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

Authors : Ebru ERGUN

Pages : 1273-1288

Doi:10.31801/cfsuasmas.419098

View : 11 | Download : 8

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