Article Dans Une Revue Pacific journal of optimization Année : 2021

Jacobi-type algorithm for low rank orthogonal approximation of symmetric tensors and its convergence analysis

Résumé

In this paper, we propose a Jacobi-type algorithm to solve the low rank orthogonal approximation problem of symmetric tensors. This algorithm includes as a special case the well-known Jacobi CoM2 algorithm for the approximate orthogonal diagonalization problem of symmetric tensors. We study the global convergence of this algorithm under a gradient based ordering for a special case: the best rank-2 orthogonal approximation of 3rd order symmetric tensors, and prove that an accumulation point is the unique limit point under some conditions. We also propose a proximal variant of this algorithm in general case, and prove its global convergence without any further condition. Numerical experiments are presented to show the efficiency of this algorithm.

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hal-03233467 , version 1 (24-05-2021)

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Jianze Li, Konstantin Usevich, Pierre Comon. Jacobi-type algorithm for low rank orthogonal approximation of symmetric tensors and its convergence analysis. Pacific journal of optimization, 2021, 17 (3), pp.357-379. ⟨10.48550/arXiv.1911.00659⟩. ⟨hal-03233467⟩
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