Chebyshev polynomials and best rank-one approximation ratio

Andrei Agrachev, Khazhgali Kozhasov, and André Uschmajew

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Submission date: 26. Mar. 2019 (revised version: March 2020)
Pages: 29
published in: SIAM journal on matrix analysis and applications, 41 (2020) 1, p. 308-331 
DOI number (of the published article): 10.1137/19M1269713
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Abstract:
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.