154 citations · 637 across the 17 of their papers we have counts for
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On the largest multilinear singular values of higher-order tensors
Ignat Domanov, Alwin Stegeman, Lieven De Lathauwer
Let denote the largest mode- multilinear singular value of an tensor . We prove that $$ σ_1^2+\dots+σ_{n-1}^2+σ_{n+1}^2+\dots+σ_{N}…
Canonical polyadic decomposition of third-order tensors: relaxed uniqueness conditions and algebraic algorithm
Ignat Domanov, Lieven De Lathauwer
Canonical Polyadic Decomposition (CPD) of a third-order tensor is a minimal decomposition into a sum of rank- tensors. We find new mild deterministic conditions for the uniquene…
Canonical polyadic decomposition of third-order tensors: reduction to generalized eigenvalue decomposition
Ignat Domanov, Lieven De Lathauwer
Canonical Polyadic Decomposition (CPD) of a third-order tensor is decomposition in a minimal number of rank- tensors. We call an algorithm algebraic if it is guaranteed to find…
On the Uniqueness of the Canonical Polyadic Decomposition of third-order tensors --- Part II: Uniqueness of the overall decomposition
Ignat Domanov, Lieven De Lathauwer
Canonical Polyadic (also known as Candecomp/Parafac) Decomposition (CPD) of a higher-order tensor is decomposition in a minimal number of rank-1 tensors. In Part I, we gave an over…
On the Uniqueness of the Canonical Polyadic Decomposition of third-order tensors --- Part I: Basic Results and Uniqueness of One Factor Matrix
Ignat Domanov, Lieven De Lathauwer
Canonical Polyadic Decomposition (CPD) of a higher-order tensor is decomposition in a minimal number of rank-1 tensors. We give an overview of existing results concerning uniquenes…