A Rayleigh quotient‐gradient neural network method for computing 𝒵‐eigenpairs of general tensors

Abstract

Recently, Zhao, Zheng, Liang and Xu (A locally and cubically convergent algorithm for computing 𝒵‐eigenpairs of symmetric tensors. Numer Linear Algebra Appl, 2020, 27:e2284) studied on an efficient method for computing 𝒵‐eigenpairs of symmetric tensors. Whereas, symmetric tensors are just special tensors. This article is concerned with the computation of 𝒵‐eigenpairs of general real tensors. We propose a Rayleigh quotient‐gradient neural network model (RGNN) for computing 𝒵‐eigenpairs of a general real tensor and the Euler‐type difference rule is used to discretize RGNN model. Theoretical analysis of the convergence for RGNN model is provided. Numerical experiments show that our method can capture all 𝒵‐eigenpairs for some small‐scale general tensors and enjoys efficient computation for large‐scale tensors.