arXiv:1604.00052 Abstract | arXiv Analytics

arXiv:1604.00052 [math.AG]Abstract References Reviews Resources

A condition number for the tensor rank decomposition

Published 2016-03-31Version 1

The tensor rank decomposition problem consists of recovering the unique set of parameters representing a robustly identifiable low-rank tensor when the coordinate representation of the tensor is presented as input. A condition number for this problem measuring the sensitivity of the parameters to an infinitesimal change to the tensor is introduced and analyzed. It is demonstrated that the absolute condition number coincides with the inverse of the least singular value of Terracini's matrix. Several basic properties of this condition number are investigated.

Comments: 45 pages, 4 figures

Categories: math.AG, math.NA

Subjects: 65F35, 15A69, 15A72, 65H04, 14Q15, 14N05, 58A05, 58A07

Keywords: tensor rank decomposition problem consists, absolute condition number coincides, identifiable low-rank tensor, basic properties, coordinate representation

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