{"paper":{"title":"Accelerated Newton Iteration: Roots of Black Box Polynomials and Matrix Eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anand Louis, Santosh S. Vempala","submitted_at":"2015-11-10T17:07:35Z","abstract_excerpt":"We study the problem of computing the largest root of a real rooted polynomial $p(x)$ to within error $\\varepsilon $ given only black box access to it, i.e., for any $x \\in {\\mathbb R}$, the algorithm can query an oracle for the value of $p(x)$, but the algorithm is not allowed access to the coefficients of $p(x)$. A folklore result for this problem is that the largest root of a polynomial can be computed in $O(n \\log (1/\\varepsilon ))$ polynomial queries using the Newton iteration. We give a simple algorithm that queries the oracle at only $O(\\log n \\log(1/\\varepsilon ))$ points, where $n$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03186","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"}