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Recovery from Power Sums

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 نشر من قبل Hana Melanova
 تاريخ النشر 2021
  مجال البحث الهندسة المعلوماتية
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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 Bezout bound, and the recovery of vectors from length measurements by $p$-norms.



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