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We propose a gradient-based Jacobi algorithm for a class of maximizationproblems on the unitary group, with a focus on approximate diagonalization ofcomplex matrices and tensors by unitary transformations. We provide weakconvergence results, and prove local linear convergence of this algorithm.Theconvergence results also apply to the case of real-valued tensors.

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