Optimal $Z$-eigenvalue bounds and rank-one approximations

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

2 Department of Mathematics, University of Hormozgan, Bandar Abbas, Iran

Abstract

This study explores the $Z$-eigenvalue inclusion theorem, focusing on its role in improving the best rank-one approximation for tensors. We propose novel inclusion sets inspired by Brauer and Brualdi’s frameworks, offering sharper bounds on $Z$-eigenvalues. These sets are demonstrated to provide more accurate results than existing approaches. Additionally, we apply these results to obtain refined estimates of best rank-one approximation, particularly for weakly symmetric nonnegative tensors. The paper includes numerical examples to validate the enhanced bounds presented.

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References

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Journal of Mahani Mathematical Research

Articles in Press, Accepted Manuscript
Available Online from 12 March 2025

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  • Receive Date: 25 October 2024
  • Revise Date: 28 January 2025
  • Accept Date: 11 March 2025

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