{"paper":{"title":"Solving rank structured Sylvester and Lyapunov equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Davide Palitta, Leonardo Robol, Stefano Massei","submitted_at":"2017-11-15T10:49:15Z","abstract_excerpt":"We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium and large scale, in case of rank-structured data, i.e., when the coefficient matrices and the right-hand side have low-rank off-diagonal blocks. This comprises problems with banded data, recently studied by Haber and Verhaegen in \"Sparse solution of the Lyapunov equation for large-scale interconnected systems\", Automatica, 2016, and by Palitta and Simoncini in \"Numerical methods for large-scale Lyapunov equations with symmetric banded data\", SISC, 2018, which often arise in the discretization of elliptic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05493","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"}