{"paper":{"title":"Sublinear Time Eigenvector Approximation via Column Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.DS","authors_text":"Cameron Musco, Dominic Rutkowski, Rajarshi Bhattacharjee","submitted_at":"2026-08-01T19:43:41Z","abstract_excerpt":"We study sublinear time sampling methods for approximating the outlying eigenvectors of large matrices. Our main result is an algorithm that uniformly samples just $\\tilde{O}(\\log n/\\epsilon^4)$ columns of a symmetric matrix $A \\in \\mathbb{R}^{n \\times n}$ with entries bounded in magnitude by $1$, and, for any eigenvalue $\\lambda$ of $A$ with $|\\lambda| \\ge \\epsilon n$, outputs an approximate eigenvector $v$ satisfying $\\|Av - \\lambda v\\|_2 \\le \\epsilon n$. For approximating just the eigenvector of the largest magnitude eigenvalue, our algorithm samples only $\\tilde{O}(\\log n/\\epsilon^2)$ colu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00840","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/2608.00840/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"}