Sharp bounds on the spectral radius of nonnegative matrices and comparison to the frobenius’ bounds

被引：0
作者：
Adam M. [1 ]
Assimakis N. [2 ]
Babouklis F. [1 ]
机构：
[1] Dept. of Computer Science & Biomedical Informatics, University of Thessaly, Lamia
[2] General Department, National and Kapodistrian University of Athens, Athens
来源：
| 1600年 / North Atlantic University Union, 942 Windemere Dr. NW.,, Salem, Oregon 97304, United States卷 / 14期
关键词：
Algorithm; Complexity; Nonnegative matrix; Row sum; Spectral radius; Stability;
D O I：
10.46300/9106.2020.14.57
中图分类号：
学科分类号：
摘要：
In this paper, a new upper bound and a new lower bound for the spectral radius of a nοnnegative matrix are proved by using similarity transformations. These bounds depend only on the elements of the nonnegative matrix and its row sums and are compared to the well-established upper and lower Frobenius’ bounds. The proposed bounds are always sharper or equal to the Frobenius’ bounds. The conditions under which the new bounds are sharper than the Frobenius' ones are determined. Illustrative examples are also provided in order to highlight the sharpness of the proposed bounds in comparison with the Frobenius’ bounds. An application to linear invariant discrete-time nonnegative systems is given and the stability of the systems is investigated. The proposed bounds are computed with complexity O(n2). © 2020, North Atlantic University Union. All rights reserved.
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页码：423 / 434
页数：11
相关论文
共 21 条
  • [1] Adam M., Aggeli D., Aretaki Aik., Some new bounds on the spectral radius of nonnegative matrices, AIMS Mathematics, 5, 1, pp. 701-716, (2019)
  • [2] Adam M., Assimakis N., Tziallas G., Generalized k,m-step Fibonacci sequences and matrices, Proceedings of the 12th International Conference of AHA-Algebraic Hyperstructures and its Applications, Int. J. of Algebraic Hyperstructures and Its Applications, 2, 1, pp. 125-134, (2015)
  • [3] Anderson B.D.O., Moore J.B., Optimal Filtering, (2005)
  • [4] Babouklis F., Adam M., Assimakis N., Bounds on the spectral radius of nonnegative matrices, Proceedings International Conference on Mathematics and Computers in Science and Engineering (MACISE), pp. 51-55, (2020)
  • [5] Canto B., Canto R., Kostova S., Stabilization of Positive Linear Discrete-Time Systems by Using a Brauer’s Theorem, The Scientific World Journal, (2014)
  • [6] Canto B., Coll C., Sanchez E., On stability and reachability of perturbed positive systems, Advances in Difference Equations, 296, pp. 1-11, (2014)
  • [7] Duan F., Zhang K., An algorithm of diagonal transformation for Perron root of nonnegative irreducible matrices, Applied Mathematics and Computation, 175, pp. 762-772, (2006)
  • [8] Duan X., Zhou B., Sharp bounds on the spectral radius of a nonnegative matrix, Linear Algebra and its Applications, 439, pp. 2961-2970, (2013)
  • [9] Fornasini E., Valcher M.E., Reachability of a class of discretetime positive switched systems, v. SIAM J. Control Optim, 49, pp. 162-184, (2011)
  • [10] Fu M., Pole placement via static output feedback is NP-hard, Institute of Electrical and Electronics Engineers, Transactions on Automatic Control, 49, 5, pp. 855-857, (2004)
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