Some New Upper Bounds for the Spectral Radius of Iterative Matrices
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:64731", author = "Guangbin Wang and Xue Li and Fuping Tan", title = "Some New Upper Bounds for the Spectral Radius of Iterative Matrices", abstract = "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 = "doubly α diagonally dominant matrix, eigenvalue,iterative matrix, spectral radius, upper bound.", volume = "4", number = "7", pages = "1048-4", }