Exclusion sets in eigenvalue inclusion sets for tensors
Numerical Analysis
2017-06-06 v1
Abstract
By excluding some sets, which don't include any eigenvalue of a tensor, from some existing eigenvalue inclusion sets, two new sets are given to locate all eigenvalues of a tensor. And it is shown that these two sets are contained in the Ger\v{s}gorin eigenvalue inclusion set of tensors provide by Qi (Journal of Symbolic Computation 2005; 40:1302-1324) and the Brauer-type eigenvalue inclusion set provide by Li et al. (Numer. Linear Algebra Appl. 2014; 21:39-50) respectively. Two sufficient conditions such that the determinant of a tensor is not zero are also provided.
Keywords
Cite
@article{arxiv.1706.00944,
title = {Exclusion sets in eigenvalue inclusion sets for tensors},
author = {Chaoqian Li and Suhua Li and Qingbing Liu and Yaotang Li},
journal= {arXiv preprint arXiv:1706.00944},
year = {2017}
}
Comments
11 pages, 4 figures