Globally convergent Jacobi-type algorithms for simultaneous orthogonal symmetric tensor diagonalization
For researchers in tensor decomposition and numerical linear algebra, this provides theoretical guarantees for Jacobi-type algorithms that previously lacked convergence proofs.
The paper proves global convergence of existing Jacobi-type algorithms for simultaneous orthogonal diagonalization of symmetric tensors up to 3rd order, and proposes a new algorithm with proven global convergence for sufficiently smooth functions.
In this paper, we consider a family of Jacobi-type algorithms for simultaneous orthogonal diagonalization problem of symmetric tensors. For the Jacobi-based algorithm of [SIAM J. Matrix Anal. Appl., 2(34):651--672, 2013], 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.