Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31014
Some New Upper Bounds for the Spectral Radius of Iterative Matrices

Authors: Guangbin Wang, Xue Li, Fuping Tan


In this paper, we present some new upper bounds for the spectral radius of iterative matrices based on the concept of doubly α diagonally dominant matrix. And subsequently, we give two examples to show that our results are better than the earlier ones.

Keywords: upper bound, eigenvalue, spectral radius, doubly α diagonally dominant matrix, iterative matrix

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1013


[1] R.A. Horn, C.R. Johnson, Matrix Analysis. Cambridge Univ. Press, Cambridge, 1985.
[2] Ji-Cheng Li, Wen-Xiu Zhang, "Criteria of H-matrix", Numerical Mathematics (a Journal of Chinese Universities), vol. 3, pp. 264-268, 1999.
[3] X.M. Wang, "The upper bound of the spectral radius of M−1N and convergence of some iterative methods", J. Comput. Math. vol. 53, pp. 203-217, 1994.
[4] J.G. Hu, "The upper and lower bounds forM−1N ", J. Comput. Math..vol. 2, pp.41-46, 1986.
[5] T.Z. Huang, Z.X. Gao, "A new upper bound for moduli of eigenvalues of iterative matrices", J. Comput. Math. vol. 80, pp.799-803, 2003.
[6] H.B. Li, T.Z. Huang, H. Li, "An improvement on a new upper bound for moduli of eigenvalues of iterative matrices", Appl. Math. Comput. vol. 173, pp.977-984, 2006.
[7] A. Berman, R.J. Plemmons, Nonnegative Matrices in Mathematical Sciences, SIAM Press, Philadelphia, 1994.