{"paper":{"title":"Rapidly Computing Sparse Legendre Expansions via Sparse Fourier Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hyejin Kim, Mark Iwen, Xianfeng Hu","submitted_at":"2015-08-19T19:56:59Z","abstract_excerpt":"In this paper we propose a general strategy for rapidly computing sparse Legendre expansions. The resulting methods yield a new class of fast algorithms capable of approximating a given function $f:[-1,1] \\rightarrow \\mathbb{R}$ with a near-optimal linear combination of $s$ Legendre polynomials of degree $\\leq N$ in just $(s \\log N)^{\\mathcal{O}(1)}$-time. When $s \\ll N$ these algorithms exhibit sublinear runtime complexities in $N$, as opposed to traditional $\\Omega(N \\log N)$-time methods for computing all of the first $N$ Legendre coefficients of $f$. Theoretical as well as numerical result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04758","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"}