154 citations · 503 across the 8 of their papers we have counts for
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From computation to comparison of tensor decompositions
Ignat Domanov, Lieven De Lathauwer
Decompositions of higher-order tensors into sums of simple terms are ubiquitous. We show that in order to verify that two tensors are generated by the same (possibly scaled) terms…
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 spectrum of the operator which is a composition of integration and substitution
Ignat Domanov
We study the spectrum of the Volterra composition operator in the space
On the spectrum and eigenfunctions of the operator
Ignat Domanov
We find spectrum and eigenfunctions of the operator in
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…