{"paper":{"title":"On efficient weighted integration via a change of variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Friedrich Pillichshammer, G.W. Wasilkowski, Leszek Plaskota, Peter Kritzer","submitted_at":"2018-12-11T08:13:36Z","abstract_excerpt":"In this paper, we study the approximation of $d$-dimensional $\\rho$-weighted integrals over unbounded domains $\\mathbb{R}_+^d$ or $\\mathbb{R}^d$ using a special change of variables, so that quasi-Monte Carlo (QMC) or sparse grid rules can be applied to the transformed integrands over the unit cube. We consider a class of integrands with bounded $L_p$ norm of mixed partial derivatives of first order, where $p\\in[1,+\\infty].$\n  The main results give sufficient conditions on the change of variables $\\nu$ which guarantee that the transformed integrand belongs to the standard Sobolev space of funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04259","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"}