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A new Z-eigenvalue localization set for tensors.

Jianxing Zhao1

  • 1College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, Guizhou 550025 P.R. China.

Journal of Inequalities and Applications
|May 12, 2017
PubMed
Summary
This summary is machine-generated.

A novel Z-eigenvalue localization set for tensors offers tighter bounds than previous methods. This advancement yields a sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors.

Keywords:
Z-eigenvaluelocalization setnonnegative tensorsspectral radiusweakly symmetric

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Area of Science:

  • Numerical Analysis
  • Linear Algebra
  • Tensor Theory

Background:

  • Eigenvalue localization sets are crucial for understanding tensor properties.
  • Existing methods, such as those by Wang et al., provide foundational Z-eigenvalue localization sets.

Purpose of the Study:

  • To introduce a new, tighter Z-eigenvalue localization set for tensors.
  • To derive a sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors.

Main Methods:

  • Development of a novel Z-eigenvalue localization set for tensors.
  • Theoretical analysis to prove the improved tightness of the new set compared to existing ones.
  • Application of the new set to establish a sharper upper bound for the Z-spectral radius.

Main Results:

  • A new Z-eigenvalue localization set for tensors has been established.
  • The new set is demonstrated to be strictly tighter than the Z-eigenvalue localization set proposed by Wang et al.
  • A sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained.

Conclusions:

  • The newly developed Z-eigenvalue localization set offers enhanced precision for tensor analysis.
  • The findings provide a more accurate estimation of the Z-spectral radius for specific tensor types.
  • Numerical examples confirm the theoretical improvements and tighter bounds achieved.