{"paper":{"title":"Interlacing Polynomial Method for the Column Subset Selection Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"cs.DS","authors_text":"Jian-Feng Cai, Zhiqiang Xu, Zili Xu","submitted_at":"2023-03-14T15:41:05Z","abstract_excerpt":"This paper investigates the spectral norm version of the column subset selection problem. Given a matrix $\\mathbf{A}\\in\\mathbb{R}^{n\\times d}$ and a positive integer $k\\leq\\text{rank}(\\mathbf{A})$, the objective is to select exactly $k$ columns of $\\mathbf{A}$ that minimize the spectral norm of the residual matrix after projecting $\\mathbf{A}$ onto the space spanned by the selected columns. We use the method of interlacing polynomials introduced by Marcus-Spielman-Srivastava to derive a new upper bound on the minimal approximation error. This new bound is asymptotically sharp when the matrix $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.07984","kind":"arxiv","version":2},"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/2303.07984/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"}