{"paper":{"title":"Strictly Balancing Matrices in Polynomial Time Using Osborne's Iteration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Arman Yousefi, Rafail Ostrovsky, Yuval Rabani","submitted_at":"2017-04-24T18:37:25Z","abstract_excerpt":"Osborne's iteration is a method for balancing $n\\times n$ matrices which is widely used in linear algebra packages, as balancing preserves eigenvalues and stabilizes their numeral computation. The iteration can be implemented in any norm over $\\mathbb{R}^n$, but it is normally used in the $L_2$ norm. The choice of norm not only affects the desired balance condition, but also defines the iterated balancing step itself.\n  In this paper we focus on Osborne's iteration in any $L_p$ norm, where $p < \\infty$. We design a specific implementation of Osborne's iteration in any $L_p$ norm that converges"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07406","kind":"arxiv","version":1},"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"}