Recovery from Power Sums

Hana Melánová; Bernd Sturmfels; Rosa Winter

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arXiv · 2106.13981

Recovery from Power Sums

Hana Melánová·Bernd Sturmfels·Rosa Winter

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Abstract

We study the problem of recovering a collection of $n$ numbers from the evaluation of $m$ power sums. This yields a system of polynomial equations, which can be underconstrained ($m < n$), square ($m = n$), or overconstrained ($m > n$). Fibers and images of power sum maps are explored in all three regimes, and in settings that range from complex and projective to real and positive. This involves surprising deviations from the B\'ezout bound, and the recovery of vectors from length measurements by $p$-norms.

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Hana Melánová, Bernd Sturmfels, Rosa Winter. 2021-06-26. Recovery from Power Sums. https://arxiv.org/abs/2106.13981

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