{"paper":{"title":"Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.OC"],"primary_cat":"stat.ML","authors_text":"Gang Wang, Georgios B. Giannakis, Yonina C. Eldar","submitted_at":"2016-05-26T13:57:49Z","abstract_excerpt":"This paper presents a new algorithm, termed \\emph{truncated amplitude flow} (TAF), to recover an unknown vector $\\bm{x}$ from a system of quadratic equations of the form $y_i=|\\langle\\bm{a}_i,\\bm{x}\\rangle|^2$, where $\\bm{a}_i$'s are given random measurement vectors. This problem is known to be \\emph{NP-hard} in general. We prove that as soon as the number of equations is on the order of the number of unknowns, TAF recovers the solution exactly (up to a global unimodular constant) with high probability and complexity growing linearly with both the number of unknowns and the number of equations"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08285","kind":"arxiv","version":5},"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"}