Trace maximization algorithm for the approximate tensor diagonalization

In this paper, we develop a Jacobi-type algorithm for the approximate diagonalization of tensors of order $ d\geq 3 $ d ≥ 3 via tensor trace maximization. For a general tensor, this is an alternating least squares algorithm and the rotation matrices are chosen in each mode one-by-one to maximize the...

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Bibliographic Details
Published in:Linear & multilinear algebra 2024-02, Vol.72 (3), p.429-450
Main Authors: Begović Kovač, Erna, Perković, Ana
Format: Article
Language:English
Subjects:
Algorithms
convergence
Jacobi-type methods
Maximization
Optimization
Rotation
tensor diagonalization
tensor trace
Tensors
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Summary:In this paper, we develop a Jacobi-type algorithm for the approximate diagonalization of tensors of order $ d\geq 3 $ d ≥ 3 via tensor trace maximization. For a general tensor, this is an alternating least squares algorithm and the rotation matrices are chosen in each mode one-by-one to maximize the tensor trace. On the other hand, for symmetric tensors, we discuss a structure-preserving variant of this algorithm where in each iteration the same rotation is applied in all modes. We show that both versions of the algorithm converge to the stationary points of the corresponding objective functions.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2022.2158997