English

On the tubular eigenvalues of third-order tensors

Numerical Analysis 2023-05-11 v1 Numerical Analysis

Abstract

This paper introduces the notion of tubular eigenvalues of third-order tensors with respect to T-products of tensors and analyzes their properties. A focus of the paper is to discuss relations between tubular eigenvalues and two alternative definitions of eigenvalue for third-order tensors that are known in the literature, namely eigentuple and T-eigenvalue. In addition, it establishes a few results on tubular spectra of tensors which can be exploited to analyze the convergence of tubular versions of iterative methods for solving tensor equations.

Keywords

Cite

@article{arxiv.2305.06323,
  title  = {On the tubular eigenvalues of third-order tensors},
  author = {Fatemeh P. A. Beik and Yousef Saad},
  journal= {arXiv preprint arXiv:2305.06323},
  year   = {2023}
}