@Article{NMTMA-18-680,
author = {Pakmanesh , MehriAfshin , Hamidreza and Hajarian , Masoud},
title = {Solving Generalized Tensor Eigenvalue Problem via Spectral Shifted Inverse Power Methods},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2025},
volume = {18},
number = {3},
pages = {680--702},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2024-0139},
url = {http://global-sci.org/intro/article_detail/nmtma/24323.html}
}