{"paper":{"title":"Improved Iteration Complexities for Overconstrained $p$-Norm Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Aaron Sidford, Arun Jambulapati, Yang P. Liu","submitted_at":"2021-11-02T19:10:19Z","abstract_excerpt":"In this paper we obtain improved iteration complexities for solving $\\ell_p$ regression. We provide methods which given any full-rank $\\mathbf{A} \\in \\mathbb{R}^{n \\times d}$ with $n \\geq d$, $b \\in \\mathbb{R}^n$, and $p \\geq 2$ solve $\\min_{x \\in \\mathbb{R}^d} \\left\\|\\mathbf{A} x - b\\right\\|_p$ to high precision in time dominated by that of solving $\\widetilde{O}_p(d^{\\frac{p-2}{3p-2}})$ linear systems in $\\mathbf{A}^\\top \\mathbf{D} \\mathbf{A}$ for positive diagonal matrices $\\mathbf{D}$. This improves upon the previous best iteration complexity of $\\widetilde{O}_p(n^{\\frac{p-2}{3p-2}})$ (Adi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.01848","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/2111.01848/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"}