{"paper":{"title":"High-dimensional periodic sampling on Smolyak grids based on B-spline quasi-interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dinh D\\~ung","submitted_at":"2015-02-05T07:46:05Z","abstract_excerpt":"We constructed linear algorithms of sampling recovery and cubature formulas on Smolyak grids parametrized by $m \\in \\mathbb{N}$ of periodic $d$-variate functions having Lipschitz-H\\\"older mixed smoothness $\\alpha > 0$ based on B-spline quasi-interpolation, and studied their optimality. We established lower estimates (for $\\alpha \\le 2$) and upper bounds of the error of the optimal sampling recovery and the optimal integration on Smolyak grids, explicit in $d$, $m$ and the number $\\nu$ of active variables of functions when $d$ and $m$ may be large."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01447","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"}