Chebyshev polynomials and best rank-one approximation ratio
Andrei Agrachev, Khazhgali Kozhasov, and André Uschmajew
Contact the author: Please use for correspondence this email.
Submission date: 26. Mar. 2019 (revised version: March 2020)
published in: SIAM journal on matrix analysis and applications, 41 (2020) 1, p. 308-331
DOI number (of the published article): 10.1137/19M1269713
Download full preprint: PDF (515 kB)
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.