TU Berlin

Fachgebiet Algorithmische AlgebraDr. Paul Breiding

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Dr. Paul Breiding


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The average number of critical rank-one-approximations to a symmetric tensor
Zitatschlüssel B-The-Average-Number-Of-Critical-Rank-One-Approximations-To-A-Symmetric-Tensor
Autor Paul Breiding
Jahr 2017
Monat 1
Zusammenfassung Given a real symmetric tensor $v\in(\Bbb R^n)^øtimes p$ of order $p$, a critical rank-one approximation of $v$ is a local minimum of the euclidean distance from the set of symmetric rank-1 tensors to $v$. We compute the expected number of critical rank-one-approximations to a random tensor drawn from the standard Gaussian distribution relative to the Bombieri norm. This answers a question posed by Draisma and Horobet, who asked for a closed formula of this expectation. The computation requires to compute the expected absolute value of the determinant of a matrix from the Gaussian Orthogonal Ensemble.
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