Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 596049, 6 pages
http://dx.doi.org/10.1155/2014/596049
Research Article

Execute Elementary Row and Column Operations on the Partitioned Matrix to Compute M-P Inverse

School of Mathematics and Computational Science, Fuyang Normal College, Fuyang, Anhui, China

Received 3 November 2013; Revised 23 January 2014; Accepted 23 January 2014; Published 10 March 2014

Academic Editor: Sergei V. Pereverzyev

Copyright © 2014 Xingping Sheng. 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. E. H. Moore, “On the reciprocal of the general algebra matrix,” Bulletin of the American Mathematical Society, vol. 26, pp. 394–395, 1920. View at Google Scholar
  2. R. Penrose, “A generalized inverse for matrices,” Proceedings of the Cambridge Philosophical Society, vol. 51, pp. 406–413, 1955. View at Google Scholar
  3. A. Ben-Israel and T. N. E. Greville, Generalized Inverse Theory and Applications, Springer, New York, NY, USA, 2nd edition, 2003. View at MathSciNet
  4. S. L. Campbell and C. D. Meyer, Jr., Generalized Inverses of Linear Transformations, Dover, New York, NY, USA, 1979. View at MathSciNet
  5. G. W. Stewart, “On the continuity of the generalized inverse,” SIAM Journal on Applied Mathematics, vol. 17, pp. 33–45, 1969. View at Google Scholar · View at MathSciNet
  6. G. W. Stewart, “On the perturbation of pseudo-inverses, projections and linear least squares problems,” SIAM Review, vol. 19, no. 4, pp. 634–662, 1977. View at Google Scholar · View at MathSciNet
  7. P.-Å. Wedin, “Perturbation theory for pseudo-inverses,” BIT Numerical Mathematics, vol. 13, no. 2, pp. 217–232, 1973. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. J. Ji, “The algebraic perturbation method for generalized inverses,” Journal of Computational Mathematics, vol. 7, no. 4, pp. 327–333, 1989. View at Google Scholar · View at MathSciNet
  9. L. Kramarz, “Algebraic perturbation methods for the solution of singular linear systems,” Linear Algebra and Its Applications, vol. 36, pp. 79–88, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  10. J. Miao and A. Ben-Israel, “Minors of the Moore-Penrose inverse,” Linear Algebra and Its Applications, vol. 195, pp. 191–207, 1993. View at Google Scholar · View at Scopus
  11. J. Cai and G. L. Chen, “On the representation of A+,AMN+ and its applications,” Numerical Mathematics, vol. 24, no. 4, pp. 320–326, 2002 (Chinese). View at Google Scholar · View at MathSciNet
  12. J. A. Fill and D. E. Fishkind, “The Moore-Penrose generalized inverse for sums of matrices,” SIAM Journal on Matrix Analysis and Applications, vol. 21, no. 2, pp. 629–635, 2000. View at Google Scholar · View at MathSciNet · View at Scopus
  13. J. Ji, “Explicit expressions of the generalized inverses and condensed Cramer rules,” Linear Algebra and Its Applications, vol. 404, no. 1–3, pp. 183–192, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. J.-F. Cai, M. K. Ng, and Y.-M. Wei, “Modified Newton's algorithm for computing the group inverses of singular Toeplitz matrices,” Journal of Computational Mathematics, vol. 24, no. 5, pp. 647–656, 2006. View at Google Scholar · View at Scopus
  15. X. Chen and J. Ji, “Computing the Moore-Penrose inverse of a matrix through sysmmetric rank one updates,” American Journal of Computational Mathematics, vol. 1, pp. 147–151, 2011. View at Google Scholar
  16. M. D. Petkovi and P. S. Stanimirovi, “Iterative method for computing the MoorePenrose inverse based on Penrose equations,” Journal of Computational and Applied Mathematics, vol. 235, no. 6, pp. 1604–1613, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. Y. Wei, J. Cai, and M. K. Ng, “Computing Moore-Penrose inverses of Toeplitz matrices by Newton's iteration,” Mathematical and Computer Modelling, vol. 40, no. 1-2, pp. 181–191, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. V. N. Katsikis, D. Pappas, and A. Petralias, “An improved method for the computation of the Moore-Penrose inverse matrix,” Applied Mathematics and Computation, vol. 217, no. 23, pp. 9828–9834, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. X. Sheng and G. Chen, “A note of computation for M-P inverse A,” International Journal of Computer Mathematics, vol. 87, no. 10, pp. 2235–2241, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. J. Ji, “Gauss-Jordan elimination methods for the Moore-Penrose inverse of a matrix,” Linear Algebra and Its Applications, vol. 437, no. 7, pp. 1835–1844, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  21. P. S. Stanimirović and M. D. Petković, “Gauss-Jordan elimination method for computing outer inverses,” Applied Mathematics and Computation, vol. 219, no. 9, pp. 4667–4679, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  22. W. Guo and T. Huang, “Method of elementary transformation to compute Moore-Penrose inverse,” Applied Mathematics and Computation, vol. 216, no. 5, pp. 1614–1617, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus