{"paper":{"title":"Sparse solution of the Lyapunov equation for large-scale interconnected systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Aleksandar Haber, Michel Verhaegen","submitted_at":"2014-08-18T05:03:59Z","abstract_excerpt":"We consider the problem of computing an approximate banded solution of the continuous-time Lyapunov equation $\\underline{A}\\underline{X}+\\underline{X}\\underline{A}^{T}=\\underline{P}$, where the coefficient matrices $\\underline{A}$ and $\\underline{P}$ are large, symmetric banded matrices. The (sparsity) pattern of $\\underline{A}$ describes the interconnection structure of a large-scale interconnected system. Recently, it has been shown that the entries of the solution $\\underline{X}$ are spatially localized or decaying away from a banded pattern. We show that the decay of the entries of $\\under"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3898","kind":"arxiv","version":6},"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"}