On the inverse problem for finite dissipative Jacobi matrices with a rank-one imaginary part

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:68 Issue:2
On the inverse problem for finite dissipative Jacobi matrices with a rank-one imaginary part

On the inverse problem for finite dissipative Jacobi matrices with a rank-one imaginary part

Pages : 1273-1288

View : 18 | Download : 10

Publication Date : 2019-08-01

Article Type : Research Paper

Abstract :This paper deals with the inverse spectral problem consisting in the reconstruction of a finite dissipative Jacobi matrix with a rank-one imaginary part from its eigenvalues. Necessary and sufficient conditions are formulated for a prescribed collection of complex numbers to be the spectrum of a finite dissipative Jacobi matrix with a rank-one imaginary part. Uniqueness of the matrix having prescribed eigenvalues is shown and an algorithm for reconstruction of the matrix from prescribed eigenvalues is given.
Keywords : Jacobi matrix, eigenvalue, normalizing number, dissipative, inverse spectral problem

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