{"paper":{"title":"A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"cs.DS","authors_text":"Alexandre Sedoglavic (CRIStAL), CASC), Cl\\'ement Pernet (UGA, Jean-Guillaume Dumas (UGA, LJK, LJK)","submitted_at":"2026-03-19T09:58:19Z","abstract_excerpt":"We propose a more accurate variant of an algorithm for multiplying 4x4 matrices using 48 multiplications over any ring containing an inverse of 2. This algorithm achieves an error bound exponent of only $\\log_{4}gamma_{\\infty,2}\\approx{2.335}$. In practice, it also reaches a better accuracy w.r.t. max-norm, when compared to previously known such fast algorithms. Furthermore, we propose a straight line program of this algorithm, giving a leading constant in its complexity bound of $\\frac{316}{32}n^{2+\\log_{4}{3}}+o(n^{2+\\log_{4}{3}})$ operations over any ring containing an inverse of 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.18699","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/2603.18699/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"}