{"paper":{"title":"Hiding the weights -- CBC black box algorithms with a guaranteed error bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexander D. Gilbert, Frances Y. Kuo, Ian H. Sloan","submitted_at":"2018-10-08T12:14:15Z","abstract_excerpt":"The component-by-component (CBC) algorithm is a method for constructing good generating vectors for lattice rules for the efficient computation of high-dimensional integrals in the \"weighted\" function space setting introduced by Sloan and Wo\\'zniakowski. The \"weights\" that define such spaces are needed as inputs into the CBC algorithm, and so a natural question is, for a given problem how does one choose the weights? This paper introduces two new CBC algorithms which, given bounds on the mixed first derivatives of the integrand, produce a randomly shifted lattice rule with a guaranteed bound o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03394","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"}