Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 518269, 8 pages
http://dx.doi.org/10.1155/2013/518269
Research Article

Sensitivity Analysis of the Matrix Equation from Interpolation Problems

1School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, China
2School of Mathematics, Shandong University, Jinan 250100, China

Received 22 July 2013; Accepted 27 September 2013

Academic Editor: Carlos J. S. Alves

Copyright © 2013 Jing Li and Yuhai Zhang. 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. W. N. Anderson, G. B. Kleindorfer, M. B. Kleindorfer, and M. B. Woodroofe, “Consistent estimates of the parameters of a linear systems,” The Annals of Mathematical Statistics, vol. 40, no. 6, pp. 2064–2075, 1969. View at Publisher · View at Google Scholar
  2. W. N. Anderson, T. D. Morley, and G. E. Trapp, “The cascade limit, the shorted operator and quadratic optimal control,” in Linear Circuits, Systems and Signal Processsing: Theory and Application, I. Christopher Byrnes, F. C. Martin, and E. Richard Saeks, Eds., pp. 3–7, North-Holland, New York, NY, USA, 1988. View at Google Scholar
  3. R. S. Bucy, “A priori bounds for the Riccati equation,” in Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability, Volume 3: Probability Theory, pp. 645–656, University of California Press, Berkeley, Calif, USA, 1972.
  4. D. V. Ouellette, “Schur complements and statistics,” Linear Algebra and Its Applications C, vol. 36, pp. 187–295, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. W. Pusz and S. L. Woronowitz, “Functional caculus for sequlinear forms and purification map,” Reports on Mathematical Physics, vol. 8, no. 2, pp. 159–170, 1975. View at Publisher · View at Google Scholar
  6. J. Zabcyk, “Remarks on the control of discrete time distributed parameter systems,” SIAM Journal on Control and Optimization, vol. 12, no. 4, pp. 721–735, 1974. View at Publisher · View at Google Scholar · View at Scopus
  7. A. C. M. Ran and M. C. B. Reurings, “A nonlinear matrix equation connected to interpolation theory,” Linear Algebra and Its Applications, vol. 379, no. 1–3, pp. 289–302, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. X. F. Duan and A. P. Liao, “On Hermitian positive definite solution of the matrix equation X-i=1mAi*XrAi=Q,” Journal of Computational and Applied Mathematics, vol. 229, no. 1, pp. 27–36, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Ferrante and B. C. Levy, “Hermitian solutions of the equation X=Q+NX-1N*,” Linear Algebra and Its Applications, vol. 247, pp. 359–373, 1996. View at Publisher · View at Google Scholar · View at Scopus
  10. C. Guo and P. Lancaster, “Iterative solution of two matrix equations,” Mathematics of Computation, vol. 68, no. 228, pp. 1589–1603, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. V. I. Hasanov, “Positive definite solutions of the matrix equations X±A*X-qA=Q,” Linear Algebra and Its Applications, vol. 404, no. 1–3, pp. 166–182, 2005. View at Publisher · View at Google Scholar · View at Scopus
  12. V. I. Hasanov, I. G. Ivanov, and F. Uhlig, “Improved perturbation estimates for the matrix equations X±A*X-1A=Q,” Linear Algebra and Its Applications, vol. 379, no. 1–3, pp. 113–135, 2004. View at Publisher · View at Google Scholar · View at Scopus
  13. J. Li and Y. H. Zhang, “The Hermitian positive definite solutions and perturbation analysis of the matrix equation X-A*X-1A=Q,” Bulletin of the Institute of Mathematics Academia Sinica, vol. 30, pp. 129–142, 2008 (Chinese). View at Google Scholar
  14. Y. Lim, “Solving the nonlinear matrix equation X=Q+i=1mMiXδiMi* via a contraction principle,” Linear Algebra and Its Applications, vol. 430, no. 4, pp. 1380–1383, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. V. I. Hasanov and I. G. Ivanov, “On two perturbation estimates of the extreme solutions to the equations X±A*X-1A=Q,” Linear Algebra and Its Applications, vol. 413, no. 1, pp. 81–92, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. J. Li and Y. Zhang, “Perturbation analysis of the matrix equation X-A*X-qA=Q,” Linear Algebra and Its Applications, vol. 431, no. 9, pp. 1489–1501, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. X. G. Liu and H. Gao, “On the positive definite solutions of the matrix equations Xs±ATX-tA=In,” Linear Algebra and Its Applications, vol. 368, pp. 83–87, 2003. View at Publisher · View at Google Scholar · View at Scopus
  18. J. G. Sun and S. F. Xu, “Perturbation analysis of the maximal solution of the matrix equation X+A*X-1A=P. II,” Linear Algebra and Its Applications, vol. 362, pp. 211–228, 2003. View at Publisher · View at Google Scholar · View at Scopus
  19. S. F. Xu, “Perturbation analysis of the maximal solution of the matrix equation X+A*X-1A=P,” Linear Algebra and Its Applications, vol. 336, no. 1–3, pp. 61–70, 2001. View at Publisher · View at Google Scholar · View at Scopus
  20. X. Y. Yin and L. Fang, “Perturbation analysis for the positive definite solution of the nonlinear matrix equation X-i=1mAi*X-1Ai=Q,” Journal of Applied Mathematics and Computing, vol. 43, no. 1, pp. 199–211, 2013. View at Publisher · View at Google Scholar