{"paper":{"title":"On the exponential of semi-infinite quasi-Toeplitz matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Beatrice Meini, Dario A. Bini","submitted_at":"2016-11-19T15:20:02Z","abstract_excerpt":"Let $a(z)=\\sum_{i\\in\\mathbb Z}a_iz^i$ be a complex valued function defined for $|z|=1$, such that $\\sum_{i\\in\\mathbb Z}|ia_i|<\\infty$, and let $E=(e_{i,j})_{i,j\\in\\mathbb {Z}^+}$ be such that $\\sum_{i,j\\in\\mathbb{Z}^+}|e_{i,j}|<\\infty$. A semi-infinite quasi-Toeplitz matrix is a matrix of the kind $A=T(a)+E$, where $T(a)=(t_{i,j})_{i,j\\in\\mathbb{Z}^+}$ is the semi-infinite Toeplitz matrix associated with the symbol $a(z)$, that is, $t_{i,j}=a_{j-i}$ for $i,j\\in\\mathbb Z^+$. We analyze theoretical and computational properties of the exponential of $A$. More specifically, it is shown that $\\exp("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06380","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1611.06380/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}