{"paper":{"title":"The Construction of High Order Convergent Look-Ahead Finite Difference Formulas for Zhang Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Frank Uhlig","submitted_at":"2019-04-23T23:38:06Z","abstract_excerpt":"Zhang Neural Networks rely on convergent 1-step ahead finite difference formulas of which very few are known. Those which are known have been constructed in ad-hoc ways and suffer from low truncation error orders. This paper develops a constructive method to find convergent look-ahead finite difference schemes of higher truncation error orders. The method consists of seeding the free variables of a linear system comprised of Taylor expansion coefficients followed by a minimization algorithm for the maximal magnitude root of the formula's characteristic polynomial. This helps us find new conver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10569","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"}