{"paper":{"title":"Quasi-Toeplitz matrix arithmetic: a MATLAB toolbox","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dario A. Bini, Leonardo Robol, Stefano Massei","submitted_at":"2018-01-24T19:16:55Z","abstract_excerpt":"A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind $A=T(a)+E$ where $T(a)=(a_{j-i})_{i,j\\in\\mathbb Z^+}$, $E=(e_{i,j})_{i,j\\in\\mathbb Z^+}$ is compact and the norms $\\lVert a\\rVert_{\\mathcal W} = \\sum_{i\\in\\mathbb Z}|a_i|$ and $\\lVert E \\rVert_2$ are finite. These properties allow to approximate any QT-matrix, within any given precision, by means of a finite number of parameters.\n  QT-matrices, equipped with the norm $\\lVert A \\rVert_{\\mathcal QT}=\\alpha\\lVert a\\rVert_{\\mathcal{W}} \\lVert E \\rVert_2$, for $\\alpha = (1+\\sqrt 5)/2$, are a Banach algebra with the standard arithmet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08158","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"}