Globally Convergent Jacobi-Type Algorithms for Simultaneous Orthogonal Symmetric Tensor Diagonalization

Abstract

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.