Computing Z-Eigenvalue Of Hankel Tensors

In recent years, Hankel tensors are widely used in various industries, such as signal processing, medical imaging, and automatic control. This paper transforms the problem of the best rank one approximation with noise Hankel tensor into the problem of solving the maximum Z-eigenvalue in signal processing. Then, this paper proposes a conjugate gradient algorithm with simple line search (CGLS) for solving Z-eigenvalue of Hankel tensors. In algorithm, using a simple line search to find a suitable step α _k is a great technique, which accelerates the calculation speed. All iteration points are generated CGLS to preserve spherical constraint by using the Cayley transform. Furthermore, section V analyzes the convergence of the CGLS algorithm and adjusts suitable parameters in the algorithm. Finally, numerical experiments have verified that the CGLS is efficient and can greatly reduce iteration.