@article{Cao2023, 
author = {Mingyuan Cao and Yueting Yang and Chaoqian Li and Xiaowei Jiang},
title = {An accelerated conjugate gradient method for the Z-eigenvalues of symmetric tensors},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {7},
pages = {15008-15023},
keywords = {symmetric tensors, Z-eigenvalues, accelerated conjugate gradient, variational, global convergence},
url = {https://www.sciopen.com/article/10.3934/math.2023766},
doi = {10.3934/math.2023766},
abstract = {We transform the Z-eigenvalues of symmetric tensors into unconstrained optimization problems with a shifted parameter. An accelerated conjugate gradient method is proposed for solving these unconstrained optimization problems. If solving problem results in a nonzero critical point, then it is a Z-eigenvector corresponding to the Z-eigenvalue. Otherwise, we solve the shifted problem to find a Z-eigenvalue. In our method, the new conjugate gradient parameter is a modified CD conjugate gradient parameter, and an accelerated parameter is presented by using the quasi-Newton direction. The global convergence of new method is proved. Numerical experiments are listed to illustrate the efficiency of the proposed method.}
}