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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 980615, 6 pages
A New Upper Bound for of a Strictly -Diagonally Dominant -Matrix
1Department of Mathematics and Statistics, Qinghai University for Nationalities, Xining 810007, China
2School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
Received 22 September 2013; Accepted 10 December 2013
Academic Editor: Ting-Zhu Huang
Copyright © 2013 Zhanshan Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. M. Varah, “A lower bound for the smallest singular value of a matrix,” Linear Algebra and Its Applications, vol. 11, pp. 3–5, 1975.
- R. S. Varga, “On diagonal dominance arguments for bounding ,” Linear Algebra and Its Applications, vol. 14, no. 3, pp. 211–217, 1976.
- G.-H. Cheng and T.-Z. Huang, “An upper bound for of strictly diagonally dominant -matrices,” Linear Algebra and Its Applications, vol. 426, no. 2-3, pp. 667–673, 2007.
- P. Wang, “An upper bound for of strictly diagonally dominant -matrices,” Linear Algebra and Its Applications, vol. 431, no. 5–7, pp. 511–517, 2009.
- R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, Mass, USA, 1991.
- C. R. Johnson, “A Hadamard product involving -matrices,” Linear and Multilinear Algebra, vol. 4, no. 4, pp. 261–264, 1977.
- M. Fiedler, C. R. Johnson, and T. L. Markham, “A trace inequality for M-matrices and the symmertrizability of a real matrix by a positive diagonal matrix,” Linear Algebra and Its Applications, vol. 102, pp. 1–8, 1988.
- P. N. Shivakumar, J. J. Williams, Q. Ye, and C. A. Marinov, “On two-sided bounds related to weakly diagonally dominant -matrices with application to digital circuit dynamics,” SIAM Journal on Matrix Analysis and Applications, vol. 17, no. 2, pp. 298–312, 1996.
- A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, NY, USA, 1994.
- Y. L. Zhang, H. M. Mo, and J. Z. Liu, “-diagonal dominance and criteria for generalized strictly diagonally dominant matrices,” Numerical Mathematics, vol. 31, no. 2, pp. 119–128, 2009.
- P. N. Shivakumar and K. H. Chew, “A sufficient condition for nonvanishing of determinants,” Proceedings of the American Mathematical Society, vol. 43, pp. 63–66, 1974.
- S. Xu, Theory and Methods about Matrix Computation, Tshua University Press, Beijing, China, 1986.