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Chebyshev polynomials and best rank-one approximation ratio
Andrei Agrachev, Khazhgali Kozhasov and 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 tensor to be a minimizer of the ratio of spectral and Frobenius norms.