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Distribution of Eigenvalues and Upper Bounds of the Spread of Interval Matrices

Author

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  • Wenshi Liao

    (College of Mathematics, Physics and Data Science, Chongqing University of Science and Technology, Chongqing 401331, China
    These authors contributed equally to this work.)

  • Pujun Long

    (College of Mathematics, Physics and Data Science, Chongqing University of Science and Technology, Chongqing 401331, China
    These authors contributed equally to this work.)

Abstract

The distribution of eigenvalues and the upper bounds for the spread of interval matrices are significant in various fields of mathematics and applied sciences, including linear algebra, numerical analysis, control theory, and combinatorial optimization. We present the distribution of eigenvalues within interval matrices and determine upper bounds for their spread using Geršgorin’s theorem. Specifically, through an equality for the variance of a discrete random variable, we derive upper bounds for the spread of symmetric interval matrices. Finally, we give three numerical examples to illustrate the effectiveness of our results.

Suggested Citation

  • Wenshi Liao & Pujun Long, 2023. "Distribution of Eigenvalues and Upper Bounds of the Spread of Interval Matrices," Mathematics, MDPI, vol. 11(19), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4032-:d:1245719
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    References listed on IDEAS

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    1. Roy, Falguni & K. Gupta, Dharmendra., 2018. "Sufficient regularity conditions for complex interval matrices and approximations of eigenvalues sets," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 193-209.
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