{"paper":{"title":"Bounds on Walsh coefficients by dyadic difference and a new Koksma-Hlawka type inequality for Quasi-Monte Carlo integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Takehito Yoshiki","submitted_at":"2015-04-10T06:54:47Z","abstract_excerpt":"In this paper we give a new Koksma-Hlawka type inequality for Quasi-Monte Carlo (QMC) integration. QMC integration of a function $f\\colon[0,1)^s\\rightarrow \\mathbb{R}$ by a finite point set $\\mathcal{P}\\subset [0,1)^s$ is the approximation of the integral $I(f):=\\int_{[0,1)^s}f(\\mathbf{x})\\,d\\mathbf{x}$ by the average $I_{\\mathcal{P}}(f):=\\frac{1}{|\\mathcal{P}|}\\sum_{\\mathbf{x} \\in \\mathcal{P}}f(\\mathbf{x})$. We treat a certain class of point sets $\\mathcal{P}$ called digital nets. A Koksma-Hlawka type inequality is an inequality bounding the integration error $\\text{Err}(f;\\mathcal{P}):=I(f)-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03175","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":""},"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"}