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Numerische Mathematik

, Volume 98, Issue 1, pp 167–176 | Cite as

On sufficient and necessary conditions for the Jacobi matrix inverse eigenvalue problem

  • Linzhang Lu
  • Michael K.  Ng
Article

Summary.

In this paper, we study the inverse eigenvalue problem of a specially structured Jacobi matrix, which arises from the discretization of the differential equation governing the axial of a rod with varying cross section (Ram and Elhay 1998 Commum. Numer. Methods Engng. 14 597-608). We give a sufficient and some necessary conditions for such inverse eigenvalue problem to have solutions. Based on these results, a simple method for the reconstruction of a Jacobi matrix from eigenvalues is developed. Numerical examples are given to demonstrate our results.

Keywords

Differential Equation Eigenvalue Problem Jacobi Matrix Vary Cross Section Inverse Eigenvalue Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Boley, D., Golub, G.H: A survey of matrix inverse eigenvalue problem. Inverse Problem 3, 595–622 (1987)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Chu, M.T.: Inverse eigenvalue problems SIAM Rev. 40, 1–39 (1998)Google Scholar
  3. 3.
    Gantmacher, F.R.: The Theory of Matrices (New York: Chelsea) 1959Google Scholar
  4. 4.
    Gladwell, G.M.L.: Inverse Problem in Vibration (Dordrecht: Nijhoff) 1986Google Scholar
  5. 5.
    Golub, G.H., Van Loan, C.: Matrix Computations (London: Academic) 1983Google Scholar
  6. 6.
    Lu, L.Z., Sun, W. W.: On necessary conditions for reconstruction of a specially structured Jacobi matrix from eigenvalues. Inverse Problem 15, 977–987 (1999)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Osborne, M.R.: On the Inverse Eigenvalue Problem for Matrices and Related Problems for Difference and Differential Equations(Lecture Notes in Mathematics vol 228) (New York: Springer) 155–168 (1971)Google Scholar
  8. 8.
    Ram, Y.M.: An inverse eigenvalue problem for modified vibrating system SIAM J Appl Math 53, 1762–1775 (1993)Google Scholar
  9. 9.
    Ram, Y.M., Elhay, S.: Constructing the shape of a rod from eigenvalues Commun. Numer. Methods Engng 14, 597–608 (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsXiamen UniversityXiamenPeople’s Republic of China
  2. 2.Department of MathematicsThe University of Hong KongHong Kong

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