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Article Dans Une Revue SIAM Journal on Optimization Année : 2020

Approximate matrix and tensor diagonalization by unitary transformations: convergence of Jacobi-type algorithms

Résumé

We propose a gradient-based Jacobi algorithm for a class of maximization problems on the unitary group, with a focus on approximate diagonalization of complex matrices and tensors by unitary transformations. We provide weak convergence results, and prove local linear convergence of this algorithm. The convergence results also apply to the case of real-valued tensors.
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Dates et versions

hal-01998900 , version 1 (29-01-2019)
hal-01998900 , version 2 (27-05-2019)
hal-01998900 , version 3 (11-02-2020)
hal-01998900 , version 4 (05-07-2020)

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Konstantin Usevich, Jianze Li, Pierre Comon. Approximate matrix and tensor diagonalization by unitary transformations: convergence of Jacobi-type algorithms. SIAM Journal on Optimization, 2020, 30 (4), pp.2998-3028. ⟨10.1137/19M125950X⟩. ⟨hal-01998900v4⟩
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