Maximum relative distance between real rank-two and rank-one tensors

Henrik Eisenmann and André Uschmajew

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Submission date: 24. Nov. 2021 (revised version: September 2022)
Pages: 17
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Abstract:
It is shown that the relative distance in Frobenius norm of a real symmetric order-d tensor of rank two to its best rank-one approximation is upper bounded by . This is achieved by determining the minimal possible ratio between spectral and Frobenius norm for symmetric tensors of border rank two, which equals ^(d−1)∕2. These bounds are also verified for arbitrary real rank-two tensors by reducing to the symmetric case.