{"paper":{"title":"Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Glenn Byrenheid, Lutz K\\\"ammerer, Tino Ullrich, Toni Volkmer","submitted_at":"2015-10-28T15:04:52Z","abstract_excerpt":"We consider the approximate recovery of multivariate periodic functions from a discrete set of function values taken on a rank-$s$ integration lattice. The main result is the fact that any (non-)linear reconstruction algorithm taking function values on a rank-$s$ lattice of size $M$ has a dimension-independent lower bound of $2^{-(\\alpha+1)/2} M^{-\\alpha/2}$ when considering the optimal worst-case error with respect to function spaces of (hybrid) mixed smoothness $\\alpha>0$ on the $d$-torus. We complement this lower bound with upper bounds that coincide up to logarithmic terms. These upper bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08336","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"}