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On Determination of a Finite Jacobi Matrix from Two Spectra

Gusein Sh. Guseinov1

Department of Mathematics, Atilim University, 06836 Incek, Ankara, Turkey. E-mail: guseinov@atilim.edu.tr

Computer Modeling in Engineering & Sciences 2012, 84(5), 405-422. https://doi.org/10.3970/cmes.2012.084.405

Abstract

In this work we study the inverse spectral problem for two spectra of finite order real Jacobi matrices (tri-diagonal matrices). 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 procedure of reconstruction of the matrix from the two spectra is given.

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Cite This Article

Guseinov, G. S. (2012). On Determination of a Finite Jacobi Matrix from Two Spectra. CMES-Computer Modeling in Engineering & Sciences, 84(5), 405–422.



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