{"paper":{"title":"Tractability of $\\mathbb{L}_2$-approximation in hybrid function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Friedrich Pillichshammer, Helene Laimer, Peter Kritzer","submitted_at":"2017-01-11T10:06:28Z","abstract_excerpt":"We consider multivariate $\\mathbb{L}_2$-approximation in reproducing kernel Hilbert spaces which are tensor products of weighted Walsh spaces and weighted Korobov spaces. We study the minimal worst-case error $e^{\\mathbb{L}_2-\\mathrm{app},\\Lambda}(N,d)$ of all algorithms that use $N$ information evaluations from the class $\\Lambda$ in the $d$-dimensional case. The two classes $\\Lambda$ considered in this paper are the class $\\Lambda^{{\\rm all}}$ consisting of all linear functionals and the class $\\Lambda^{{\\rm std}}$ consisting only of function evaluations.\n  The focus lies on the dependence o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02910","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"}