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(i) An S-type singular value inclusion set.
An S-type singular value inclusion set for rectangular tensors is given.
In this paper, we give an S-type singular value inclusion set (Upsilon^{S}(mathcal{A})) for rectangular tensors.
It is easy to see that (Upsilon^{S}(mathcal{A})) can capture all singular values of (mathcal{A}) from Figure 1. Figure 1 The singular value inclusion set (pmb{Upsilon ^{S}(mathcal{A})}) and the exact singular values.
It is easy to see that (Upsilon^{S}(mathcal{A})) captures exactly all singular values of (mathcal{A}) from Figure 2. Figure 2 The singular value inclusion set (pmb{Upsilon ^{S}(mathcal{A})}) and the exact singular values.
Our goal in this paper is to propose a singular value inclusion set for rectangular tensors and use the set to obtain new upper and lower bounds for the largest singular value of nonnegative rectangular tensors.
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