{"paper":{"title":"Randomized strong rank-revealing QR for column subset selection and low-rank matrix approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Laura Grigori, Zhipeng Xue","submitted_at":"2025-03-24T09:52:06Z","abstract_excerpt":"We discuss a randomized strong rank-revealing QR factorization that effectively reveals the spectrum of a matrix $\\textbf{M}$. This factorization can be used to address problems such as selecting a subset of the columns of $\\textbf{M}$, computing its low-rank approximation, estimating its rank, or approximating its null space. Given a random sketching matrix $\\pmb{\\Omega}$ that satisfies the $\\epsilon$-embedding property for a subspace within the range of $\\textbf{M}$, the factorization relies on selecting columns that allow to reveal the spectrum via a deterministic strong rank-revealing QR f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.18496","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/2503.18496/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"}