{"paper":{"title":"Simple Approximate Varieties for Sets of Empirical Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AC","authors_text":"Claudia Fassino, Maria-Laura Torrente","submitted_at":"2010-08-02T10:20:11Z","abstract_excerpt":"We present a symbolic-numeric approach for the analysis of a given set of noisy data, represented as a finite set $\\X$ of limited precision points. Starting from $\\X$ and a permitted tolerance $\\varepsilon$ on its coordinates, our method automatically determines a low degree monic polynomial whose associated variety passes close to each point of $\\X$ by less than the given tolerance $\\varepsilon$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0274","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"}