# Approximate matrix and tensor diagonalization by unitary transformations: convergence of Jacobi-type algorithms

## TL;DR

This paper introduces a gradient-based Jacobi algorithm for approximate diagonalization of matrices and tensors using unitary transformations, proving its convergence properties including local linear convergence.

## Contribution

It presents a novel Jacobi algorithm with proven convergence for complex and real tensors, advancing methods for matrix and tensor diagonalization.

## Key findings

- Weak convergence results established
- Local linear convergence proved
- Applicable to complex and real tensors

## Abstract

We propose a gradient-based Jacobi algorithm for a class of maximization problems on the unitary group, with a focus on approximate diagonalization of complex matrices and tensors by unitary transformations. We provide weak convergence results, and prove local linear convergence of this algorithm.The convergence results also apply to the case of real-valued tensors.