Jianxing Zhao, Caili Sang
Some monotone increasing sequences of the lower bounds for the minimum eigenvalue of $M$-matrices are given. It is proved that these sequences are convergent and improve some existing results. Numerical examples show that these sequences are more accurate than some existing results and could reach the true value of the minimum eigenvalue in some cases.
Caili Sang
A new S-type singular value inclusion set for rectangular tensors is given and proved to be tighter than that in [Sang C.L., An S-type singular value inclusion set for rectangular tensors, J. Inequal. Appl. 2017: 141, 2017]. Based on this set, new bounds for the largest singular value of nonnegative rectangular tensors are obtained and proved to be better than some existing results. Compared with the results in the paper mentioned above, the advantage of the new results is that, under the same computations, we can obtain a tighter singular value inclusion set for rectangular tensors and sharper bounds for the largest singular value of nonnegative rectangular tensors. Finally, a numerical example is given to verify the theoretical results.