{"paper":{"title":"Conditioning and backward error of block-symmetric block-tridiagonal linearizations of matrix polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"F. M. Dopico, L. Medina, M. I. Bueno, S. Furtado","submitted_at":"2017-06-13T16:35:12Z","abstract_excerpt":"For each square matrix polynomial $P(\\lambda)$ of odd degree, a block-symmetric block-tridiagonal pencil $\\mathcal{T}_{P}(\\lambda)$ was introduced by Antoniou and Vologiannidis in 2004, and a variation $\\mathcal{R}_P(\\lambda)$ was introduced by Mackey et al. in 2010. These two pencils have several appealing properties, namely they are always strong linearizations of $P(\\lambda)$, they are easy to construct from the coefficients of $P(\\lambda)$, the eigenvectors of $P(\\lambda)$ can be recovered easily from those of $\\mathcal{T}_P(\\lambda)$ and $\\mathcal{R}_P(\\lambda)$, the two pencils are symme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04150","kind":"arxiv","version":1},"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"}