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Journal of Applied Mathematics
Volume 2012, Article ID 219025, 15 pages
http://dx.doi.org/10.1155/2012/219025
Research Article

Relative and Absolute Perturbation Bounds for Weighted Polar Decomposition

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received 21 October 2011; Accepted 20 December 2011

Academic Editor: Juan Manuel Peña

Copyright © 2012 Pingping Zhang 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. G. R. Wang and Y. M. Wei, Generalized Inverses: Theory and Computations, Science, Beijing, China, 2004.
  2. C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and Its Applications, John Wiley & Sons, New York, NY, USA, 1971. View at Zentralblatt MATH
  3. H. Yang and H. Li, “Weighted UDV-decomposition and weighted spectral decomposition for rectangular matrices and their applications,” Applied Mathematics and Computation, vol. 198, no. 1, pp. 150–162, 2008. View at Publisher · View at Google Scholar
  4. H. Yang and H. Li, “Weighted polar decomposition and WGL partial ordering of rectangular complex matrices,” SIAM Journal on Matrix Analysis and Applications, vol. 30, no. 2, pp. 898–924, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. H. Yang and H. Y. Li, “Weighted polar decomposition,” Journal of Mathematical Research and Exposition, vol. 29, no. 5, pp. 787–798, 2009. View at Google Scholar
  6. J. G. Sun and C. H. Chen, “Generalized polar decomposition,” Mathematica Numerica Sinica, vol. 11, no. 3, pp. 262–273, 1989 (Chinese). View at Google Scholar · View at Zentralblatt MATH
  7. C. H. Chen and J. G. Sun, “Perturbation bounds for the polar factors,” Journal of Computational Mathematics, vol. 7, no. 4, pp. 397–401, 1989. View at Google Scholar · View at Zentralblatt MATH
  8. R. C. Li, “A perturbation bound for the generalized polar decomposition,” BIT, vol. 33, no. 2, pp. 304–308, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. R.-C. Li, “Relative perturbation bounds for the unitary polar factor,” BIT. Numerical Mathematics, vol. 37, no. 1, pp. 67–75, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. W. Li and W. Sun, “Perturbation bounds of unitary and subunitary polar factors,” SIAM Journal on Matrix Analysis and Applications, vol. 23, no. 4, pp. 1183–1193, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. R. Mathias, “Perturbation bounds for the polar decomposition,” SIAM Journal on Matrix Analysis and Applications, vol. 14, no. 2, pp. 588–597, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. X. S. Chen and W. Li, “Perturbation bounds for polar decomposition under unitarily invariant norms,” Mathematica Numerica Sinica, vol. 27, no. 2, pp. 121–128, 2005. View at Google Scholar
  13. R. C. Li, “New perturbation bounds for the unitary polar factor,” SIAM Journal on Matrix Analysis and Applications, vol. 16, no. 1, pp. 327–332, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. W. Li and W. Sun, “New perturbation bounds for unitary polar factors,” SIAM Journal on Matrix Analysis and Applications, vol. 25, no. 2, pp. 362–372, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. W. Li and W. Sun, “Some remarks on the perturbation of polar decompositions for rectangular matrices,” Numerical Linear Algebra with Applications, vol. 13, no. 4, pp. 327–338, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. X.-S. Chen and W. Li, “Variations for the Q- and H-factors in the polar decomposition,” Calcolo, vol. 45, no. 2, pp. 99–109, 2008. View at Publisher · View at Google Scholar
  17. X. S. Chen, “Absolute and relative perturbation bounds for the Hermitian positive semidefinite polar factor under unitarily invariant norm,” Journal of South China Normal University, no. 3, pp. 1–3, 2010 (Chinese). View at Google Scholar
  18. A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 15, Springer, New York, NY, USA, 2nd edition, 2003.
  19. C. R. Rao and M. B. Rao, Matrix Algebra and Its Applications to Statistics and Econometrics, World Scientific, River Edge, NJ, USA, 1998.
  20. H. Li and H. Yang, “Relative perturbation bounds for weighted polar decomposition,” Computers & Mathematics with Applications, vol. 59, no. 2, pp. 853–860, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. H. Yang and H. Li, “Perturbation bounds for weighted polar decomposition in the weighted unitarily invariant norm,” Numerical Linear Algebra with Applications, vol. 15, no. 8, pp. 685–700, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. C. Davis and W. M. Kahan, “The rotation of eigenvectors by a perturbations III,” SIAM Journal on Scientific and Statistical Computing, no. 12, pp. 488–504, 1991. View at Google Scholar
  23. R.-C. Li, “Relative perturbation theory. II. Eigenspace and singular subspace variations,” SIAM Journal on Matrix Analysis and Applications, vol. 20, no. 2, pp. 471–492, 1998. View at Publisher · View at Google Scholar