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

Year 2019, Volume: 68 Issue: 2, 1273 - 1288, 01.08.2019

Ebru Ergun

https://doi.org/10.31801/cfsuasmas.419098

Cited By: 1

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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