{"paper":{"title":"Robust Smoothed Analysis of a Condition Number for Linear Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Dennis Amelunxen, Peter B\\\"urgisser","submitted_at":"2008-03-06T17:42:38Z","abstract_excerpt":"We perform a smoothed analysis of the GCC-condition number C(A) of the linear programming feasibility problem \\exists x\\in\\R^{m+1} Ax < 0. Suppose that \\bar{A} is any matrix with rows \\bar{a_i} of euclidean norm 1 and, independently for all i, let a_i be a random perturbation of \\bar{a_i} following the uniform distribution in the spherical disk in S^m of angular radius \\arcsin\\sigma and centered at \\bar{a_i}. We prove that E(\\ln C(A)) = O(mn / \\sigma). A similar result was shown for Renegar's condition number and Gaussian perturbations by Dunagan, Spielman, and Teng [arXiv:cs.DS/0302011]. Our "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.0925","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}