{"paper":{"title":"On algebraic properties of low rank approximations of Prony systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Gil Goldman, Yosef Yomdin","submitted_at":"2018-03-25T12:43:59Z","abstract_excerpt":"We consider the reconstruction of spike train signals of the form $$F(x) = \\sum_{i=1}^d a_i \\delta(x-x_i),$$ from their moments measurements $m_k(F)=\\int x^k F(x) dx = \\sum_{i=1}^d a_ix^k$. When some of the nodes $x_i$ near collide the inversion becomes unstable. Given noisy moments measurements, a typical consequence is that reconstruction algorithms estimate the signal $F$ with a signal having fewer nodes, $\\tilde{F}$. We derive lower bounds for the moments difference between a signal $F$ with $d$ nodes and a signal $\\tilde{F}$ with strictly less nodes, $l$. Next we consider the geometry of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09243","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"}