In the particular case 92X&_mathId=si6.gif&_user=111111111&_pii=S002437951630492X&_rdoc=1&_issn=00243795&md5=ce7737c9ed7edde190c7645e4a21d2ec" title="Click to view the MathML source">R=K, the new bound above is equivalent to the bound 92X&_mathId=si194.gif&_user=111111111&_pii=S002437951630492X&_rdoc=1&_issn=00243795&md5=d43df3f83f3ee7be3a942149e8bcf315" title="Click to view the MathML source">R≤(I−1)(J−1) 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 92X&_mathId=si8.gif&_user=111111111&_pii=S002437951630492X&_rdoc=1&_issn=00243795&md5=fc633c849a1f3849b8e7eb69ba9e9b03" title="Click to view the MathML source">R(R−1)≤I(I−1)J(J−1)/2 (implying that 92X&_mathId=si9.gif&_user=111111111&_pii=S002437951630492X&_rdoc=1&_issn=00243795&md5=2caf5463fa1b9b944ab5dd1f0871ed50">92X-si9.gif">). 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 92X&_mathId=si10.gif&_user=111111111&_pii=S002437951630492X&_rdoc=1&_issn=00243795&md5=486125734e02de25e433221b8d83af6f" title="Click to view the MathML source">R≤24, our algorithm can recover the rank-1 tensors in the CPD up to 92X&_mathId=si194.gif&_user=111111111&_pii=S002437951630492X&_rdoc=1&_issn=00243795&md5=d43df3f83f3ee7be3a942149e8bcf315" title="Click to view the MathML source">R≤(I−1)(J−1).
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