{"paper":{"title":"On Subsample Size of Quantile-Based Randomized Kaczmarz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Anna Ma, Jian-Feng Cai, Junren Chen, Tong Wu","submitted_at":"2025-07-21T02:06:39Z","abstract_excerpt":"Quantile-based randomized Kaczmarz (QRK) was recently introduced to efficiently solve sparsely corrupted linear systems $\\mathbf{A} \\mathbf{x}^*+\\mathbf{\\epsilon} = \\mathbf{b}$ [SIAM J. Matrix Anal. Appl., 43(2), 605-637], where $\\mathbf{A}\\in \\mathbb{R}^{m\\times n}$ and $\\mathbf{\\epsilon}$ is an arbitrary $(\\beta m)$-sparse corruption. However, all existing theoretical guarantees for QRK require quantiles to be computed using all $m$ samples (or a subsample of the same order), thus negating the computational advantage of Kaczmarz-type methods. This paper overcomes the bottleneck. We analyze a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.15185","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/2507.15185/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"}