Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2014), Article ID 329490, 4 pages.

On Comparison Theorems for Splittings of Different Semimonotone Matrices

Shu-Xin Miao and Yang Cao

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Comparison theorems between the spectral radii of different matrices are useful tools for judging the efficiency of preconditioners. In this paper, some comparison theorems for the spectral radii of matrices arising from proper splittings of different semimonotone matrices are presented.

Article information

J. Appl. Math., Volume 2014, Special Issue (2014), Article ID 329490, 4 pages.

First available in Project Euclid: 1 October 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)


Miao, Shu-Xin; Cao, Yang. On Comparison Theorems for Splittings of Different Semimonotone Matrices. J. Appl. Math. 2014, Special Issue (2014), Article ID 329490, 4 pages. doi:10.1155/2014/329490.

Export citation


  • D. Mishra and K. Sivakumar, “Comparison theorems for a subclass of proper splittings of matrices,” Applied Mathematics Letters, vol. 25, no. 12, pp. 2339–2343, 2012.
  • A. Ben-Israel and T. Greville, Generalized Inverses: Theory and Applications, Springer, New York, NY, USA, 2003.
  • G. Wang, Y. Wei, and S. Qiao, Generalized Inverses: Theory and Computations, Science Press, Beijing, China, 2004.
  • A. Berman and R. J. Plemmons, “Cones and iterative methods for best least squares solutions of linear systems,” SIAM Journal on Numerical Analysis, vol. 11, pp. 145–154, 1974.
  • R. S. Varga, Matrix Iterative Analysis, vol. 27, Springer, Berlin, Germany, 2000.
  • A. Berman and R. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, Pa, USA, 1994.
  • J.-J. Climent and C. Perea, “Iterative methods for least-square problems based on proper splittings,” Journal of Computational and Applied Mathematics, vol. 158, no. 1, pp. 43–48, 2003.
  • L. Jena, D. Mishra, and S. Pani, “Convergence and comparison theorems for single and double decompositions of rectangular matrices,” Calcolo, vol. 51, no. 1, pp. 141–149, 2014.
  • J.-J. Climent, A. Devesa, and C. Perea, “Convergence results for proper splittings,” in Recent Advances in Applied and Theoretical Mathematics, N. Mastorakis, Ed., pp. 39–44, 2000.
  • S.-X. Miao and B. Zheng, “A note on double splittings of different monotone matrices,” Calcolo, vol. 46, no. 4, pp. 261–266, 2009.
  • L. Elsner, A. Frommer, R. Nabben, and D. B. Szyld, “Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices,” Linear Algebra and Its Applications, vol. 363, pp. 65–80, 2003.
  • C.-X. Li, Q.-F. Cui, and S.-L. Wu, “Comparison theorems for single and double splittings of matrices,” Journal of Applied Mathematics, vol. 2013, Article ID 827826, 4 pages, 2013.
  • D. Mishra, “Nonnegative splittings for rectangular matrices,” Computers & Mathematics with Applications, vol. 67, no. 1, pp. 136–144, 2014. \endinput