{"paper":{"title":"Function approximation on arbitrary domains using Fourier extension frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Daan Huybrechs, Roel Matthysen","submitted_at":"2017-06-15T12:52:01Z","abstract_excerpt":"Fourier extension is an approximation scheme in which a function on an arbitary bounded domain is approximated using a classical Fourier series on a bounding box. On the smaller domain the Fourier series exhibits redundancy, and it has the mathematical structure of a frame rather than a basis. It is not trivial to construct approximations in this frame using function evaluations in points that belong to the domain only, but one way to do so is through a discrete least squares approximation. The corresponding system is extremely ill-conditioned, due to the redundancy in the frame, yet its solut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04848","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"}