AIMS Mathematics, 2020, 5(1): 701-716. doi: 10.3934/math.2020047

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Some new bounds on the spectral radius of nonnegative matrices

Department of Computer Science and Biomedical Informatics, University of Thessaly

## Abstract    Full Text(HTML)    Figure/Table    Related pages

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.
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# References

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.

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.

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.

10. A. Melman, Upper and lower bounds for the Perron root of a nonnegative matrix, Linear Multilinear Algebra, 61 (2013), 171-181.

11. R. Xing, B. Zhou, Sharp bounds for the spectral radius of nonnegative matrices, Linear Algebra its Appl., 449 (2014), 194-209.

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.