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Convergence of a Jacobi-type method for the approximate orthogonal tensor diagonalization

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Abstract

For a general third-order tensor \({{\mathcal {A}}}\in {\mathbb {R}}^{n\times n\times n}\) the paper studies two closely related problems, an SVD-like tensor decomposition and an (approximate) tensor diagonalization. We develop a Jacobi-type algorithm that works on \(2\times 2\times 2\) subtensors and, in each iteration, maximizes the sum of squares of its diagonal entries. We show how the rotation angles are calculated and prove convergence of the algorithm. Different initializations of the algorithm are discussed, as well as the special cases of symmetric and antisymmetric tensors. The algorithm can be generalized to work on higher-order tensors.

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Acknowledgements

This work has been supported in part by Croatian Science Foundation under the project UIP-2019-04-5200. The author is grateful to the anonymous referees for their detailed comments that improved the paper.

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  1. Faculty of Chemical Engineering and Technology, University of Zagreb, Marulićev Trg 19, Zagreb, 10000, Croatia

    Erna Begović Kovač

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  1. Erna Begović Kovač
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Correspondence to Erna Begović Kovač.

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Begović Kovač, E. Convergence of a Jacobi-type method for the approximate orthogonal tensor diagonalization. Calcolo 60, 3 (2023). https://doi.org/10.1007/s10092-022-00498-x

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  • DOI: https://doi.org/10.1007/s10092-022-00498-x

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