Towards a condition number theorem for the tensor rank decomposition
Paul Breiding and Nick Vannieuwenhoven
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Submission date: 09. Jan. 2018
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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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).