Numerical Algorithms

, Volume 70, Issue 3, pp 669–690 | Cite as

A finite difference method for an inverse Sturm-Liouville problem in impedance form

  • Qin Gao
  • Zhengda Huang
  • Xiaoliang Cheng
Original Paper


In this paper, the inverse Sturm-Liouville problem for a symmetric impedance is considered and a new iterative method is proposed. Based on the discretization of the Sturm-Liouville operator by a finite difference method, the inverse Sturm-Liouville problem for a symmetric impedance is approximated by a related matrix inverse eigenvalue problem. In solving the matrix inverse eigenvalue problem, the correction technique is discussed to obtain eigenvalues which are close to the finite difference eigenvalues. Then an approximation to the impedance function is achieved by solving the nonlinear equations with modified Newton’s method. Convergence of the method is established and the effectiveness is shown by the numerical experiments.


Sturm-Liouville operator Finite difference method Generalized inverse eigenvalue problem Correction Modified Newton’s method 

Mathematics Subject Classification (2010)

34L16 65F05 65F15 65F18 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsHubei University of EducationWuhanChina
  2. 2.Department of MathematicsZhejiang UniversityHangzhouChina

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