{"paper":{"title":"Structure-preserving $H^2$ optimal model reduction based on Riemannian trust-region method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hiroyuki Sato, Kazuhiro Sato","submitted_at":"2018-03-12T02:48:13Z","abstract_excerpt":"This paper studies stability and symmetry preserving $H^2$ optimal model reduction problems of linear systems which include linear gradient systems as a special case. The problem is formulated as a nonlinear optimization problem on the product manifold of the manifold of symmetric positive definite matrices and the Euclidean spaces. To solve the problem by using the trust-region method, the gradient and Hessian of the objective function are derived. Furthermore, it is shown that if we restrict our systems to gradient systems, the gradient and Hessian can be obtained more efficiently. More conc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04097","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"}