Finding the symmetric rank-1 approximation to a given symmetric tensor is an important problem due to its wide applications and its close relationship to the Z-eigenpair of a tensor. In this paper, we propose a method based on the proximal alternating linearized minimization to directly solve the optimization problem. Global convergence of our algorithm is established. Numerical experiments show that our algorithm is very competitive in speed, accuracy and robustness compared to other state-of-the-art methods.

中文翻译：

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对称高阶张量的对称秩1逼近

找到一个给定的对称张量的对称秩1近似是一个重要的问题，因为它的广泛应用及其与张量的Z-本征对的紧密关系。在本文中，我们提出了一种基于近端交替线性化最小化的方法来直接解决优化问题。建立了我们算法的全局收敛性。数值实验表明，与其他最新方法相比，我们的算法在速度，准确性和鲁棒性方面具有很高的竞争力。