{"paper":{"title":"Dynamics of the symmetric eigenvalue problem with shift strategies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.DS","authors_text":"Carlos Tomei, Nicolau C. Saldanha, Ricardo S. Leite","submitted_at":"2011-08-30T18:20:51Z","abstract_excerpt":"A common algorithm for the computation of eigenvalues of real symmetric tridiagonal matrices is the iteration of certain special maps $F_\\sigma$ called shifted $QR$ steps. Such maps preserve spectrum and a natural common domain is ${\\cal T}_\\Lambda$, the manifold of real symmetric tridiagonal matrices conjugate to the diagonal matrix $\\Lambda$. More precisely, a (generic) shift $s \\in \\RR$ defines a map $F_s: {\\cal T}_\\Lambda \\to {\\cal T}_\\Lambda$. A strategy $\\sigma: {\\cal T}_\\Lambda \\to \\RR$ specifies the shift to be applied at $T$ so that $F_\\sigma(T) = F_{\\sigma(T)}(T)$. Good shift strateg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6030","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"}