Research article

Some new bounds on the spectral radius of nonnegative matrices

  • Received: 01 August 2019 Accepted: 02 December 2019 Published: 19 December 2019
  • MSC : 15A18, 15A42, 05C50

  • In this paper, we determine some new bounds for the spectral radius of a nonnegative matrix with respect to a new defined quantity, which can be considered as an average of average 2-row sums. The new formulas extend previous results using the row sums and the average 2-row sums of a nonnegative matrix. We also characterize the equality cases of the bounds if the matrix is irreducible and we provide illustrative examples comparing with the existing bounds.

    Citation: Maria Adam, Dimitra Aggeli, Aikaterini Aretaki. Some new bounds on the spectral radius of nonnegative matrices[J]. AIMS Mathematics, 2020, 5(1): 701-716. doi: 10.3934/math.2020047

    Related Papers:

  • In this paper, we determine some new bounds for the spectral radius of a nonnegative matrix with respect to a new defined quantity, which can be considered as an average of average 2-row sums. The new formulas extend previous results using the row sums and the average 2-row sums of a nonnegative matrix. We also characterize the equality cases of the bounds if the matrix is irreducible and we provide illustrative examples comparing with the existing bounds.


    加载中


    [1] M. Adam, Aik. Aretaki, Sharp bounds for eigenvalues of the generalized k, m-step Fibonacci matrices, Proceedings of the 3rd International Conference on Numerical Analysis and Scientific Computation with Applications (NASCA18), Kalamata, Greece, (2018). Available from: http://nasca18.math.uoa.gr/participants-nbsp.html.
    [2] A. Brauer, I.C. Gentry, Bounds for the greatest characteristic root of an irreducible nonnegative matrix, Linear Algebra its Appl., 8 (1974), 105-107. doi: 10.1016/0024-3795(74)90048-2
    [3] F. Duan, K. Zhang, An algorithm of diagonal transformation for Perron root of nonnegative irreducible matrices, Appl. Math. Comput., 175 (2006), 762-772.
    [4] X. Duan, B. Zhou, Sharp bounds on the spectral radius of a nonnegative matrix, Linear Algebra its Appl., 439 (2013), 2961-2970. doi: 10.1016/j.laa.2013.08.026
    [5] G. Frobenius, Über Matrizen aus nicht negativen Elementen, Sitzungsber, Kön. Preuss. Akad. Wiss. Berlin, (1912), 465-477.
    [6] J. He, Y.M. Liu, J.K. Tian, et al., Some new sharp bounds for the spectral radius of a nonnegative matrix and its application, J. Inequalities Appl., 260 (2017), 1-6.
    [7] W. Hong, L. You, Further results on the spectral radius of matrices and graphs, Appl. Math. Comput., 239 (2014), 326-332.
    [8] R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, second edition, 2013.
    [9] H. Lin, B. Zhou, On sharp bounds for spectral radius of nonnegative matrices, Linear Multilinear Algebra, 65 (2017), 1554-1565. doi: 10.1080/03081087.2016.1246514
    [10] A. Melman, Upper and lower bounds for the Perron root of a nonnegative matrix, Linear Multilinear Algebra, 61 (2013), 171-181. doi: 10.1080/03081087.2012.667096
    [11] R. Xing, B. Zhou, Sharp bounds for the spectral radius of nonnegative matrices, Linear Algebra its Appl., 449 (2014), 194-209. doi: 10.1016/j.laa.2014.02.031
    [12] C. Wen, T. Z. Huang, A modified algorithm for the Perron root of a nonnegative matrix, Appl. Math. Comput., 217 (2011), 4453-4458.
    [13] P. Walters, An introduction to ergodic theory, New York (NY), Springer-Verlag, 1982.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3311) PDF downloads(524) Cited by(4)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog