Table of Contents Author Guidelines Submit a Manuscript
Computational and Mathematical Methods in Medicine
Volume 2013, Article ID 707381, 7 pages
http://dx.doi.org/10.1155/2013/707381
Research Article

On Optimal Backward Perturbation Analysis for the Linear System with Skew Circulant Coefficient Matrix

1Department of Mathematics, Linyi University, Linyi, Shandong 276000, China
2Department of Mathematics, Shandong Normal University, Ji’nan, Shandong 250014, China

Received 22 July 2013; Accepted 6 October 2013

Academic Editor: Jianlong Qiu

Copyright © 2013 Juan Li 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. D. Bertaccini and M. K. Ng, “Skew-circulant preconditioners for systems of LMF-based ODE codes,” Numerical Analysis and Its Applications, vol. 1988, pp. 93–101, 2001. View at Google Scholar
  2. R. H. Chan and X.-Q. Jin, “Circulant and skew-circulant preconditioners for skew-hermitian type Toeplitz systems,” BIT Numerical Mathematics, vol. 31, no. 4, pp. 632–646, 1991. View at Publisher · View at Google Scholar · View at Scopus
  3. R. H. Chan and K.-P. Ng, “Toeplitz preconditioners for Hermitian Toeplitz systems,” Linear Algebra and Its Applications, vol. 190, pp. 181–208, 1993. View at Google Scholar · View at Scopus
  4. T. Huclke, “Circulant and skew-circulant matrices for solving Toeplitz matrix problems,” SIAM Journal on Matrix Analysis and Applications, vol. 13, pp. 767–777, 1992. View at Google Scholar
  5. J. N. Lyness and T. Sörevik, “Four-dimensional lattice rules generated by skew-circulant matrices,” Mathematics of Computation, vol. 73, no. 245, pp. 279–295, 2004. View at Publisher · View at Google Scholar · View at Scopus
  6. H. Karner, J. Schneid, and C. W. Ueberhuber, “Spectral decomposition of real circulant matrices,” Linear Algebra and Its Applications, vol. 367, pp. 301–311, 2003. View at Publisher · View at Google Scholar · View at Scopus
  7. N. Akhondi and F. Toutounian, “Accelerated circulant and skew circulant splitting methods for Hermitian positive definite to eplitz systems,” Advances in Numerical Analysis, vol. 2012, Article ID 973407, 17 pages, 2012. View at Publisher · View at Google Scholar
  8. M. J. Narasimha, “Linear convolution using skew-cyclic convolutions,” IEEE Signal Processing Letters, vol. 14, no. 3, pp. 173–176, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. V. C. Liu and P. P. Vaidyanathan, “Circulant and skew-circulant matrices as new normal-form realization of IIR digital filters,” IEEE transactions on circuits and systems, vol. 35, no. 6, pp. 625–635, 1988. View at Publisher · View at Google Scholar · View at Scopus
  10. P. P. Vaidyanathan and P. Pal, “Adjugate pairs of sparse arrays for sampling two dimensional signals,” in Proceedings of the 36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011, pp. 3936–3939, May 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. J. L. Vernet, “Real signals fast Fourier transform. Storage capacity and step number reduction by means of an odd discrete Fourier transform,” Proceedings of the IEEE, vol. 59, no. 10, pp. 1531–1532, 1971. View at Publisher · View at Google Scholar · View at Scopus
  12. T. M. Foltz and B. M. Welsh, “Symmetric convolution of asymmetric multidimensional sequences using discrete trigonometric transforms,” IEEE Transactions on Image Processing, vol. 8, no. 5, pp. 640–651, 1999. View at Publisher · View at Google Scholar · View at Scopus
  13. X. G. Liu and X. X. Guo, “On optimal backward perturbation analysis for the linear system with block cyclic coefficient matrix,” Numerical Mathematics, vol. 12, no. 2, pp. 162–172, 2003. View at Google Scholar
  14. J.-G. Sun and Z. Sun, “Optimal backward perturbation bounds for underdetermined systems,” SIAM Journal on Matrix Analysis and Applications, vol. 18, no. 2, pp. 393–402, 1997. View at Google Scholar · View at Scopus
  15. J. L. Rigal and J. Gaches, “On the compatibility of a given solution with the data of a linear system,” Journal of the ACM, vol. 14, pp. 543–548, 1967. View at Google Scholar
  16. H.-J. Wittsack, A. M. Wohlschläger, E. K. Ritzl et al., “CT-perfusion imaging of the human brain: advanced deconvolution analysis using circulant singular value decomposition,” Computerized Medical Imaging and Graphics, vol. 32, no. 1, pp. 67–77, 2008. View at Publisher · View at Google Scholar · View at Scopus