Table of Contents Author Guidelines Submit a Manuscript
Table of Contents Alerts

To receive news and publication updates for Abstract and Applied Analysis, enter your email address in the box below.

Abstract and Applied Analysis
Volume 2015 (2015), Article ID 951340, 9 pages
http://dx.doi.org/10.1155/2015/951340
Research Article

Skew Circulant Type Matrices Involving the Sum of Fibonacci and Lucas Numbers

Zhaolin Jiang and Yunlan Wei

School of Science, Linyi University, Shuangling Road, Linyi, Shandong 276000, China

Received 27 June 2014; Revised 8 August 2014; Accepted 11 August 2014

Academic Editor: Yongli Song

Copyright © 2015 Zhaolin Jiang and Yunlan Wei. 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,” in Numerical Analysis and Its Applications, Lecture Notes in Computer Science, pp. 93–101, 2001. View at Google Scholar
  2. J. R. Claeyssen, M. Davila, and T. Tsukazan, “Factor circulant block matrices and even order undamped matrix differential equations,” Matemática Aplicada e Computacional, vol. 3, no. 1, pp. 81–96, 1983. View at Google Scholar · View at MathSciNet
  3. B. Karasözen and G. Şimşek, “Energy preserving integration of bi-Hamiltonian partial differential equations,” Applied and Engineering Mathematics, vol. 26, no. 12, pp. 1125–1133, 2013. View at Google Scholar · View at MathSciNet
  4. A. Meyer and S. Rjasanow, “An effective direct solution method for certain boundary element equations in 3D,” Mathematical Methods in the Applied Sciences, vol. 13, no. 1, pp. 43–53, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. S. J. Guo, Y. M. Chen, and J. H. Wu, “Equivariant normal forms for parameterized delay differential equations with applications to bifurcation theory,” Acta Mathematica Sinica, vol. 28, no. 4, pp. 825–856, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. X. Q. Jin, S. L. Lei, and Y. Wei, “Circulant preconditioners for solving singular perturbation delay differential equations,” Numerical Linear Algebra with Applications, vol. 12, no. 2-3, pp. 327–336, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. 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 MathSciNet · View at Scopus
  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. D. Q. Fu, Z. L. Jiang, Y. F. Cui, and S. T. Jhang, “New fast algorithm for optimal design of block digital filters by skew-cyclic convolution,” IET Signal Processing, vol. 8, no. 6, pp. 633–638, 2014. View at Publisher · View at Google Scholar
  10. 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 MathSciNet · View at Scopus
  11. J. Li, Z. Jiang, N. Shen, and J. Zhou, “On optimal backward perturbation analysis for the linear system with skew circulant coefficient matrix,” Computational and Mathematical Methods in Medicine, vol. 2013, Article ID 707381, 7 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  12. P. J. Davis, Circulant Matrices, John Wiley & Sons, New York, NY, USA, 1979. View at MathSciNet
  13. Z. L. Jiang and Z. X. Zhou, Circulant Matrices, Chengdu Technology University, Chengdu, China, 1999.
  14. S. Q. Shen, J. M. Cen, and Y. Hao, “On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers,” Applied Mathematics and Computation, vol. 217, no. 23, pp. 9790–9797, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Y. Gao, Z. L. Jiang, and Y. P. Gong, “On the determinants and inverses of skew circulant and skew left circulant matrices with Fibonacci and Lucas numbers,” WSEAS Transactions on Mathematics, vol. 12, no. 4, pp. 472–481, 2013. View at Google Scholar · View at Scopus
  16. Z. L. Jiang, J. J. Yao, and F. L. Lu, “On skew circulant type matrices involving any continuous Fibonacci numbers,” Abstract and Applied Analysis, vol. 2014, Article ID 483021, 10 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  17. X. Y. Jiang and K. Hong, “Exact determinants of some special circulant matrices involving four kinds of famous numbers,” Abstract and Applied Analysis, vol. 2014, Article ID 273680, 12 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  18. Z. Jiang and D. Li, “The invertibility, explicit determinants, and inverses of circulant and left circulant and g-circulant matrices involving any continuous Fibonacci and Lucas numbers,” Abstract and Applied Analysis, vol. 2014, Article ID 931451, 14 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  19. S. Solak, “On the norms of circulant matrices with the Fibonacci and Lucas numbers,” Applied Mathematics and Computation, vol. 160, no. 1, pp. 125–132, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. A. İpek, “On the spectral norms of circulant matrices with classical Fibonacci and Lucas numbers entries,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 6011–6012, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. L. Mirsky, “The spread of a matrix,” Mathematika, vol. 3, pp. 127–130, 1956. View at Google Scholar · View at MathSciNet
  22. R. Sharma and R. Kumar, “Remark on upper bounds for the spread of a matrix,” Linear Algebra and its Applications, vol. 438, no. 11, pp. 4359–4362, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  23. J. Wu, P. Zhang, and W. Liao, “Upper bounds for the spread of a matrix,” Linear Algebra and Its Applications, vol. 437, no. 11, pp. 2813–2822, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. C. R. Johnson, R. Kumar, and H. Wolkowicz, “Lower bounds for the spread of a matrix,” Linear Algebra and its Applications, vol. 71, pp. 161–173, 1985. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. Z. Jiang, Y. Gong, and Y. Gao, “Invertibility and explicit inverses of circulant-type matrices with {$k$}-Fibonacci and {$k$}-Lucas numbers,” Abstract and Applied Analysis, vol. 2014, Article ID 238953, 9 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  26. J. Li, Z. L. Jiang, and F. L. Lu, “Determinants, norms, and the spread of circulant matrices with Tribonacci and generalized Lucas numbers,” Abstract and Applied Analysis, vol. 2014, Article ID 381829, 9 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet