TY - JOUR T1 - Solving Generalized Tensor Eigenvalue Problem via Spectral Shifted Inverse Power Methods AU - Pakmanesh , Mehri AU - Afshin , Hamidreza AU - Hajarian , Masoud JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 680 EP - 702 PY - 2025 DA - 2025/09 SN - 18 DO - http://doi.org/10.4208/nmtma.OA-2024-0139 UR - https://global-sci.org/intro/article_detail/nmtma/24323.html KW - Spectral shifted inverse power method, shifted symmetric higher-order power method, $Z$-eigenpair, $H$-eigenpair, generalized tensor eigenvalue problem. AB -

In this paper, we propose a generalized eigenproblem algorithm, called spectral shifted inverse power method (SIPM) for computing tensor generalized eigenvalue. The SIPM method is developed to overcome the limitations of existing approaches, such as the generalized eigenproblem adaptive power, tensor Noda iteration, modified tensor Noda iteration, and generalized Newton-Noda iteration. These methods often suffer from slow convergence, sensitivity to initial conditions, and computational inefficiency. First, we express SIPM as a fixed point iteration form and establish the connection between the fixed points and generalized eigenvectors of symmetric tensors. Moreover, we introduce a shift power method that further enhances SIPM. Next, we provide a technique for selecting the optimal starting point. Finally, we present numerical results that confirm the effectiveness of our method in solving the tensor generalized eigenvalue problem more efficiently than other methods.