{"paper":{"title":"Better and Simpler Error Analysis of the Sinkhorn-Knopp Algorithm for Matrix Scaling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Deeparnab Chakrabarty, Sanjeev Khanna","submitted_at":"2018-01-09T04:24:01Z","abstract_excerpt":"Given a non-negative $n \\times m$ real matrix $A$, the {\\em matrix scaling} problem is to determine if it is possible to scale the rows and columns so that each row and each column sums to a specified target value for it. This problem arises in many algorithmic applications, perhaps most notably as a preconditioning step in solving a linear system of equations. One of the most natural and by now classical approach to matrix scaling is the Sinkhorn-Knopp algorithm (also known as the RAS method) where one alternately scales either all rows or all columns to meet the target values. In addition to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02790","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":""},"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"}