Preprint 3/2018

Towards a condition number theorem for the tensor rank decomposition

Paul Breiding and Nick Vannieuwenhoven

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Submission date: 09. Jan. 2018
Pages: 16
published in: IMA journal of numerical analysis (2019), pp not yet known
DOI number (of the published article): 10.1093/imanum/drz026
with the following different title: On the average condition number of tensor rank decompositions
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Link to arXiv: See the arXiv entry of this preprint.

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).

23.01.2020, 02:15