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Abstract and Applied Analysis
Volume 2012, Article ID 736929, 9 pages
http://dx.doi.org/10.1155/2012/736929
Research Article

Proper Splitting for the Generalized Inverse and Its Application on Banach Spaces

School of Science, Guangxi University for Nationalities and Guangxi Key Laborarory of Hybrid Computational and IC Design Analysis, Nanning 530006, China

Received 7 December 2011; Accepted 16 March 2012

Academic Editor: Jean Michel Combes

Copyright © 2012 Xiaoji Liu and Shaowu Huang. 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.

Linked References

  1. B. Načevska, “Iterative methods for computing generalized inverses and splittings of operators,” Applied Mathematics and Computation, vol. 208, no. 1, pp. 186–188, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. D. S. Djordjević and Y. Wei, “Outer generalized inverses in rings,” Communications in Algebra, vol. 33, no. 9, pp. 3051–3060, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. Y. Wei and H. Wu, “{T,S} splitting methods for computing the generalized inverse AT,S(2) and rectangular systems,” International Journal of Computer Mathematics, vol. 77, no. 3, pp. 401–424, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. X. Chen, W. Wang, and Y. Song, “Splitting based on the outer inverse of matrices,” Applied Mathematics and Computation, vol. 132, no. 2-3, pp. 353–368, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. Z. Chao and G. Chen, “Index splitting for the Drazin inverse of linear operator in Banach space,” Applied Mathematics and Computation, vol. 135, no. 2-3, pp. 201–209, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. A. Berman and M. Neumann, “Proper splittings of rectangular matrices,” SIAM Journal on Applied Mathematics, vol. 31, no. 2, pp. 307–312, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. G. Wang and Y. Wei, “Proper splittings for restricted linear equations and the generalized inverse AT,S(2),” Numerical Mathematics, vol. 7, no. 1, pp. 1–13, 1998. View at Google Scholar · View at Zentralblatt MATH
  8. D. H. Cai, “The Drazin generalized inverses of linear operators,” Journal of Mathematics. Shuxue Zazhi, vol. 5, no. 1, pp. 81–88, 1985 (Chinese). View at Google Scholar
  9. D. S. Djordjević and V. Rakočević, Lectures on Generalized Inverses, Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia, 2008.
  10. A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, John Wiley & Sons, New York, NY, USA, 1974.
  11. D. S. Djordjević, “Iterative methods for computing generalized inverses,” Applied Mathematics and Computation, vol. 189, no. 1, pp. 101–104, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH