{"paper":{"title":"Block subspace expansions for eigenvalues and eigenvectors approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.FA"],"primary_cat":"math.NA","authors_text":"Demetrio Stojanoff, Francisco Arrieta Zuccalli, Pedro Massey","submitted_at":"2024-11-21T20:46:11Z","abstract_excerpt":"Let $A\\in\\mathbb C^{n\\times n}$ and let $\\mathcal X\\subset \\mathbb C^n$ be an $A$-invariant subspace with $\\dim \\mathcal X=d\\geq 1$, corresponding to exterior eigenvalues of $A$. Given an initial subspace $\\mathcal V\\subset \\mathbb C^n$ with $\\dim \\mathcal V=r\\geq d$, we search for expansions of $\\mathcal V$ of the form $\\mathcal V+A(\\mathcal W_0)$, where $\\mathcal W_0\\subset \\mathcal V$ is such that $\\dim \\mathcal W_0\\leq d$ and such that the expanded subspace is closer to $\\mathcal X$ than the initial $\\mathcal V$. We show that there exist (theoretical) optimal choices of such $\\mathcal W_0$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14578","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.14578/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}