# A tighter S-type singular value inclusion set for rectangular tensors

## TL;DR

This paper introduces a new, tighter S-type singular value inclusion set for rectangular tensors, leading to improved bounds for the largest singular value of nonnegative rectangular tensors, verified through numerical examples.

## Contribution

It presents a novel, more precise singular value inclusion set for rectangular tensors and derives sharper bounds for their largest singular value, improving upon previous methods.

## Key findings

- New tighter S-type singular value inclusion set for rectangular tensors
- Improved bounds for the largest singular value of nonnegative rectangular tensors
- Numerical example confirms theoretical improvements

## Abstract

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.