标题： Jacobi类型算法用于对称张量的低秩正交逼近及其收敛性分析 显示英文标题

标题： Jacobi-type algorithm for low rank orthogonal approximation of symmetric tensors and its convergence analysis

摘要： 在本文中，我们提出了一种雅可比类型算法来解决对称张量的低秩正交逼近问题。 该算法包括用于对称张量的近似正交对角化问题的著名雅可比CoM2算法作为特殊情况。 我们首先证明了该算法的弱收敛性，\textit{即}任何聚点都是驻点。 然后我们在一种基于梯度的排序下研究该算法的全局收敛性，针对一个特例：三阶对称张量的最佳秩-2正交逼近，并证明在某些条件下，一个聚点是唯一的极限点。 数值实验展示了该算法的效率。 显示英文摘要

摘要： In this paper, we propose a Jacobi-type algorithm to solve the low rank orthogonal approximation problem of symmetric tensors. This algorithm includes as a special case the well-known Jacobi CoM2 algorithm for the approximate orthogonal diagonalization problem of symmetric tensors. We first prove the weak convergence of this algorithm, \textit{i.e.} any accumulation point is a stationary point. Then we study the global convergence of this algorithm under a gradient based ordering for a special case: the best rank-2 orthogonal approximation of 3rd order symmetric tensors, and prove that an accumulation point is the unique limit point under some conditions. Numerical experiments are presented to show the efficiency of this algorithm.