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

## TL;DR

This paper introduces and proves the global convergence of new Jacobi-type algorithms for the simultaneous orthogonal diagonalization of symmetric tensors and matrices, advancing tensor decomposition methods.

## Contribution

It extends Jacobi algorithms to symmetric tensors and establishes their global convergence, including a new algorithm for smooth functions.

## Key findings

- Proved global convergence for existing Jacobi algorithm on matrices and third-order tensors.
- Developed a new Jacobi-based algorithm with proven convergence for smooth functions.
- Enhanced tensor diagonalization techniques for symmetric tensors.

## Abstract

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.