Optimal Z-eigenvalue bounds and rank-one approximations

This study explores the Z-eigenvalue inclusion theorem, focusing on its role in improving the best rank-one approximation for tensors. We propose novel inclusion sets inspired by Brauer and Brualdi’s frameworks, offering sharper bounds on Z-eigenvalues. These sets are demonstrated to provide more accurate results than existing approaches. Additionally, we apply these results to obtain refined estimates of best rank-one approximation, particularly for weakly symmetric nonnegative tensors. The paper includes numerical examples to validate the enhanced bounds presented.

کلیدواژه ها:

Weakly symmetric tensor ، Z-eigenvalue inclusion set ، best rank-one approximation ، Z-identity tensors ، Z-spectral radius