Recovery of a quadratic analytic pencil

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Başkaya E., Boumenir A.

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, vol.29, no.6, pp.882-902, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 6
  • Publication Date: 2021
  • Doi Number: 10.1080/17415977.2020.1814281
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.882-902
  • Keywords: Inverse problems, quadratic pencil operator, numerical reconstruction algorithm, INVERSE PROBLEM, OPERATOR
  • Karadeniz Technical University Affiliated: Yes


We are concerned with the inverse spectral problem for a quadratic pencil operator. We show that one given spectrum is enough for its reconstruction in the case of one analytic potential. To do so we first prove few identities between the Taylor coefficients of the sought function and the Taylor coefficients of the characteristic function of the operator, whose zeros are the given eigenvalues. The method leads to solving an upper triangular nonlinear algebraic system, which is easily solved by Gaussian elimination. Convergence of the algorithm is proven in casepis a polynomial and several examples are used at the end to illustrate the accuracy and speed of the algorithm.