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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( 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

Towards a condition number theorem for the tensor rank decomposition

Paul Breiding and Nick Vannieuwenhoven


We show that a natural weighted distance from a tensor rank decomposition to the locus of ill-posed decompositions (i.e., decompositions with unbounded geometric condition number, derived in [P. Breiding and N. Vannieuwenhoven, The condition number of join decompositions, SIAM J. Matrix Anal. Appl. (2018)]) is bounded from below by the inverse of this condition number. That is, we prove one inequality towards a condition number theorem for the tensor rank decomposition. Numerical experiments suggest that the other inequality could also hold (at least locally).


Related publications

2020 Repository Open Access
Paul Breiding and Nick Vannieuwenhoven

On the average condition number of tensor rank decompositions

In: IMA journal of numerical analysis, 40 (2020) 3, pp. 1908-1936