{"paper":{"title":"Interlacing Polynomial Method for Matrix Approximation via Generalized Column and Row Selection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OA"],"primary_cat":"math.FA","authors_text":"Jian-Feng Cai, Zhiqiang Xu, Zili Xu","submitted_at":"2023-12-04T08:14:23Z","abstract_excerpt":"This paper delves into the spectral norm aspect of the Generalized Column and Row Subset Selection (GCRSS) problem. Given a target matrix $\\mathbf{A}\\in \\mathbb{R}^{n\\times d}$, the objective of GCRSS is to select a column submatrix $\\mathbf{B}_{:,S}\\in\\mathbb{R}^{n\\times k}$ from the source matrix $\\mathbf{B}\\in\\mathbb{R}^{n\\times d_B}$ and a row submatrix $\\mathbf{C}_{R,:}\\in\\mathbb{R}^{r\\times d}$ from the source matrix $\\mathbf{C}\\in\\mathbb{R}^{n_C\\times d}$, such that the residual matrix $(\\mathbf{I}_n-\\mathbf{B}_{:,S}\\mathbf{B}_{:,S}^{\\dagger})\\mathbf{A}(\\mathbf{I}_d-\\mathbf{C}_{R,:}^{\\d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.01715","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/2312.01715/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"}