{"paper":{"title":"Some Observations on Khovanskii's Matrix Methods for extracting Roots of Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"B. Sury, James Mc Laughlin","submitted_at":"2019-01-03T04:40:17Z","abstract_excerpt":"In this article we apply a formula for the $n$-th power of a $3\\times 3$ matrix (found previously by the authors) to investigate a procedure of Khovanskii's for finding the cube root of a positive integer. We show, for each positive integer $\\alpha$, how to construct certain families of integer sequences such that a certain rational expression, involving the ratio of successive terms in each family, tends to $\\alpha^{1/3}$. We also show how to choose the optimal value of a free parameter to get maximum speed of convergence. We apply a similar method, also due to Khovanskii, to a more general c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00607","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"}