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Author: Guseinov, Gusein Sh.Subject: inverse spectral problem

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    Citation - WoS: 1
    Citation - Scopus: 1
    An Inverse Problem for Two Spectra of Complex Finite Jacobi Matrices
    (Tech Science Press, 2012) Guseinov, Gusein Sh.; Mathematics
    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.
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    Citation - WoS: 3
    Citation - Scopus: 3
    Inverse Spectral Problem for Finite Jacobi Matrices With Zero Diagonal
    (Taylor & Francis Ltd, 2015) Aydin, Ayhan; Guseinov, Gusein Sh.
    In this study, the necessary and sufficient conditions for solvability of an inverse spectral problem about eigenvalues and normalizing numbers for finite-order real Jacobi matrices with zero diagonal elements are established. Anexplicit procedure of reconstruction of the matrix from the spectral data consisting of the eigenvalues and normalizing numbers is given. Numerical examples and error analysis are provided to demonstrate the solution technique of the inverse problem. The results obtained are used to justify the solving procedure of the finite Langmuir lattice by the method of inverse spectral problem.