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An Inverse Problem for Two Spectra of Complex Finite Jacobi Matrices

Gusein Sh. Guseinov1

Department of Mathematics, Atilim University, 06836 Incek, Ankara, Turkey. E-mail:

Computer Modeling in Engineering & Sciences 2012, 86(4), 301-320.


This paper deals with the inverse spectral problem for two spectra of finite order complex Jacobi matrices (tri-diagonal symmetric matrices with complex entries). The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the first diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit algorithm of reconstruction of the matrix from the two spectra is given.


Cite This Article

Guseinov, G. S. (2012). An Inverse Problem for Two Spectra of Complex Finite Jacobi Matrices. CMES-Computer Modeling in Engineering & Sciences, 86(4), 301–320.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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