Systems of Polynomial Equations, Higher-Order Tensor Decompositions, and Multidimensional Harmonic Retrieval: A Unifying Framework. Part II: The Block Term Decomposition

Subspaces in general topology (54B05) Multilinear algebra, tensor calculus (15A69) Numerical computation of roots of polynomial equations (65H04) Solving polynomial systems; resultants (13P15)

Related Items (1)

A Fast Algorithm for Computing Macaulay Null Spaces of Bivariate Polynomial Systems

Uses Software

Tensorlab
PARAFAC
HomotopyContinuation

Cites Work

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Tensor Decompositions and Applications
On the null spaces of the Macaulay matrix
On the non-existence of optimal solutions and the occurrence of ``degeneracy in the CANDECOMP/PARAFAC model
HomotopyContinuation.jl: a package for homotopy continuation in Julia
Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
Exact probabilities for typical ranks of $2 \times 2 \times 2$ and $3 \times 3 \times 2$ tensors
Optimization-Based Algorithms for Tensor Decompositions: Canonical Polyadic Decomposition, Decomposition in Rank-$(L_r,L_r,1)$ Terms, and a New Generalization
A Three-Way Jordan Canonical Form as Limit of Low-Rank Tensor Approximations
Candecomp/Parafac: From Diverging Components to a Decomposition in Block Terms
Multiple zeros of nonlinear systems
Blind Separation of Exponential Polynomials and the Decomposition of a Tensor in Rank-$(L_r,L_r,1)$ Terms
The Generalized Vandermonde Matrix
The Elimination Matrix: Some Lemmas and Applications
A Multilinear Singular Value Decomposition
Multidimensional realisation theory and polynomial system solving
Multidimensional Harmonic Retrieval via Coupled Canonical Polyadic Decomposition—Part I: Model and Identifiability
Solving Polynomial Systems via Truncated Normal Forms
Accurate solution of polynomial equations using Macaulay resultant matrices
Numerical Polynomial Algebra
Systems of Polynomial Equations, Higher-order Tensor Decompositions, and Multidimensional Harmonic Retrieval: A Unifying Framework. Part I: The Canonical Polyadic Decomposition
Computing the multiplicity structure in solving polynomial systems
Invariant Subspaces of Matrices with Applications
Computing the multiplicity structure from geometric involutive form
Decompositions of a Higher-Order Tensor in Block Terms—Part I: Lemmas for Partitioned Matrices
Decompositions of a Higher-Order Tensor in Block Terms—Part II: Definitions and Uniqueness
Decompositions of a Higher-Order Tensor in Block Terms—Part III: Alternating Least Squares Algorithms
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem

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