An inverse problem for two spectra of complex finite Jacobi matrices
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Date
2012
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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. Copyright © 2012 Tech Science Press.
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Keywords
Difference equation, Eigenvalue, Inverse spectral problem, Jacobi matrix, Normalizing numbers
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1
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Source
CMES - Computer Modeling in Engineering and Sciences
Volume
86
Issue
4
Start Page
301
End Page
319