{"paper":{"title":"Lattice rules in non-periodic subspaces of Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Kosuke Suzuki, Takashi Goda, Takehito Yoshiki","submitted_at":"2017-12-07T11:41:29Z","abstract_excerpt":"We investigate quasi-Monte Carlo (QMC) integration over the $s$-dimensional unit cube based on rank-1 lattice point sets in weighted non-periodic Sobolev spaces $\\mathcal{H}(K_{\\alpha,\\boldsymbol{\\gamma},s}^{\\mathrm{sob}})$ and their subspaces of high order smoothness $\\alpha>1$, where $\\boldsymbol{\\gamma}$ denotes a set of the weights. A recent paper by Dick, Nuyens and Pillichshammer has studied QMC integration in half-period cosine spaces with smoothness parameter $\\alpha>1/2$ consisting of non-periodic smooth functions, denoted by $\\mathcal{H}(K_{\\alpha,\\boldsymbol{\\gamma},s}^{\\mathrm{cos}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02572","kind":"arxiv","version":2},"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/1712.02572/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"}