{"paper":{"title":"A New Class of Fully Discrete Sparse Fourier Transforms: Faster Stable Implementations with Guarantees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andrew Christlieb, Mark A. Iwen, Ruochuan Zhang, Sami Merhi","submitted_at":"2017-06-08T19:40:28Z","abstract_excerpt":"In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best $s$-term approximation of the Discrete Fourier Transform (DFT) $\\mathbf{\\hat{f}} \\in \\mathbb{C}^N$ of any given input vector $\\mathbf{f} \\in \\mathbb{C}^N$ in just $\\left( s \\log N\\right)^{\\mathcal{O}(1)}$-time using only a similarly small number of entries of $\\mathbf{f}$. In particular, we present a deterministic SFT algorithm which is guaranteed to always recover a near best $s$-term approximation of the DFT of any given input vector $\\mathbf{f} \\in \\mathbb{C}^N$ in $\\mathcal{O} \\left( s^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02740","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"}