory framework for weighted-$\\mathcal{H}_2$ model reduction of MIMO dynamical systems. A new representation of the weighted-$\\mathcal{H}_2$ inner products in MIMO settings is introduced and used to derive associated first-order necessary conditions satisfied by optimal weighted-$\\mathcal{H}_2$ reduced-order models. Equivalence of these new interpolatory conditions with earlier Riccati-based conditions given by Halevi is also shown. An examination of realizations for equivalent weighted-$\\mathcal{H}_2$ systems leads then to an algorithm that remains tractable for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0136","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":""},"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"}