Globally convergent Jacobi-type algorithms for symmetric tensor diagonalization

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Date(s) - 03/07/2017
14 h 00 min - 15 h 00 min

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Symmetric tensors (or sets of symmetric matrices), in general, cannot be diagonalized (jointly diagonalized). Motivated by applications in signal processing and machine learning, we consider the problem of approximate diagonalization by orthogonal transformations. For the Jacobi-type algorithm of [SIAM J. Matrix Anal. Appl., 2(34):651–672, 2013], we prove its global convergence in the case of simultaneous orthogonal diagonalization
of symmetric matrices or 3rd-order tensors. We also propose a new proximal Jacobi-type algorithm and prove its global convergence for a wide range of tensor approximation problems.

This is joint work with Jianze Li (Tianjin University) and Pierre Comon (GIPSA-lab, CNRS and Univ. Grenoble Alpes).

This work was supported by the ERC project ‘DECODA’ no.320594, in the frame of the European program FP7/2007-2013. Jianze Li was partially supported by the National Natural Science Foundation of China (No.11601371).

http://www.gipsa-lab.grenoble-inp.fr/~konstantin.usevich/

Olivier CHABROL
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