Title: On generic nonexistence of the Schmidt-Eckart-Young decomposition for complex tensors
Authors: Vannieuwenhoven, Nick
Nicaise, Johannes
Vandebril, Raf
Meerbergen, Karl
Issue Date: May-2013
Publisher: Department of Computer Science, KU Leuven
Series Title: TW Reports vol:TW628
Abstract: The Schmidt-Eckart-Young theorem for matrices states that the optimal rank-r approximation to a matrix is obtained by retaining the first r terms from the singular value decomposition of that matrix. This work considers a generalization of this optimal truncation property to the CANDECOMP/PARAFAC decomposition of tensors and establishes a necessary orthogonality condition. We prove that this condition is not satisfied at least by an open set of positive Lebesgue measure in complex tensor spaces. It is proved moreover that for complex tensors of small rank this condition can only be satisfied by a set of tensors of Lebesgue measure zero.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
Algebra Section

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