A tighter S-type singular value inclusion set for rectangular tensors
Provides a tighter inclusion set and sharper bounds for the largest singular value of nonnegative rectangular tensors, benefiting researchers in tensor analysis and related fields, but the improvement is incremental.
The authors propose a new S-type singular value inclusion set for rectangular tensors that is tighter than a previous set from 2017, leading to improved bounds for the largest singular value of nonnegative rectangular tensors. Numerical example confirms the theoretical improvements.
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.