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Abstract and Applied Analysis
Volume 2014, Article ID 563787, 7 pages
http://dx.doi.org/10.1155/2014/563787
Research Article

A New Iterative Method for Finding Approximate Inverses of Complex Matrices

1Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
2Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Received 24 May 2014; Revised 25 July 2014; Accepted 28 July 2014; Published 14 September 2014

Academic Editor: Juan R. Torregrosa

Copyright © 2014 M. Kafaei Razavi 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.

Linked References

  1. Y. Saad, Iterative Methods for Sparse Linear Systems, SIAM, 2nd edition, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  2. F. Soleimani, F. Soleymani, A. Cordero, and J. R. Torregrosa, “On the extension of Householder's method for weighted Moore-Penrose inverse,” Applied Mathematics and Computation, vol. 231, pp. 407–413, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  3. G. Schulz, “Iterative Berechnung der Reziproken matrix,” Zeitschrift für Angewandte Mathematik und Mechanik, vol. 13, pp. 57–59, 1933. View at Google Scholar
  4. A. Ben-Israel and T. N. E. Greville, Generalized Inverses, Berlin, Germany, Springer, 2nd edition, 2003. View at MathSciNet
  5. M. Benzi, “Preconditioning techniques for large linear systems: a survey,” Journal of Computational Physics, vol. 182, no. 2, pp. 418–477, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. H.-B. Li, T.-Z. Huang, Y. Zhang, V.-P. Liu, and T.-V. Gu, “Chebyshev-type methods and preconditioning techniques,” Applied Mathematics and Computation, vol. 218, no. 2, pp. 260–270, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. V. Y. Pan, M. Van Barel, X. Wang, and G. Codevico, “Iterative inversion of structured matrices,” Theoretical Computer Science, vol. 315, no. 2-3, pp. 581–592, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. W. Li and Z. Li, “A family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non-square matrix,” Applied Mathematics and Computation, vol. 215, no. 9, pp. 3433–3442, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. E. V. Krishnamurthy and S. K. Sen, Numerical Algorithms: Computations in Science and Engineering, Affiliated East-West Press, New Delhi, India, 2007. View at MathSciNet
  10. F. Toutounian and F. Soleymani, “An iterative method for computing the approximate inverse of a square matrix and the Moore-Penrose inverse of a non-square matrix,” Applied Mathematics and Computation, vol. 224, pp. 671–680, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  11. V. Y. Pan and R. Schreiber, “An improved Newton iteration for the generalized inverse of a matrix, with applications,” SIAM: Journal on Scientific and Statistical Computing, vol. 12, no. 5, pp. 1109–1130, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  12. E. Isaacson and H. B. Keller, Analysis of Numerical Methods, John Wiley & Sons, New York, NY, USA, 1966. View at MathSciNet
  13. L. Weiguo, L. Juan, and Q. Tiantian, “A family of iterative methods for computing Moore-Penrose inverse of a matrix,” Linear Algebra and Its Applications, vol. 438, no. 1, pp. 47–56, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. F. Soleymani, “A fast convergent iterative solver for approximate inverse of matrices,” Numerical Linear Algebra with Applications, vol. 21, pp. 439–452, 2014. View at Publisher · View at Google Scholar · View at Scopus
  15. J. F. Traub, Iterative Methods for the Solution of Equations, Prentice Hall, New York, NY, USA, 1964. View at MathSciNet
  16. http://reference.wolfram.com/language/tutorial/LinearAlgebraInMathematicaOverview.
  17. S. Wolfram, The Mathematica Book, Wolfram Media, 5th edition, 2003. View at MathSciNet
  18. L. Grosz, “Preconditioning by incomplete block elimination,” Numerical Linear Algebra with Applications, vol. 7, no. 7-8, pp. 527–541, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus