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Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 6, pp 1697–1712 | Cite as

Inverse Eigenvalue Problem for Quasi-tridiagonal Matrices

  • Xing Tao WangEmail author
  • Mei Ling Jin
Original Paper
  • 50 Downloads

Abstract

The inverse eigenvalue problem of quasi-tridiagonal matrices involves reconstruction of quasi-tridiagonal matrices with the given eigenvalues satisfying some properties. In particular, we first analyze the eigenvalue properties from two aspects. On this basis, we investigate the inverse eigenvalue problem of quasi-tridiagonal matrices from the theoretic issue on solvability and the practical issue on computability. Sufficient conditions of existence of solutions of the inverse eigenvalue problem of quasi-tridiagonal matrices concerning solvability are found, and algorithms concerning computability are given with the unitary matrix tool from which we construct matrices. Finally, examples are presented to illustrate the algorithms.

Keywords

Quasi-tridiagonal matrix Eigenvalue Inverse eigenvalue problem 

Mathematics Subject Classification

65F15 15A18 

Notes

Acknowledgements

The research was supported partially by National Natural Science Foundation of China (Grant nos. 10871056 and 10971150).

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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinPeople’s Republic of China

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