{"paper":{"title":"Error Formulas for Ideal Interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Shugong Zhang, Xue Jiang, Yihe Gong, Zhe Li","submitted_at":"2015-06-17T08:41:21Z","abstract_excerpt":"In this paper we study the algebraic structure of error formulas for ideal interpolation. We introduce the so-called \"normal\" error formulas and prove that the lexicographic order reduced Gr\\\"obner basis admits such a formula for all ideal interpolation. This formula is a generalization of the \"good\" error formula proposed by Carl de Boor. Finally, we discuss a Shekhtman's example and give an explicit form of \"normal\" error formula for this example."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05242","kind":"arxiv","version":3},"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"}