Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898099 | Linear Algebra and its Applications | 2017 | 42 Pages |
Abstract
In the particular case R=K, the new bound above is equivalent to the bound Râ¤(Iâ1)(Jâ1) which is known to be necessary and sufficient for the generic uniqueness of the CPD. An existing algebraic algorithm (based on simultaneous diagonalization of a set of matrices) computes the CPD under the more restrictive constraint R(Râ1)â¤I(Iâ1)J(Jâ1)/2 (implying that R<(Jâ12)(Iâ12)/2+1). We give an example of a low-dimensional but high-rank CPD that cannot be found by optimization-based algorithms in a reasonable amount of time while our approach takes less than a second. We demonstrate that, at least for Râ¤24, our algorithm can recover the rank-1 tensors in the CPD up to Râ¤(Iâ1)(Jâ1).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ignat Domanov, Lieven De Lathauwer,