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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 513513, 7 pages
http://dx.doi.org/10.1155/2014/513513
Research Article

Extremal Inverse Eigenvalue Problem for a Special Kind of Matrices

1School of Sciences, Jiujiang University, Jiujiang 332005, China
2Faculty of Library, Jiujiang University, Jiujiang 332005, China

Received 11 June 2013; Accepted 13 December 2013; Published 5 February 2014

Academic Editor: Hui-Shen Shen

Copyright © 2014 Zhibing Liu 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. J. Peng, X.-Y. Hu, and L. Zhang, “Two inverse eigenvalue problems for a special kind of matrices,” Linear Algebra and Its Applications, vol. 416, no. 2-3, pp. 336–347, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. H. Pickmann, J. Egaña, and R. L. Soto, “Extremal inverse eigenvalue problem for bordered diagonal matrices,” Linear Algebra and its Applications, vol. 427, no. 2-3, pp. 256–271, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. M. Nazari and Z. Beiranvand, “The inverse eigenvalue problem for symmetric quasi anti-bidiagonal matrices,” Applied Mathematics and Computation, vol. 217, no. 23, pp. 9526–9531, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. H. Pickmann, R. L. Soto, J. Egaña, and M. Salas, “An inverse eigenvalue problem for symmetrical tridiagonal matrices,” Computers & Mathematics with Applications, vol. 54, no. 5, pp. 699–708, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. Boley and G. H. Golub, “A survey of matrix inverse eigenvalue problems,” Inverse Problems, vol. 3, no. 4, pp. 595–622, 1987. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. T. Chu and G. H. Golub, Inverse Eigenvalue Problems: Theory, Algorithms, and Applications, Oxford University Press, New York, NY, USA, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  7. J. C. Egaña, N. M. Kuhl, and L. C. Santos, “An inverse eigenvalue method for frequency isolation in spring-mass systems,” Numerical Linear Algebra with Applications, vol. 9, no. 1, pp. 65–79, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. G. M. L. Gladwell, “Inverse problems in vibration,” Applied Mechanics Reviews, vol. 39, 1986. View at Google Scholar
  9. O. H. Hald, “Inverse eigenvalue problems for Jacobi matrices,” Linear Algebra and Its Applications, vol. 14, no. 1, pp. 63–85, 1976. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. X. Y. Hu, L. Zhang, and Z. Y. Peng, “The construction of a Jacobi matrix from its defective eigen-pair and a principal submatrix,” Mathematica Numerica Sinica, vol. 22, no. 3, pp. 345–354, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. A. P. Liao and Z. Z. Bai, “Construction of positive definite Jacobian matrices from two eigenpairs,” Journal on Numerical Methods and Computer Applications, vol. 23, no. 2, pp. 131–138, 2002 (Chinese). View at Google Scholar · View at MathSciNet
  12. L. Lu and M. K. Ng, “On sufficient and necessary conditions for the Jacobi matrix inverse eigenvalue problem,” Numerische Mathematik, vol. 98, no. 1, pp. 167–176, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet