{"paper":{"title":"On lower bounds for integration of multivariate permutation-invariant functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Markus Weimar","submitted_at":"2013-10-15T08:34:44Z","abstract_excerpt":"In this note we study multivariate integration for permutation-invariant functions from a certain Banach space E_{d,\\alpha} of Korobov type in the worst case setting. We present a lower error bound which particularly implies that in dimension d every cubature rule which reduces the initial error necessarily uses at least d+1 function values. Since this holds independently of the number of permutation-invariant coordinates, this shows that the integration problem can never be strongly polynomially tractable in this setting. Our assertions generalize results due to Sloan and Wo\\'zniakowski. More"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3959","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"}