{"paper":{"title":"On Topologically Controlled Model Reduction for Discrete-Time Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.DS","math.NA"],"primary_cat":"math.OA","authors_text":"Fredy Vides","submitted_at":"2019-05-10T01:57:40Z","abstract_excerpt":"In this document the author proves that several problems in data-driven numerical approximation of dynamical systems in $\\mathbb{C}^n$, can be reduced to the computation of a family of constrained matrix representations of elements of the group algebra $\\mathbb{C}[\\mathbb{Z}/m]$ in $\\mathbb{C}^{n\\times n}$, factoring through the commutative algebra $Circ(m)$ of circulant matrices in $\\mathbb{C}^{m\\times m}$, for some integers $m\\leq n$.\n  The solvability of the previously described matrix representation problems is studied. Some connections of the aforementioned results, with numerical analysi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03910","kind":"arxiv","version":3},"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"}