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A new S-type upper bound for the largest singular value of nonnegative rectangular tensors
1College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, Guizhou 550025 P.R. China.
Journal of Inequalities and Applications
|May 30, 2017
Summary
Researchers developed a new S-type upper bound for the largest singular value of nonnegative rectangular tensors. This novel method improves upon existing bounds and is validated by numerical examples.
Area of Science:
- Linear Algebra
- Numerical Analysis
- Tensor Theory
Background:
- Singular values are crucial for understanding tensor properties.
- Existing upper bounds for nonnegative rectangular tensors have limitations.
Purpose of the Study:
- To introduce a novel S-type upper bound for the largest singular value of nonnegative rectangular tensors.
- To demonstrate the superiority of the new bound compared to existing methods.
Main Methods:
- Decomposition of the tensor index set into disjoint subsets S and its complement.
- Development and proof of the S-type upper bound inequality.
Main Results:
- A new S-type upper bound for the largest singular value was derived.
- The proposed bound was proven to be tighter than several existing bounds.
- Numerical examples confirmed the theoretical findings and the effectiveness of the new bound.
Conclusions:
- The new S-type upper bound offers an improved estimation for the largest singular value of nonnegative rectangular tensors.
- This method provides a valuable tool for analyzing and understanding tensor properties in various applications.
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