{"paper":{"title":"Low Rank Matrix-Valued Chernoff Bounds and Approximate Matrix Multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"cs.DS","authors_text":"Anastasios Zouzias, Avner Magen","submitted_at":"2010-05-16T06:08:16Z","abstract_excerpt":"In this paper we develop algorithms for approximating matrix multiplication with respect to the spectral norm. Let A\\in{\\RR^{n\\times m}} and B\\in\\RR^{n \\times p} be two matrices and \\eps>0. We approximate the product A^\\top B using two down-sampled sketches, \\tilde{A}\\in\\RR^{t\\times m} and \\tilde{B}\\in\\RR^{t\\times p}, where t\\ll n such that \\norm{\\tilde{A}^\\top \\tilde{B} - A^\\top B} \\leq \\eps \\norm{A}\\norm{B} with high probability. We use two different sampling procedures for constructing \\tilde{A} and \\tilde{B}; one of them is done by i.i.d. non-uniform sampling rows from A and B and the othe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2724","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"}