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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: guseinov@atilim.edu.tr

Computer Modeling in Engineering & Sciences 2012, 86(4), 301-320. https://doi.org/10.3970/cmes.2012.086.301

Abstract

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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APA Style
Guseinov, G.S. (2012). An inverse problem for two spectra of complex finite jacobi matrices. Computer Modeling in Engineering & Sciences, 86(4), 301-320. https://doi.org/10.3970/cmes.2012.086.301
Vancouver Style
Guseinov GS. An inverse problem for two spectra of complex finite jacobi matrices. Comput Model Eng Sci. 2012;86(4):301-320 https://doi.org/10.3970/cmes.2012.086.301
IEEE Style
G.S. Guseinov, "An Inverse Problem for Two Spectra of Complex Finite Jacobi Matrices," Comput. Model. Eng. Sci., vol. 86, no. 4, pp. 301-320. 2012. https://doi.org/10.3970/cmes.2012.086.301



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