{"paper":{"title":"Approximation of Generalized Ridge Functions in High Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NA","authors_text":"Sandra Keiper","submitted_at":"2017-01-24T09:23:04Z","abstract_excerpt":"This paper studies the approximation of generalized ridge functions, namely of functions which are constant along some submanifolds of $\\mathbb{R}^N$. We introduce the notion of linear-sleeve functions, whose function values only depend on the distance to some unknown linear subspace $L$. We propose two effective algorithms to approximate linear-sleeve functions $f(x)=g(\\text{dist}(x,L)^2)$, when both the linear subspace $L\\subset \\mathbb{R}^N$ and the function $g\\in C^s[0,1]$ are unknown. We will prove error bounds for both algorithms and provide an extensive numerical comparison of both. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07018","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"}