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The average number of critical rank-one-approximations to a symmetric tensor
Citation key B-The-Average-Number-Of-Critical-Rank-One-Approximations-To-A-Symmetric-Tensor
Author Paul Breiding
Year 2017
Month 1
Abstract 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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