Globally convergent Jacobi-type algorithms for simultaneous orthogonal symmetric tensor diagonalization

Jianze Li (1) , Konstantin Usevich (2) , Pierre Comon (3)

1 TJU - Tianjin University
2 CRAN - Centre de Recherche en Automatique de Nancy
3 GIPSA-CICS - GIPSA - Communication Information and Complex Systems

In this paper, we consider a family of Jacobi-type algorithms for a simultaneous orthogonal diagonalization problem of symmetric tensors. For the Jacobi-based algorithm of [M. Ishteva, P.-A. Absil, and P. Van Dooren, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 651--672], we prove its global convergence for simultaneous orthogonal diagonalization of symmetric matrices and 3rd-order tensors. We also propose a new Jacobi-based algorithm in the general setting and prove its global convergence for sufficiently smooth functions.

Mots clés: Jacobi rotation; orthogonal tensor diagonalization; global convergence; Łojasiewicz gradient inequality; Proximal algorithms

Domaines: Traitement du signal et de l'image [eess.SP]; Théorie de l'information et codage [math.IT]; Optimisation et contrôle [math.OC]

Jianze Li, Konstantin Usevich, Pierre Comon. Globally convergent Jacobi-type algorithms for simultaneous orthogonal symmetric tensor diagonalization. SIAM Journal on Matrix Analysis and Applications, 2018, 39 (1), pp.1-22. ⟨10.1137/17M1116295⟩. ⟨hal-01628257⟩