{"paper":{"title":"Bivariate polynomial histopolation techniques on Padua, Fekete and Leja triangles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Federico Nudo, Francesco Dell'Accio, Ludovico Bruni Bruno, Wolfgang Erb","submitted_at":"2025-06-03T16:00:34Z","abstract_excerpt":"This paper explores the reconstruction of a real-valued function $f$ defined over a domain $\\Omega \\subset \\mathbb{R}^2$ using bivariate polynomials that satisfy triangular histopolation conditions. More precisely, we assume that only the averages of $f$ over a given triangulation $\\mathcal{T}_N$ of $\\Omega$ are available and seek a bivariate polynomial that approximates $f$ using a histopolation approach, potentially flanked by an additional regression technique. This methodology relies on the selection of a subset of triangles $\\mathcal{T}_M \\subset \\mathcal{T}_N$ for histopolation, ensuring"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03025","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.03025/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}