Spectral computation with third-order tensors using the t-product
Numerical Analysis
2023-05-16 v2 Numerical Analysis
Abstract
The tensor t-product, introduced by Kilmer and Martin [26], is a powerful tool for the analysis of and computation with third-order tensors. This paper introduces eigentubes and eigenslices of third-order tensors under the t-product. The eigentubes and eigenslices are analogues of eigenvalues and eigenvectors for matrices. Properties of eigentubes and eigenslices are investigated and numerical methods for their computation are described. The methods include the tensor power method, tensor subspace iteration, and the tensor QR algorithm. Computed examples illustrate the performance of these methods.
Cite
@article{arxiv.2304.04224,
title = {Spectral computation with third-order tensors using the t-product},
author = {Anas El Hachimi and Khalide Jbilou and Ahmed Ratnani and Lothar Reichel},
journal= {arXiv preprint arXiv:2304.04224},
year = {2023}
}