{"paper":{"title":"On Inner Iterations in the Shift-Invert Residual Arnoldi Method and the Jacobi--Davidson Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Cen Li, Zhongxiao Jia","submitted_at":"2011-09-26T06:58:01Z","abstract_excerpt":"Using a new analysis approach, we establish a general convergence theory of the Shift-Invert Residual Arnoldi (SIRA) method for computing a simple eigenvalue nearest to a given target $\\sigma$ and the associated eigenvector. In SIRA, a subspace expansion vector at each step is obtained by solving a certain inner linear system. We prove that the inexact SIRA method mimics the exact SIRA well, that is, the former uses almost the same outer iterations to achieve the convergence as the latter does if all the inner linear systems are iteratively solved with {\\em low} or {\\em modest} accuracy during"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5455","kind":"arxiv","version":5},"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"}