Shifted power method for computing tensor H-eigenpairs

In this paper, we propose a shifted symmetric higher-order power method for computing the H-eigenpairs of a real symmetric even-order tensor. The local convergence of the method is proved. In addition, by utilizing the fixed-point analysis, we can characterize exactly which H-eigenpairs can be found and which cannot be found by the method. Numerical examples are presented to illustrate the performance of the method.