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math.AG2021
Maximum relative distance between real rank-two and rank-one tensors
Henrik Eisenmann, André Uschmajew
It is shown that the relative distance in Frobenius norm of a real symmetric order- tensor of rank two to its best rank-one approximation is upper bounded by $\sqrt{1-(1-1/d)^{d…
math.AG2019
Chebyshev polynomials and best rank-one approximation ratio
Andrei Agrachev, Khazhgali Kozhasov, André Uschmajew
We establish a new extremal property of the classical Chebyshev polynomials in the context of best rank-one approximation of tensors. We also give some necessary conditions for a t…