TY - JOUR
T1 - On the (non)existence of best low-rank approximations of generic IxJx2 arrays
AU - Stegeman, Alwin
PY - 2022/3
Y1 - 2022/3
N2 - Several conjectures and partial proofs have been formulated on the (non)existence of a best low-rank approximation of real-valued IxJx2 arrays. We analyze this problem using the Generalized Schur Decomposition and prove (non)existence of a best rank-R approximation for generic IxJx2 arrays, for all values of I,J,R. Moreover, for cases where a best rank-R approximation exists on a set of positive volume only, we provide easy-to-check necessary and sufficient conditions for the existence of a best rank-R approximation.
AB - Several conjectures and partial proofs have been formulated on the (non)existence of a best low-rank approximation of real-valued IxJx2 arrays. We analyze this problem using the Generalized Schur Decomposition and prove (non)existence of a best rank-R approximation for generic IxJx2 arrays, for all values of I,J,R. Moreover, for cases where a best rank-R approximation exists on a set of positive volume only, we provide easy-to-check necessary and sufficient conditions for the existence of a best rank-R approximation.
UR - https://arxiv.org/abs/1309.5727
U2 - 10.48550/arXiv.1309.5727
DO - 10.48550/arXiv.1309.5727
M3 - Article
SN - 0024-3795
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -