{"paper":{"title":"Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alexander D. Gilbert, Dirk Nuyens, Frances Y. Kuo, Grzegorz W. Wasilkowski","submitted_at":"2017-12-19T05:08:50Z","abstract_excerpt":"In this paper we focus on efficient implementations of the Multivariate Decomposition Method (MDM) for approximating integrals of $\\infty$-variate functions. Such $\\infty$-variate integrals occur for example as expectations in uncertainty quantification. Starting with the anchored decomposition $f = \\sum_{\\mathfrak{u}\\subset\\mathbb{N}} f_\\mathfrak{u}$, where the sum is over all finite subsets of $\\mathbb{N}$ and each $f_\\mathfrak{u}$ depends only on the variables $x_j$ with $j\\in\\mathfrak{u}$, our MDM algorithm approximates the integral of $f$ by first truncating the sum to some `active set' a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06782","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"}