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A new inclusion interval for the real eigenvalues of real matrices

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Abstract

By properties of Cvetković-Kostić-Varga-type (or, for short, CKV-type) B-matrices, a new class of nonsingular matrices called CKV-type \(\overline{B}\)-matrices is given, and a new inclusion interval of the real eigenvalues of real matrices is presented. It is shown that the new inclusion interval is sharper than those provided by J. M. Peña (2003), and by H. B. Li et al. (2007). We also propose a direct algorithm for computing the new inclusion interval. Numerical examples are included to illustrate the effectiveness of the obtained results.

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Acknowledgements

The authors would like to thank the editor and the anonymous referees for their valuable suggestions and comments.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Baoji University of Arts and Sciences, No. 1 Hi-Tech Avenue, Baoji, 721013, P. R. China

    Yinghua Wang, Xinnian Song & Lei Gao

Authors
  1. Yinghua Wang
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  2. Xinnian Song
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  3. Lei Gao
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Corresponding author

Correspondence to Lei Gao.

Additional information

The research has been supported by in parts the National Natural Science Foundation of China (31600299), the Young Science and Technology Nova Program of Shaanxi Province (2022KJXX-01), the Scientific Research Program Funded by Yunnan Provincial Education Department (2022J0949), and the Postgraduate Research Innovation Project of Baoji University of Arts and Sciences (YJSCX22ZD04).

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Wang, Y., Song, X. & Gao, L. A new inclusion interval for the real eigenvalues of real matrices. Czech Math J 73, 979–992 (2023). https://doi.org/10.21136/CMJ.2023.0420-22

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  • DOI: https://doi.org/10.21136/CMJ.2023.0420-22

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