{"paper":{"title":"Fast Approximate Polynomial Multipoint Evaluation and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.NA"],"primary_cat":"cs.NA","authors_text":"Alexander Kobel, Michael Sagraloff","submitted_at":"2013-04-30T17:01:11Z","abstract_excerpt":"It is well known that, using fast algorithms for polynomial multiplication and division, evaluation of a polynomial $F \\in \\mathbb{C}[x]$ of degree $n$ at $n$ complex-valued points can be done with $\\tilde{O}(n)$ exact field operations in $\\mathbb{C},$ where $\\tilde{O}(\\cdot)$ means that we omit polylogarithmic factors. We complement this result by an analysis of approximate multipoint evaluation of $F$ to a precision of $L$ bits after the binary point and prove a bit complexity of $\\tilde{O}(n(L + \\tau + n\\Gamma)),$ where $2^\\tau$ and $2^\\Gamma,$ with $\\tau, \\Gamma \\in \\mathbb{N}_{\\ge 1},$ ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.8069","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"}