Logo Max-Planck-Institute for Mathematics in the Sciences, Go to Homepage

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
27/2021

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

Henrik Eisenmann and André Uschmajew

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 1−(1−1/d)d−1. This is achieved by determining the minimal possible ratio between spectral and Frobenius norm for symmetric tensors of border rank two, which equals (1−1/d)(d−1)/2. These bounds are also verified for arbitrary real rank-two tensors by reducing to the symmetric case.

Contact the author per mail Download full preprint 456 KB
Received:
24.11.21
Published:
24.11.21

Related publications

inJournal
2023 Journal Open Access
Henrik Eisenmann and André Uschmajew

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

In: Annali di matematica pura ed applicata, 202 (2023) 2, pp. 993-1009
BibTex DOI: 10.1007/s10231-022-01268-w ArXiv: 2111.12611